JP4730144B2 - Decoding device, inverse quantization method, and program thereof - Google Patents

Description

  The present invention relates to a decoding device that decodes code data generated by an encoding process. In particular, the present invention relates to a decoding apparatus that decodes code data generated by an encoding process involving data quantization by performing inverse quantization.

For example, Non-Patent Document 1 discloses a JPEG standard and Non-Patent Document 2 discloses a JPEG 2000 standard.
Non-Patent Document 3 discloses a technique for synthesizing images having similar textures by matching the frequency distribution of transform coefficients.
Patent Document 1 discloses a method of obtaining a correction value between an actual amplitude value and a quantized value in advance at the time of encoding, and correcting using the correction value at the time of decoding.
ITU-T recommendation 81 ITU-T recommendation 800 D. Heeger and J. Bergen, "Pyramid based texture analysis / synthesis," Computer Graphics, pp. 229-238, SIGGRAPH 95, 1995. JP-A-7-248797

  The present invention has been made from the above-described background, and an object thereof is to provide a decoding device that decodes code data more appropriately.

[Decryption device]
To achieve the above object, the decoding apparatus according to the present invention, the distribution generation means for generating a frequency distribution of quantization index values in the frequency distribution of the quantization index value generated by the distribution generation unit, adjacent Calculating a linear function connecting the frequency values of two quantized index values to be calculated and calculating an expected value of a probability density function of the quantized index value using the linear function, and calculating by the expected value calculating means Correction means for correcting the inverse quantized value corresponding to each quantized index value based on the expected value .

  Preferably, when the expected value calculation means determines the probability density function for the target quantization index value, the frequency value of the target quantization index value and the quantization index value adjacent to the target quantization index value A linear function that approximates the frequency distribution is determined in accordance with the ratio between the frequency value and the difference between the frequency value of the target quantization index value and the frequency value of the adjacent quantization index value.

Preferably, when the probability value function is determined for the target quantization index value, the expectation value calculating means and the mode quantization value corresponding to the target quantization index value and the quantization interval corresponding to the target quantization index value Are used to determine a linear function that approximates the frequency distribution.

Preferably, when the probability value function is determined for the target quantization index value, the expected value calculation means sets the frequency value of the target quantization index value as h (q), and is adjacent to the target quantization index value. When the frequency values of the quantized index values of h (q-1) and h (q + 1) are h (q) ² (1 / (h (q) + h (q-1)) + 1 / (h (q) + h (q + 1))}, and using this central value, a linear function approximating the frequency distribution is determined.

Preferably, the expected value calculation unit, said generating a distribution function approximating the generated frequency distribution by distribution generation unit, by using the generated distribution function, to generate the probability density function.

  Preferably, the expected value calculation means generates the probability density function using the distribution function for a quantization interval in which the absolute value of the quantized index value is equal to or less than a predetermined value, and the absolute value of the quantized index value For a quantization interval in which is greater than a predetermined value, the probability density function is generated using a function that approximates the frequency distribution generated by the distribution generation means with at least one straight line.

  Preferably, the expected value calculating means continuously connects a probability density function generated using the distribution function and a probability density function generated using a function approximated by the straight line.

  Preferably, the expected value calculation unit generates a distribution function such that an area difference from the frequency distribution generated by the distribution generation unit is equal to or less than a predetermined value.

  Preferably, the expected value calculation means calculates a standard deviation of the quantization index based on the frequency distribution generated by the distribution generation means, and generates the distribution function based on the calculated standard deviation. .

とを用いて、補正値ｒを算出する。 Preferably, the distribution generation unit calculates a standard deviation σ indicating a frequency distribution of quantization index values, and the correction unit calculates the standard deviation σ calculated by the distribution generation unit and the width D of the quantization interval. And the following two formulas:

Are used to calculate the correction value r.

  Preferably, based on the frequency distribution generated by the distribution generation means, further comprising an expected value calculation means for calculating an expected value of a probability density function of a quantization index for each quantization section, and the correction means Based on the expected value for each quantization interval calculated by the expected value calculation means, an individual correction value for each quantization interval is calculated, and the calculated individual correction value and the quantization corresponding to each quantization interval The correction value to be applied is determined based on the number of indexes.

  Preferably, the quantization index is associated with a type of transform coefficient generated by the transform coding process, and the distribution generation unit calculates a frequency distribution of the quantization index value for each type of transform coefficient. An expectation value calculation means for generating the expected value of the probability density function of the quantization index for each type of transform coefficient based on the frequency distribution generated by the distribution generation means, and the correction means Based on the expected value calculated by the expected value calculation means, an individual correction value for each type of transform coefficient is calculated, and the calculated individual correction value and the number of quantization indexes corresponding to each quantization interval Based on the above, the correction value to be applied is determined.

  Preferably, based on the frequency distribution generated by the distribution generation means, further comprising an expected value calculation means for calculating an expected value of a probability density function of a quantization index for each quantization section, and the correction means A correction value for each quantization interval is calculated based on the expected value for each quantization interval calculated by the expected value calculation means, and the quantization index to be dequantized among the correction values calculated by the correction means The image processing apparatus further includes inverse quantization value calculation means for calculating an inverse quantization value by applying a correction value in which the quantization intervals coincide with each other.

  Preferably, the quantization index is associated with a type of transform coefficient generated by the transform coding process, and the distribution generation unit calculates a frequency distribution of the quantization index value for each type of transform coefficient. An expectation value calculation means for generating the expected value of the probability density function of the quantization index for each type of transform coefficient based on the frequency distribution generated by the distribution generation means, and the correction means Based on the expected value calculated by the expected value calculation means, a correction value for each type of transform coefficient is calculated, and among the correction values calculated by the correction means, the quantization index to be dequantized and the transform coefficient In addition, there is further provided an inverse quantization value calculation means for calculating an inverse quantization value by applying correction values having the same type.

  Preferably, the distribution generation unit creates a quantization index histogram, and the expectation value calculation unit uses the histogram generated by the distribution generation unit to determine the frequency of the boundary positions of adjacent quantization sections. A frequency value is calculated, and the probability density function is generated using the calculated frequency values of the boundary positions, and the frequency values of the boundary positions of the adjacent quantization intervals are symmetric with respect to the frequency values of these quantization intervals Is calculated as follows.

  Preferably, the expected value calculation means uses a predetermined function F () when the frequency values of two adjacent quantization intervals are h (q) and h (q-1). As a frequency value of the boundary position of the quantization interval, a value that internally divides between h (q) and h (q-1) into F (h (q)): F (h (q-1)) is calculated. To do.

Preferably, the expected value calculation means uses a function that can be expressed as F (x) = x ⁿ (n is a constant) as the function F ().

Preferably, the expected value calculation means calculates the probability density function value I at the intermediate position of the second quantization interval among the three consecutive quantization intervals, and the first quantization interval and 2 Probability density function value A at the boundary position with the first quantization interval, probability density function value B at the boundary position between the second quantization interval and the third quantization interval, and frequency of the second quantization interval The probability density function value I is calculated using the value H (q) and the following formula: I = 2 × H (q) − (A + B) / 2.

  Preferably, when the calculated probability density function value becomes a negative value, the expected value calculating means sets the probability density function value as 0 and calculates an expected value.

[Inverse quantization method]
In addition, the inverse quantization method according to the present invention generates a frequency distribution of quantized index values, and connects the frequency values of two adjacent quantized index values in the generated frequency distribution of quantized index values. A function is obtained, the expected value of the probability density function of the quantized index value is calculated using this linear function, and the inverse quantized value corresponding to each quantized index value is corrected based on the calculated expected value .

[program]
The program according to the present invention, step a, the frequency distribution of the generated quantization index value, a linear function connecting the frequency values of the two quantization index values adjacent to each other to generate a frequency distribution of quantization index values And calculating the expected value of the probability density function of the quantized index value using this linear function, and correcting the inverse quantized value corresponding to each quantized index value based on the calculated expected value Causing the computer to execute the steps.

  According to the decoding device of the present invention, code data can be decoded more appropriately.

First, in order to help understanding of the present invention, its background and outline will be described.
Since image data, audio data, and the like have an enormous amount of data, it is common to compress, reduce, and hold and transmit data. For example, multi-value image data generated when a color document or photograph is digitized by an image scanner, or multi-value image data generated when a photograph of a landscape or the like is taken with a digital camera is JPEG or By compressing with an irreversible encoding method such as JPEG2000, a smaller amount of data can be obtained.

  When such lossy encoding is performed, there is a problem that encoding distortion occurs. In particular, when the JPEG method is applied, block distortion (encoding distortion) occurring at the DCT block boundary of a decoded image (decoded image) is a problem.

First, the mechanism by which encoding distortion of lossy encoding occurs will be described.
FIG. 1 is a diagram for explaining the outline of a transform coding system such as the JPEG system and the JPEG 2000 system. FIG. 1 (A) shows an outline of the encoding process, and FIG. 1 (B) shows the decoding process. An outline is shown.
FIG. 2 is a diagram for explaining a quantization process in the transform coding method. Note that the transform coefficient T (c, i, j) and the quantization index Q (c, i, j) shown in FIG. 2 are functions of the variables c, i, j. The variable c is an index indicating the type of transform coefficient. For example, in the case of DCT transform using 8 × 8 blocks, a value (1) indicating any of 64 types (8 × 8) of transform coefficients exists. In the case of wavelet transform, it is a value indicating one of 1HH component, 1LH component, 1HL component, 2HH component, 2LH component, 2HL component,..., NLLL component. The variables i and j are variables indicating the positions of the respective transform coefficients. For example, in the case of DCT transform, the c-th transform coefficient of the i-th block from the top and the j-th block from the left is T (c, i , J), and in the case of wavelet transform, the i-th data from the top and the j-th data from the left of the c-th transform coefficient are represented as T (c, i, j).

As shown in FIG. 1A, in the coding process of the transform coding method, a transform process such as discrete cosine transform or wavelet transform is performed on the input image G to generate a transform coefficient T of the input image G. The transform coefficient T is further quantized to become a quantized index Q. The quantization index Q is entropy-encoded (losslessly encoded) to become a compression code F.
Here, the quantization index is information for identifying a quantization value. The quantized value is a value by which a group of numerical values in a certain range (quantization interval) is degenerated. As illustrated in FIG. 2, each of the quantization intervals “A-2” to “A2” is representative. Discrete values (in this example, “−2 × D (c)” to “2 × D (c)”).

The code data (compression code F) generated in this way is entropy-decoded and becomes a quantized index Q as shown in FIG. This quantization index Q is the same as the quantization index Q at the time of encoding.
Further, the quantization index Q is inversely quantized to become a transform coefficient (that is, an inverse quantized value) R, and the transform coefficient R is inversely transformed to generate a decoded image H.

  Here, the dequantized value is a value generated based on the quantization index or the quantization value and used for decoding the decoded data. For example, a JPEG or JPEG2000 conversion coefficient (quantized index) is used. Associated conversion coefficients).

  In the above process, coding distortion occurs when quantization is performed. Comparing the accuracy of the transform coefficient T of the original image and the quantization index Q, the accuracy of the transform coefficient T is generally higher than that of the quantization index Q. Therefore, the transform coefficient R reproduced using the quantization index Q is different from the original transform coefficient T. This is the cause of coding distortion.

Next, quantization and inverse quantization will be described in more detail with reference to FIG.
The quantization is performed using a quantization step width D (c) prepared for each transform coefficient c. The quantization step width D is a function of the transform coefficient type c. For example, in the case of the JPEG method, the quantization index Q is calculated by the following equation at the time of quantization.

Q (c, i, j) = round (T (c, i, j) / D (c))

Here, round () is a function that outputs an integer closest to the input value.
At the time of inverse quantization, the inverse quantization value R is calculated by the following equation.

R (c, i, j) = Q (c, i, j) × D (c)

  Alternatively, in the case of the JPEG2000 system, the quantization index Q and the inverse quantization value R are calculated by the following equation (Equation 1).

Q (c, i, j) = sign (T (c, i, j)) × floor (| T (c, i, j) | / D (c))
When Q (c, i, j)> 0, R (c, i, j) = (Q (c, i, j) + r) × D (c)
When Q (c, i, j) <0, R (c, i, j) = (Q (c, i, j) -r) × D (c)
When Q (c, i, j) = 0, R (c, i, j) = 0
... (Equation 1)

Here, sign () is a function that outputs a positive / negative sign, floor is a function that makes the decimal part 0, and || is a symbol that indicates an absolute value.
R is a numerical value in the range from 0 to 1, and typically r = 0.5 is used. However, in the JPEG2000 system, there are cases where the lower bits are not encoded, but here, a case where all the least significant bits are encoded will be described as a specific example.

  In the JPEG2000 system, a decoded image with smaller distortion can be obtained by appropriately setting the correction value r shown in Equation (1). Thus, in the JPEG2000 system, the decoded image quality can be improved by setting the inverse quantization value to a value other than the center of the quantization range.

  Also in the JPEG system, the image quality of a decoded image can be improved by introducing a similar correction value r. Specifically, the inverse quantization value is calculated using the following equation (Equation 2).

R (c, i, j) = (Q (c, i, j) + r-0.5) × D (c) when Q (c, i, j)> 0
When Q (c, i, j) <0, R (c, i, j) = (Q (c, i, j) -r + 0.5) × D (c)
When Q (c, i, j) = 0, R (c, i, j) = 0
... (Equation 2)

  Thus, by calculating the inverse quantization value using the appropriate correction value r, a decoding process with higher reproducibility is possible.

Next, an appropriate calculation method of the correction value r becomes a problem.
FIG. 2 is a diagram for explaining quantization and inverse quantization in transform coding processing.
As shown in FIG. 2, transform coefficients T (original data) are distributed on the number line x-axis. In the JPEG method, the number line x is divided into areas (quantization sections) of A0, A1,..., A-1, A-2,... As shown in FIG.
When the transform coefficient T is present in the quantization interval A0, the quantization index Q corresponding to the transform coefficient T is 0. Similarly, when the transform coefficient T exists in the region of the quantization interval Aq, the quantization index Q corresponding to this transform coefficient T is q.

In the JPEG2000 system, as shown in FIG. 2B, when the transform coefficient T is present in the quantization section Aq, the quantization index Q corresponding to the transform coefficient T is q and Become.
Further, when the quantization index is inversely quantized, the inverse quantization value shown in FIG.

Here, in order to simplify the problem, only the quantization interval Aq in which the quantization index Q has a q value will be considered. It is assumed that the transform coefficient T exists in the quantization interval Aq.
In this case, as shown in FIG. 2C, the quantization interval region Aq is assumed to be in a range of d1 ≦ x <d2. At this time, d1 ≦ T <d2.
Here, a probability density function fT (x) indicating the appearance probability of the transform coefficient T in the quantization interval Aq is considered. The probability density function fT (x) is defined in the range of d1 ≦ x <d2, and indicates the occurrence probability of the value x.
Further, the probability density function fT (x) is defined to be 1 when the integration is performed over the entire range of the quantization interval d1 ≦ x <d2.
When such a probability density function fT (x) exists, the inverse quantization value that minimizes the square error between the transform coefficient T (original data) before quantization and the inverse quantization value R is According to “Vector Quantization and Signal Compression, Kluwer Academic Publishers, pp. 177 to 178”, it is the inverse quantization value R calculated by the following equation (Equation 3).

By substituting the value R calculated by the above equation (Equation 3) into the equation (Equation 1) or the equation (Equation 2), the correction value r that minimizes the square error can be determined.
That is, it is only necessary to estimate the probability density function of the original conversion coefficient T.

Therefore, the decoding device 2 in the present embodiment estimates the probability density of the transform coefficient T (c, i, j) based on the quantization index Q (c, i, j), and obtains the estimated probability density. Based on this, the correction value r is determined.
FIG. 3 is a diagram illustrating the frequency distribution of the conversion coefficient T.
In general, the DCT coefficient or the wavelet transform coefficient is considered to have a Laplace distribution or a generalized Gaussian distribution as exemplified in FIG. When quantizing a random variable having such a distribution, the quantization range is divided as shown in FIG. In such a case, the probability density within each quantization range has a shape illustrated in FIGS. 3B, 3C, and 3D.
The decoding apparatus 2 creates a frequency distribution (for example, a histogram) of the quantization index Q (c, i, j), and estimates the distribution of the transform coefficient T using the created histogram.

[Embodiment]
Embodiments of the present invention will be described below.
In the present embodiment, a case where code data encoded by the JPEG2000 system is decoded will be described as a specific example. Note that the decoding process described in the present embodiment is roughly the same as that described in ITU-T recommendation T.800, but differs in that the inverse quantization process according to the present invention is applied.

[Hardware configuration]
First, the hardware configuration of the decoding device 2 in this embodiment will be described.
FIG. 4 is a diagram illustrating a hardware configuration of the decoding apparatus 2 to which the inverse quantization method according to the present invention is applied, centering on the control apparatus 20.
As illustrated in FIG. 4, the decoding device 2 includes a control device 20 including a CPU 202 and a memory 204, a communication device 22, a recording device 24 such as an HDD / CD device, an LCD display device or a CRT display device, and a keyboard. A user interface device (UI device) 26 including a touch panel and the like is included.
The decoding device 2 is, for example, a general-purpose computer in which a decoding program 5 (described later) is installed. The decoding device 2 acquires code data via the communication device 22 or the recording device 24, and decodes the acquired code data. Output.

[Decryption program]
FIG. 5 is a diagram illustrating a functional configuration of the decoding program 5 which is executed by the control device 20 (FIG. 4) and implements the inverse quantization method according to the present invention.
As illustrated in FIG. 5, the decoding program 5 includes an entropy decoding unit 40, an inverse quantization unit 50, and an inverse transform unit 60.
The inverse quantization unit 50 includes a histogram acquisition unit 500, a probability density function estimation unit 510, a correction value estimation unit 540, and an inverse quantization value output unit 550. The probability density function estimation unit 510 includes a polygonal line approximation unit 520. And a function estimation unit 530.

In the decoding program 5, the entropy decoding unit 40 entropy-decodes the input code data and outputs it to the inverse quantization unit 50.
The entropy decoding unit 40 of the present example decodes the input code data, generates a quantization index Q, and outputs the generated quantization index to the inverse quantization unit 50.

  The inverse quantization unit 50 generates an inverse quantization value based on the quantization index input from the entropy decoding unit 40, and outputs the generated inverse quantization value to the inverse transform unit 60.

  The inverse transform unit 60 performs an inverse transform process based on the inverse quantization value input from the inverse quantization unit 50 to generate a decoded image.

In the inverse quantization unit 50, the histogram acquisition unit 500 acquires a histogram h (q) for each quantization index value q based on the quantization index Q (c, i, j) input from the entropy decoding unit 40. To do.
More specifically, the histogram acquisition unit 500 measures the number of quantization index values q for all combinations of c, i, j for the input quantization index Q (c, i, j). Thus, let h (q) be the number of quantization indexes Q whose quantization matrix value is q.

The polygonal line approximation unit 520 creates a polygonal line function by approximating the histogram (frequency distribution) acquired by the histogram acquisition unit 500 with a polygonal line. That is, the polygonal line approximation unit 520 approximates the probability density function of the conversion coefficient T using the histogram acquired by the histogram acquisition unit 500. Thereafter, the probability density function of T (c, i, j) / D (c), which is not the probability density function of the transform coefficient T itself but the value obtained by normalizing the transform coefficient T with the quantization step width D (c). think of.
For example, the polygonal line approximation unit 520
f (x) = h (q) (when x ≦ 1 and q ≦ x <q + 1, or when x ≦ −1 and q-1 <x ≦ q)
f (x) = h (0) (when -1 <x <1)
Then, the probability density function of T (c, i, j) / D (c) may be approximated by f (x) / ∫f (x). Since it is a function, it is considered that the probability density of the actual conversion coefficient T is different. Therefore, the polygonal line approximation unit 520 of this example estimates a probability density function that is considered continuous and more appropriate.

The polygonal line approximation unit 520 of this example extracts histogram values h (q−1), h (q), and h (q + 1) corresponding to three consecutive quantized index values q from the histogram h (q). Then, a polygonal line function is created using the extracted histogram values h (q−1), h (q), h (q + 1).
More specifically, the polygonal line approximation unit 520 extracts histogram values h (q−1), h (q), h (q + 1) adjacent to each q of | q |> 0. .

Here, the range of x = T (c, i, j) / D (c) where the quantization index value is q (that is, the quantization range of the quantization index q) is
When q> 0, M1 (q) ≦ x <M2 (q),
When q <0, M1 (q) <x ≦ M2 (q)
Let M (q) be the midpoint between M1 (q) and M2 (q).
In the case of JPEG2000,
When q = 0, M (q) = 0, M1 (q) =-1, M2 (q) = 1
When q> 0, M (q) = 1.5 × q, M1 (q) = q, M2 (q) = q + 1
When q <0, M (q) = 1.5 × q, M1 (q) = q-1, M2 (q) = q
It becomes.

The polygonal line approximation unit 520 approximates the probability density function represented by the histogram in a polygonal line range from M1 (q) to M2 (q).
Specifically, a line segment A connecting the coordinates (M (q-1), h (q-1)) and the coordinates (M (q), h (q)) and the coordinates (M (q + 1), h (q + 1)) and the line segment B connecting the coordinates (M (q), h (q)), the broken line approximation unit 520 uses a function corresponding to these two line segments A and B. , The range from M1 (q) to M2 (q) is approximated by a polygonal line. This broken line approximation function is defined as Fq (x).
For example, as shown in FIG. 6, when there are histogram values h (q-1), h (q), and h (q + 1), the probability density is estimated by a line segment connecting the histogram values. Will be.

The function estimation unit 530 generates a partial probability density function fq (x) corresponding to the quantization index value q based on the polygonal line function created by the polygonal line approximation unit 520.
More specifically, the function estimation unit 530 converts the polygonal line approximation function Fq (x) generated by the polygonal line approximation unit 520 into a partial probability density function fq (x).
Here, the partial probability density function fq (x) with respect to the quantization index value q is defined as follows.
The probability density function Fq (x) defined by the line segment A and the line segment B is defined in the range from M1 (q) to M2 (q). Here, if the range from M1 (q) to M2 (q) can be converted to the range from 0 to 1, the range from 0 to 1 should correspond to the r value in formula (1) or formula (2) as it is. Can do. The partial probability density function fq (x) is obtained by converting the range from M1 (q) to M2 (q) into the range from 0 to 1. In addition, in order to correspond to Formula (1) or Formula (2), when the q value is positive and when the q value is negative, the opposite correspondence is taken. That is, the partial probability density function fq (x) is defined as follows.

When q> 0, take M1 → 0, M2 → 1.
fq (x) = Fq {(M2 (q) -M1 (q)) x + M1 (q)}
When q <0, take M1 → 1 and M2 → 0.
fq (x) = Fq {(M1 (q) -M2 (q)) x + M2 (q)}
The function estimation unit 530 obtains the partial probability density function fq (x) by the above conversion formula.

The correction value estimation unit 540 uses the partial probability density function fq (x) generated by the function estimation unit 530 to calculate the correction value r corresponding to each quantization index (each quantization interval).
The correction value estimation unit 540 of this example calculates the correction value r by performing calculation according to the following equation (Equation 4).

  That is, the correction value estimation unit 540 uses the probability density function obtained by normalizing all partial probability density functions fq (x) by adding all x in the range of 0 to 1, and then expecting x A value is calculated, and the calculated expected value is set as a correction value r.

The inverse quantization value output unit 550 calculates an inverse quantization value to be applied using the correction value r calculated by the correction value estimation unit 540, and outputs the calculated inverse quantization value to the inverse conversion unit 60. To do.
The inverse quantization value output unit 550 of this example calculates the inverse quantization value to be applied by substituting the correction value r into the above equation (Equation 1) or Equation (Equation 2).

  As described above, the decoding device 2 in the present embodiment generates the partial probability density function fq (x) by folding and approximating the histogram of the quantization index, and the generated probability density function fq (x). Is used to calculate the correction value r.

[Modification 1]
In the above embodiment, the probability density function of the conversion coefficient is estimated by connecting the histogram values as they are. Such estimation has the advantage of being simple, but has the following problems.
First, as a premise, an estimation method in which the area in each quantization range of the probability density estimation function approximated by stepping the histogram value as it is and the area in each quantization range of the estimated probability density function are good Suppose that
The points to be improved are as follows.
(1) In the polygonal line approximation in the above-described embodiment, the area of the shaded portion illustrated in FIG. 7A is added, so that it becomes larger than the area of the original stepwise probability density function approximation. To avoid this, the value of Fq (x) when x = M (q) should be smaller than h (q), but the adjacent histogram values h (q-1) and h (q ) Value is large and h (q) value is small, there is a limit to the correction.
(2) When the adjacent histogram values h (q-1), h (q), and h (q + 1) are not monotonously increasing or monotonically decreasing, they are subtracted by the area of the hatched portion illustrated in FIG. 7B. Therefore, the area becomes smaller than the area of the original step-like probability density function approximation. Conversely, when the histogram values h (q−1), h (q), and h (q + 1) are valley-shaped, the area becomes large.
Therefore, in the first modified example, although it is slightly more complicated than the above embodiment, the following polygonal line approximation that solves these problems is performed.

Note that the configuration of the decryption program 5 in this modification is substantially the same as that of the above embodiment (FIG. 5), but only the operation of the polygonal line approximation unit 520 is different.
Hereinafter, the operation of the broken line approximation unit 520 will be described.

The polygonal line approximation unit 520 of the present modification implements the following two points.
(First point) Estimated values Fq (M1 (q)) and Fq (M2 (q)) at boundaries M1 (q) and M2 (q) of the quantization range are set to values that can be corrected. Here, the correction in this modification means that the areas of the step-like probability density function and the estimated probability density function are made as equal as possible within the quantization range.
(Second point) The estimated value Fq (x) at a certain point x within the quantization range is defined so that the area does not change as much as possible.

A specific polygonal line approximation method is shown below.
(1) First, the polygonal line approximation unit 520 converts the estimated value Fq (M1 (q)) at the boundary M1 (q) of the quantization range to Fq (M1 (q)) as illustrated in FIG. It is defined as a point that internally divides between h (q) and h (q-1) (that is, line segment AB) into h (q): h (q-1).
Specifically, the broken line approximation unit 520 calculates the estimated value Fq (M1 (q)) by the following calculation.
Fq (M1 (q)) = 2 × h (q) × h (q-1) / (h (q) + h (q-1))

Similarly, the polygonal line approximation unit 520 estimates Fq (M2 (q)) (that is, Fq (M2 (q)) = h (q) and h (q + 1) at the boundary M2 (q) of the quantization range. H (q): h (q + 1) is internally divided by the following calculation.
Fq (M2 (q)) = 2 × h (q) × h (q + 1) / (h (q) + h (q + 1))

By doing this,
When h (q-1)> h (q), Fq (M1 (q))-h (q) <h (q) can be established.
Or
When h (q + 1)> h (q), Fq (M2 (q))-h (q) <h (q) can be obtained.
Therefore, since the value of Fq (M (q)) can be set small, the shaded portion as illustrated in FIG. 7 can be sufficiently corrected.

(2) Next, the broken line approximation unit 520 divides the quantization range M1 (q) to M2 (q) into four. That is, a point that internally divides the quantization range M1 (q) to M2 (q) into 1: 3 (that is, a point C illustrated in FIG. 8B) is defined as M3 (q), and 3: 1 A point that is internally divided (that is, a point D illustrated in FIG. 8B) is M4 (q).
M3 (q) = M1 (q) + (1/4) × (M2 (q) -M1 (q))
M4 (q) = M1 (q) + (3/4) × (M2 (q) -M1 (q))
It is. here,
Fq (M3 (q)) = h (q), Fq (M4 (q)) = h (q)
And

(3) Next, when the h (q-1), h (q), and h (q + 1) are not monotonously increasing or monotonically decreasing, the polygonal line approximating unit 520 uses the four points shown above to form a polyline. Approximate. That is, as illustrated in FIG.
Point A: Coordinates (M1 (q), 2 × h (q) × h (q-1) / (h (q) + h (q-1))
Point B: Coordinates (M2 (q), 2 × h (q) × h (q + 1) / (h (q) + h (q + 1))
Point C: Coordinates (M3 (q), h (q))
Point D: Coordinates (M4 (q), h (q))
Point E: When the intersection of the straight line AC and the straight line BD is assumed, the broken line approximation is represented by a line segment AE and a line segment BE.
When h (q-1), h (q), and h (q + 1) are monotonically increasing or monotonically decreasing, as a coordinate of point F (M (q), h (q)), the polygonal line approximation is a line segment Expressed as AF and line segment BF.
That is, the polygonal line approximation unit 520 determines that the straight line AC and the straight line BD intersect each other within the quantization range when h (q-1), h (q), and h (q + 1) are monotonously increasing or monotonically decreasing. Because it does not always have, case classification is necessary.
By performing the polygonal line approximation as described above, the areas of the step-like probability density function and the estimated probability density function can be made more equal within the quantization range.

[Modification 2]
In the first modification, the load for obtaining the intersection of the straight line AC and the straight line BD is large. In addition, the case of whether h (q-1), h (q), and h (q + 1) are monotonously increasing or monotonically decreasing is also a load.
Therefore, in the second modified example, a polygonal line approximation is performed using the average value of the values when x = M (q) of the straight line AC and the straight line BD without obtaining the intersection. That is,
Point A: Coordinates (M1 (q), 2 × h (q) × h (q-1) / (h (q) + h (q-1))
Point B: Coordinates (M2 (q), 2 × h (q) × h (q + 1) / (h (q) + h (q + 1))
Point G: Coordinates (M (q), h (q) + {h (q) -2 × h (q) × h (q-1) / (h (q) + h (q-1))})
And
That is, the point G is set as coordinates (M (q), 2 × h (q) ² / (h (q) + h (q-1))), and similarly, the point H is set as coordinates (M (q), 2 Xh (q) ² / (h (q) + h (q + 1))) and point I is the midpoint of the line segment GH.
The coordinates of this point I are (M (q), h (q) ² {1 / (h (q) + h (q-1)) + 1 / (h (q) + h (q + 1)) }.
When the points are defined in this way, the polygonal line approximation unit 520 in the present modification performs polygonal line approximation using functions corresponding to the line segment AI and the line segment BI.

FIG. 9A corresponds to the case where the histograms h (q−1), h (q), and h (q + 1) show a mountain shape, and FIG. 9B shows the histogram h (q− 1), h (q), h (q + 1) corresponds to a monotonically increasing shape.
In either case, the polygonal line approximation unit 520 defines each point as follows and approximates the polygonal line with a function corresponding to the line segment AI and the line segment BI.
Point A: Coordinates (M1 (q), 2 × h (q) × h (q-1) / (h (q) + h (q-1))
Point B: Coordinates (M2 (q), 2 × h (q) × h (q + 1) / (h (q) + h (q + 1))
Point I: Coordinate (M (q), h (q) ² {1 / (h (q) + h (q-1)) + 1 / (h (q) + h (q + 1))}

In addition, you may apply this modification according to a case.
That is, when the histograms h (q−1), h (q), and h (q + 1) are not monotonously increasing or decreasing, the polygonal line approximating unit 520, as illustrated in FIG. Introducing a midpoint I and a line approximation with a function corresponding to the line segment AI and line segment BI, the histograms h (q-1), h (q), h (q + 1) are monotonically increasing or monotonic When it is a decrease, a point F (that is, coordinates (M (q), h (q))) may be introduced, and a polyline may be approximated by a function corresponding to the line segment AF and the line segment BF.

Further, in this modification, as illustrated in FIG. 9, the probability density function is continuous using the midpoint I between the point G and the point H, but it is not necessarily continuous.
For example, the broken line approximation unit 520 may perform broken line approximation with a function corresponding to the line segment AG and the line segment BH illustrated in FIG. That is, the function fq (x) is defined as follows.
fq (x) = Line segment AG (M1 (q) ≦ x <M (q))
fq (x) = Line segment BH (where M (q) ≦ x <M2 (q))

The polygonal line approximation unit 520 is configured such that when h (q−1), h (q), and h (q + 1) are not monotonically increasing or monotonically decreasing,
fq (x) = Line segment AG (M1 (q) ≦ x <M (q))
fq (x) = Line segment BH (where M (q) ≦ x <M2 (q))
Is used to perform a discontinuous broken line approximation, and when h (q-1), h (q), h (q + 1) is monotonically increasing or monotonically decreasing, the point F is represented by coordinates (M (q), h (q)) may be approximated by a broken line with a function corresponding to the line segment AF and the line segment BF.

In addition, the said modification 2 can be generalized as follows.
Point A is a point that internally divides h (q) and h (q-1) into h (q) ⁿ : h (q-1) ⁿ . That is,
Point A: Coordinates (M1 (q), 2 × h (q) ⁿ × h (q-1) ⁿ / (h (q) ⁿ + h (q-1) ⁿ ))
Similarly, point B is a point that internally divides h (q) and h (q + 1) into h (q) ⁿ : h (q + 1) ⁿ . That is,
Point B: Coordinates (M2 (q), 2 × h (q) ⁿ × h (q + 1) ⁿ / (h (q) ⁿ + h (q + 1) ⁿ ))
The coordinates of point I are as follows.
Point I: Coordinates (M (q), 2 × h (q) − (Pa + Pb) / 2)
However,
Pa = 2 × h (q) ⁿ × h (q-1) ⁿ / (h (q) ⁿ + h (q-1) ⁿ )
Pb = 2 × h (q) ⁿ × h (q + 1) ⁿ / (h (q) ⁿ + h (q + 1) ⁿ )
The value of n is a real number, and the second modification described with reference to FIG. 9 corresponds to the case where n = 1.

Further, the polygonal line approximation unit 520 may calculate points (point A and point B) located at the boundary of the histogram using a predetermined function F () and approximate the polygonal line using the calculated points. That is, in the above, the point A is a point that internally divides between h (q) and h (q-1) into h (q) ⁿ : h (q-1) ⁿ , but the predetermined function F ( ), The point A may be a point that internally divides between h (q) and h (q-1) into F (h (q)): F (h (q-1)). The reason for adopting such point A is that the probability density function is to be continuous. Then, the probability density function can be made continuous by determining points using the functions F () of various shapes in this way.

  Furthermore, in the above, the point A is a point that internally divides between h (q) and h (q-1) into F (h (q)): F (h (q-1)). In order to make the density function continuous, the same value can be obtained even if the position of point A is replaced by h (q) and h (q-1) with h (q) and h (q-1) as inputs. The function value should be such that That is, it is desirable that values at the boundaries of adjacent histograms (values of point A or point B) are symmetrical with respect to the frequency values h (q) and h (q-1) of these histograms.

Next, since it is a probability density function, the range of the function is desired to be positive or zero. Therefore, the polygonal line approximation unit 520 performs exception processing with I = 0 when I <0.
However, in the case of F (x) = x ⁿ and n? 1, since I ≧ 0, the above exception processing (processing for setting I = 0) is not necessary.

[Modification 3]
In the above embodiment, the probability density function is performed by polygonal line approximation, but in the third modification, the probability density function is approximated by a curve.
FIG. 10 is a diagram illustrating a decryption program 52 in the third modification. Of the components shown in the figure, those substantially the same as those shown in FIG. 5 are given the same reference numerals.
As illustrated in FIG. 10, the decoding program 52 of this modification has a configuration in which the broken line approximation unit 520 of the decoding program 5 shown in FIG. 5 is replaced with a parameter estimation unit 560.
The parameter estimation unit 560 approximates the distribution of the conversion coefficient T with a curve based on the histogram h (q) acquired by the histogram acquisition unit 500.
The parameter estimation unit 560 of this example estimates the distribution of the transform coefficient T as a Laplace distribution based on the quantization index histogram.
First, the Laplace distribution equation can be expressed as follows.

In order to estimate the shape of the Laplace distribution, the parameter estimation unit 560 may estimate σ in the above equation.
First, the parameter estimation unit 560 calculates the probability density function fhc (x) from the histogram h (q) using the following equation (Equation 6).

In this case, however, q = 0 corresponds to -1 <x <1. Further, q = 1, 2,... Corresponds to q.ltoreq.x <q + 1, and q = -1, -2,... Corresponds to q-1 <x.ltoreq.q.
At this time, as illustrated in FIG. 11, σ may be obtained so that the difference between the Laplace function L (x) and the histogram fhc (x) is as small as possible.
The following error function Err (σ) is defined as a function for evaluating that “the difference is as small as possible”.

This error function Err is obtained by adding the absolute value of the difference in area of the probability density function obtained for each quantization index value q. It can be said that fhc (x) and L (x) are more similar as the value of the error function Err (σ) is smaller. The parameter estimation unit 560 may obtain σ that minimizes the Err (σ) by performing numerical calculation.
Alternatively, the parameter estimation unit 560 may prepare many values of σ, and among them, σ that minimizes the Err function may be adopted.
Alternatively, the parameter estimation unit 560 may simply calculate the standard deviation of the quantization index Q (c, i, j) for each transform coefficient type c to obtain σ.

In this modification, the form using the Laplace distribution has been described as a specific example. However, the present invention is not limited to this, and any function can be used as long as the shape can be determined by inputting parameters. When there are N parameters, a numerical operation that performs multidimensional minimization may be performed.
For example, the parameter estimation unit 560 may approximate the histogram using a generalized Gaussian distribution GG (x) shown below.

  Note that Γ () in the above formula is a gamma function. The shape of this distribution is determined by parameters α and β. For example, the parameter estimation unit 560 applies the error function Err to the gamma function GG (x) (that is, changes the Laplace function L (x) in the above equation (Equation 7) to the gamma function GG (x)). , Parameters α and β that minimize Err may be obtained.

The function estimation unit 530 will be described.
Here, it is assumed that the probability density function calculated by the parameter estimation unit 560 is LL (x).
The function estimation unit 530 may obtain the partial probability density function fq () by the following equation with Fq (x) = LL (x).
When q> 0, take M1 → 0, M2 → 1.
fq (x) = Fq {(M2 (q) -M1 (q)) x + M1 (q)}
When q <0, take M1 → 1 and M2 → 0.
fq (x) = Fq {(M1 (q) -M2 (q)) x + M2 (q)}

[Modification 4]
In the third modification, if a parameter function is estimated on the assumption of a parameterized distribution function, a more precise probability density function composed of curves can be estimated. However, the problem is that the distribution function assumed in advance as described above does not always match the actual transform coefficient distribution. For example, the Laplace distribution or the generalized Gaussian distribution decreases monotonically with respect to | x |, but the actual distribution does not always decrease monotonously.
Therefore, in the fourth modified example, the broken line approximation and the curve approximation using the distribution function are used in combination. More specifically, a relatively parameterized distribution function approximation is applied to a region where | q | having a large number of signals (appearance frequency of quantization index) is relatively small. On the other hand, for regions with a relatively large | q |, the approximation by the parameterized distribution function may not apply, so in regions with a relatively large | q | Since it is small, a polygonal line approximation is applied.

FIG. 12 is a diagram showing the configuration of the decryption program 54 in the fourth modified example. Of the components shown in the figure, those substantially the same as those shown in FIG. 5 or 10 are denoted by the same reference numerals.
As illustrated in FIG. 12, the decoding program 54 in the present modification has a configuration in which a parameter estimation unit 560 is added to the configuration illustrated in FIG. 5.
The polygonal line approximation unit 520 prepares a positive integer threshold TH1. Typically, the value is TH1 = 1 or TH1 = 2.
Further, it is assumed that the probability density function estimated by the parameter estimation unit 560 is LL (x).

The broken line approximation unit 520 performs the broken line approximation shown in the embodiment or the modified example when | q |> TH1, and obtains Fq (x).
The broken line approximation unit 520 defines the left and right points when | q | = TH1. That is, when q = TH, the polygonal line approximation unit 520 sets the value Fq (M1 (q)) of the left point as the substitution value LL (M1 (q)) of the function obtained by the parameter estimation unit 560, The right point Fq (M2 (q)) is assumed to be the substitution value of the function obtained by the parameter estimation unit 560 = LL (M2 (q)).
As shown in the embodiment or the modified example, the polygonal line approximation unit 520 performs polygonal line approximation using a line segment connecting three points (or four points). For other points not shown above, the polygonal line approximation unit 520 performs the polygonal line approximation by taking the same points as those shown in the embodiment or the modification.

  When | q | ≦ TH1, the function estimation unit 530 converts Fq (x) obtained by the polygonal line approximation unit 520 into a partial density function fq () by the same method as in the above embodiment, and | q When | <TH1, the partial density function fq () is obtained by the same method as in the third modification.

[Other variations]
In the embodiment and the modification described above, an example in which a unified r value is obtained for each transform coefficient type c and quantization index value q has been described. However, the r value may take a different value for each quantization index q. For example, r (q) can be used as a function of q.
In this case, the correction value estimation unit 540 can obtain the correction value r (q) for each quantization index value q by the following equation.

  At this time, the inverse quantization value output unit 550 calculates an inverse quantization value using the correction value r (q) corresponding to the quantization index value q.

Similarly, the r value may take different values for the conversion coefficient type c. For example, r (c) can be used as a function of c.
In this case, the histogram acquisition unit 500 calculates the histogram value h (q) for each conversion coefficient type c and sets it as hc (q).
Further, all h (q) in the above embodiment may be read as hc (q), and all the processes may be performed for each conversion coefficient type.
As a result, the partial probability density function fq (x) is also calculated for each conversion coefficient type c. Let fcq (x) be the partial probability density function corresponding to the conversion coefficient type c.
In this case, the correction value estimation unit 540 can obtain r (c) for each conversion coefficient type c.
At this time, the inverse quantized value output unit 550 calculates an inverse quantized value using r (c) corresponding to the transform coefficient type c.

Similarly, the r value may take different values for the combination of the transform coefficient type c and the quantization index value q. For example, the correction value r can be set to r (c, q) as a function of the transform coefficient type c and the quantization index value q.
In this case, the histogram acquisition unit 500 may calculate the histogram value h (q) for each conversion coefficient type and set it as hc (q). Moreover, all h (q) may be read as hc (q), and all processing may be performed for each conversion coefficient.
At this time, the inverse quantization value output unit 550 calculates an inverse quantization value using r (c, Q (c, i, j)) corresponding to the combination of the quantization index value q and the transform coefficient type c. To do.

In the above embodiment, when the histogram is measured, the frequency number is measured regardless of the conversion coefficient type c, and the sum of partial probability density functions is finally obtained to estimate the r value.
However, the decoding program 5 may first obtain a unified r value by taking a weighted average using the r value estimated for each transform coefficient type c or for each quantized index value q. .
Here, the number of signals with transform coefficient type c and quantized index q is p (c, q), the number of signals with quantized index value q is p (q), and transform coefficient type c Let p (c) be the number of signals.
In this case, the decryption program 5 calculates r, r (q), or r (c) by the following equation.

  In the above embodiment, Fq () is obtained and then converted to fq (). However, the decoding program 5 first calculates T (c, i, j) / D (c within the quantization range. ) May be converted to 0 to 1 and fq () may be directly obtained.

Further, in the above embodiment, the form applied to the JPEG2000 system has been described as a specific example. However, the inverse quantization described in the above embodiment can be used for the inverse quantization of the JPEG system.
In this case, the following changes may be made.
That is, the histogram acquisition unit 500 calculates f (x) = h (q) (where x ≦ 0.5 and q−0.5 ≦ x <q + 0.5, or x ≦ −0.5 and q−0.5 <x ≦ q + 0.5). ), F (x) = h (0) (where −0.5 <x <0.5), a histogram function is defined, and the polygonal line approximation unit 520 has M (q) = q, M1 (q) Polygonal line approximation is performed with = q-0.5 and M2 (q) = q + 0.5.

  In addition, the parameter estimation unit 560 associates q = 0 with −0.5 <x <0.5, associates q = 1, 2,... With q−0.5 ≦ x <q + 0.5, and q = −1. The histogram h (q) is converted into a probability density function fhc (x) by making −2,... Correspond to q−0.5 <x ≦ q + 0.5.

In the third modification, a method in which the parameter estimation unit 560 simply calculates the standard deviation of the quantization index Q (c, i, j) for each transform coefficient type c to obtain σ will be described.
The parameter estimation unit 560 can obtain the partial probability density function fq (x) by the following equation.

However, the range of x where the quantization index is q is defined as d1 (q) to d2 (q). Further, the value r in the quantization index q is r (q).
here,

Then, r (q) is expressed as follows.

  When f (x) has a Laplace distribution, r (q) is a constant that does not depend on q (that is, depends only on the ratio of σ and D). Therefore, the function G (q) is expressed as the following equation.

  However,

And q ≠ 0 and q = 0 are obtained.
Therefore, the parameter estimation unit 560 can calculate the correction value r by the following equation.

That is, the parameter estimation unit 560 estimates the standard deviation σ of the conversion coefficient type from the histogram of the quantization index Q. As a technique for estimating the standard deviation of the transform coefficient from the quantization index, a technique disclosed in Japanese Patent Application Laid-Open No. 2004-80741 may be used.
Then, parameter estimation unit 560 calculates an r value based on the estimated standard deviation (that is, the standard deviation of the quantization index).
The r value may be calculated at the time of encoding. In this case, the r value is calculated by calculating the r value by the above formula (14) and formula (15) based on the standard deviation of the actual transform coefficient. The r value is embedded in the code data. The decoding program 5 can perform inverse quantization based on the r value embedded in the code data.
This modification is preferable because the r value can be easily obtained simply by obtaining the standard deviation of the conversion coefficient.

It is a figure explaining the outline of transform coding systems, such as a JPEG system and a JPEG2000 system, (A) shows the outline of encoding processing, and (B) shows the outline of decoding processing. It is a figure explaining the quantization process in a transform coding system. It is a figure which illustrates distribution of a conversion coefficient. It is a figure which illustrates the hardware constitutions of the decoding apparatus 2 with which the inverse quantization method concerning this invention is applied centering on the control apparatus 20. FIG. It is a figure which illustrates the functional structure of the decoding program 5 which is performed by the control apparatus 20 (FIG. 4), and implement | achieves the inverse quantization method concerning this invention. It is a figure which illustrates a polygonal line approximation. It is a figure which illustrates the area difference of a broken line approximation and a histogram. It is a figure explaining the broken line approximation in the 1st modification. It is a figure explaining the broken line approximation in the 2nd modification. It is a figure which illustrates the structure of the 2nd decoding program 52. FIG. It is a figure explaining the approximation using a Laplace distribution (distribution function). It is a figure which illustrates the structure of the 3rd decoding program.

Explanation of symbols

DESCRIPTION OF SYMBOLS 2 ... Decoding apparatus 5 ... Decoding program 40 ... Entropy decoding part 50 ... Inverse quantization part 500 ... Inverse quantization value estimation part 520 ... Distribution estimation part 540 ... Expected value estimating unit 560... Random number generating unit 580... Correcting unit 582 .. distribution information specifying unit 584... Expected value shifting unit 586 .. expected value correcting unit 590. 60: Inverse conversion unit

Claims (21)

A distribution generating means for generating a frequency distribution of quantized index values;
In the frequency distribution of the quantized index values generated by the distribution generating means, a linear function connecting the frequency values of two adjacent quantized index values is obtained, and the probability density function of the quantized index value using the linear function An expected value calculating means for calculating an expected value of
A decoding device comprising: correction means for correcting an inverse quantization value corresponding to each quantized index value based on the expected value calculated by the expected value calculation means . When determining the probability density function for the target quantization index value, the expectation value calculating means, the frequency value of the target quantization index value, and the frequency value of the quantization index value adjacent to the target quantization index value, The decoding according to claim 1 , wherein a linear function that approximates a frequency distribution is determined in accordance with a ratio between the frequency value of the target quantization index value and a frequency value of the adjacent quantization index value. apparatus. When determining the probability density function for the target quantization index value, the expected value calculation means uses the target quantization index value and the mode value of the quantization interval corresponding to the target quantization index value. the decoding apparatus according to claim 1 or 2 for determining a linear function that approximates the frequency distribution. When determining the probability density function for the target quantization index value, the expected value calculation means sets the frequency value of the target quantization index value to h (q), and the quantization index on both sides of the target quantization index value. When the frequency values of the values are h (q-1) and h (q + 1), the central value is h (q) ² {1 / (h (q) + h (q-1)) + 1 / ( and h (q) + h (q + 1))}, using the value of the center, the decoding apparatus according to claim 1 or 2 for determining a linear function that approximates the frequency distribution. The expected value calculation unit, said generating a distribution function approximating the generated frequency distribution by distribution generation unit, by using the generated distribution function, decoding according to claim 1 to generate the probability density function apparatus. The expected value calculation means generates the probability density function using the distribution function for a quantization interval in which the absolute value of the quantized index value is equal to or less than a predetermined value, and the absolute value of the quantized index value is greater than the predetermined value. The decoding apparatus according to claim 5 , wherein the probability density function is generated using a function that approximates the frequency distribution generated by the distribution generation means with at least one straight line for a quantization interval that becomes larger. 7. The decoding according to claim 6 , wherein the expectation value calculating means continuously connects a probability density function generated using the distribution function and a probability density function generated using a function approximated by the straight line. Device. The decoding apparatus according to claim 5 , wherein the expected value calculation unit generates a distribution function such that an area difference from the frequency distribution generated by the distribution generation unit is equal to or less than a predetermined value. The expected value calculation means, based on the frequency distribution generated by the distribution generation unit calculates the standard deviation of the quantization indices, based on the standard deviation calculated, to claim 5 to generate the distribution function The decoding apparatus as described. The distribution generation means calculates a standard deviation σ indicating a frequency distribution of quantization index values,
The correction means includes a standard deviation σ calculated by the distribution generation means, a quantization interval width D, and the following two formulas:

The decoding device according to claim 1, wherein the correction value r is calculated using Based on the frequency distribution generated by the distribution generating means, further comprising an expected value calculating means for calculating an expected value of the probability density function of the quantization index for each quantization section;
The correction unit calculates an individual correction value for each quantization interval based on the expected value for each quantization interval calculated by the expected value calculation unit, and calculates the individual correction value and each quantization interval. The decoding device according to claim 1, wherein a correction value to be applied is determined based on the number of quantization indexes corresponding to. The quantization index is associated with the type of transform coefficient generated by transform coding processing,
The distribution generation means generates a frequency distribution of quantized index values for each type of transform coefficient,
Based on the frequency distribution generated by the distribution generation means, further comprising an expected value calculation means for calculating the expected value of the probability density function of the quantization index for each type of transform coefficient,
The correction unit calculates an individual correction value for each type of transform coefficient based on the expected value calculated by the expected value calculation unit, and calculates the calculated individual correction value and a quantum corresponding to each quantization interval. The decoding device according to claim 1, wherein a correction value to be applied is determined based on the number of digitized indexes. Based on the frequency distribution generated by the distribution generating means, further comprising an expected value calculating means for calculating an expected value of the probability density function of the quantization index for each quantization section;
The correction means calculates a correction value for each quantization interval based on the expected value for each quantization interval calculated by the expected value calculation means,
An inverse quantization value calculation unit that calculates an inverse quantization value by applying a correction value that matches a quantization interval of a quantization index to be inversely quantized among the correction values calculated by the correction unit. Item 4. The decoding device according to Item 1. The quantization index is associated with the type of transform coefficient generated by transform coding processing,
The distribution generation means generates a frequency distribution of quantized index values for each type of transform coefficient,
Based on the frequency distribution generated by the distribution generation means, further comprising an expected value calculation means for calculating the expected value of the probability density function of the quantization index for each type of transform coefficient,
The correction means calculates a correction value for each type of transform coefficient based on the expected value calculated by the expected value calculation means,
Of the correction values calculated by the correction means, further includes a dequantized value calculation means for calculating a dequantized value by applying a correction value whose type of transform coefficient matches the quantization index to be dequantized. The decoding device according to claim 1. The distribution generation means creates a histogram of quantization indexes,
The expected value calculation means is based on the histogram generated by the distribution generation means,
Calculating a frequency value of a boundary position between adjacent quantization intervals, and using the calculated frequency value of the boundary position to generate the probability density function;
The decoding device according to claim 1 , wherein the frequency values of the boundary positions of the adjacent quantization intervals are calculated so as to be symmetric with respect to the frequency values of the quantization intervals. The expectation value calculation means uses a predetermined function F () when the frequency values of two adjacent quantization intervals are h (q) and h (q−1), and uses these predetermined quantization intervals. 16. A value that internally divides between h (q) and h (q−1) into F (h (q)): F (h (q−1)) is calculated as a frequency value of the boundary position of The decoding device according to 1. The decoding apparatus according to claim 16 , wherein the expected value calculation means uses a function that can be expressed as F (x) = xn (n is a constant) as the function F (). The expected value calculating means calculates the probability density function value I at the intermediate position of the second quantization interval among the three consecutive quantization intervals, when the first quantization interval and the second quantization interval are calculated. The probability density function value A at the boundary position with the interval, the probability density function value B at the boundary position between the second quantization interval and the third quantization interval, and the frequency value H (q of the second quantization interval ) And the following formula:
I = 2 × H (q) - (A + B) / 2 and using a decoding apparatus according to claim 1 for calculating a probability density function value I. The decoding apparatus according to claim 18 , wherein the expected value calculation means calculates an expected value by setting the probability density function value to 0 when the calculated probability density function value becomes a negative value. Generate a frequency distribution of quantized index values,
In the frequency distribution of the generated quantized index values , obtain a linear function that connects the frequency values of two adjacent quantized index values, and use this linear function to calculate the expected value of the probability density function of the quantized index value And
An inverse quantization method for correcting an inverse quantization value corresponding to each quantization index value based on a calculated expected value . Generating a frequency distribution of quantized index values;
In the frequency distribution of the generated quantized index values , obtain a linear function that connects the frequency values of two adjacent quantized index values, and use this linear function to calculate the expected value of the probability density function of the quantized index value And steps to
A program for causing a computer to execute a step of correcting an inverse quantized value corresponding to each quantized index value based on a calculated expected value .

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