JP2010199959A - Image-coding apparatus, image-coding method and image-coding program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To improve the coding efficiency, by appropriately narrowing down transform coefficients by the threshold setting for attaining improvement in energy compaction, in redundant conversion using an overcomplete basis in image coding. <P>SOLUTION: A redundant converting section 10 performs transform by using a transform basis of a redundant system for a signal to be coded, and an update transform coefficient calculating section 12 performs clipping of the transform coefficient by using a set threshold to calculate the update conversion coefficient. In setting of the threshold, the threshold is adaptively varied by a threshold-setting section 11 and a threshold update processing section 15; a threshold that maximizes the evaluation scale for energy compaction is selected by an evaluation section 16; and finally, the conversion coefficient that maximizes energy compaction is selected. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

  The present invention relates to a high-efficiency image signal encoding method, and more particularly, to an image encoding apparatus and an image encoding method for improving encoding efficiency by selecting an appropriate transform coefficient in image encoding using conversion by a redundant conversion base. And an image encoding program.

  One of important elemental techniques in image coding is transform coding represented by discrete cosine transform (DCT). The role of transform coding in image coding is to remove spatial correlation between pixels. This is because, as a whole position of the encoder, information is concentrated on a small number of transform coefficients by transform coding, and the transform coefficient with low information concentration is rounded down by quantizing the transform coefficients, so that Is intended to reduce the amount of information.

  FIG. 6 shows an example of a general encoding apparatus 100 that encodes a video signal. When a video signal is input, a prediction residual signal is obtained from the difference from the prediction signal predicted by the prediction unit 106. The transform unit 101 performs orthogonal transform on the prediction residual signal. The output transform coefficient is quantized by the quantization unit 102, and the quantized value is variable-length encoded by the entropy encoding unit 107 and output as an encoded stream. On the other hand, the output of the quantization unit 102 is inversely quantized by the inverse quantization unit 103 and further inversely orthogonally transformed by the inverse transform unit 104. A decoded signal is generated by adding a prediction signal to the conversion result. The decoded signal is subjected to noise removal processing by the distortion removal filter 105 and input to the prediction unit 106 as a reference decoded signal. The prediction unit 106 generates a prediction signal for encoding the next video signal by motion search or the like.

  Up to now, in application to image coding, many transform coding schemes such as discrete cosine transform (DCT) and overlapping orthogonal transform discrete wavelet transform (DWT) have been studied.

  For example, as transform coding, discrete cosine transform (DCT) is adopted in JPEG, and discrete wavelet transform (DWT) is adopted in JPEG2000. In addition, since orthogonal transformation uses a complete basis, the number of data before and after the transformation is unchanged. For this reason, the orthogonal transform is a non-redundant transform. In the moving image encoding apparatus, the conversion unit 101 in FIG. 6 corresponds to the above technique.

  On the other hand, there is a transform called a redundant transform using an overcomplete basis in which the number of bases is larger than the number of samples of the original signal. For this reason, the redundant transformation cannot be an orthogonal transformation, but by giving redundancy to the data after the transformation, it is possible to have characteristics that cannot be realized by the non-redundant transformation. For example, a discrete stationary wavelet transform (SWT) that is a DWT that does not perform downsampling processing can establish shift invariance lost in the DWT due to redundancy after the transformation.

  In the field of image processing, “conversion with direction separation characteristics” has attracted attention. Such conversion is generally redundant conversion, and a typical example is Curvelet conversion. A parallel tree complex wavelet transform (DTCWT) is a transform having similar characteristics.

  The conversion having the direction separation characteristic is a conversion in which a curve such as an edge included in the image signal is expressed using a direction base defined in two dimensions. Since a two-dimensional structure is approximated with high accuracy using a direction basis, it is more effective for noise removal and feature extraction than a transformation with poor direction separation characteristics such as DWT.

  However, conversion with direction separation characteristics has a problem that the number of data after conversion increases. When x is an input signal to transform coding and Ψ is a transform matrix, a transform coefficient y obtained by the transform is expressed as follows.

y = Ψx (1)
In the case of DTCWT, if x is an n-dimensional vector, the conversion coefficient y obtained by the conversion is a 2n-dimensional vector. For this reason, when the transformation is applied to image coding, it is necessary to appropriately select a transformation coefficient from the viewpoint of reducing the number of data. This selection of transform coefficients can be formulated as the following constrained minimization problem.

min _y ‖y‖ ₀ subject to Ψ ^-1 y = x (2)
Here, min _y is a function for obtaining the minimum value of the following expression. ‖ · ‖ ₀ is an L ⁰ norm and represents the number of non-zero coefficients. ‖ · ‖ ₂ ² is the square value of the L ² norm and represents the sum of squares. Ψ ⁻¹ is a matrix representing the inverse transformation of a transformation consisting of an overcomplete basis set. The above minimization problem with constraints is reduced to the following minimization problem by Lagrange's undetermined multiplier method.

min _y ‖y‖ ₀ + λ‖Ψ ^-1 yx ₂ ² (3)
Here, λ is a weight parameter given from the outside. The first term is the number of selected transform coefficients, and is an approximate value of the information amount of transform coefficients. The second term represents the reconstruction error associated with the selection of the transform coefficient and represents the coding distortion. However, since the above minimization problem is difficult to NP, conventionally, a method of approximating the following L ¹ norm as a minimization problem has been adopted.

min _y ‖y‖ ₁ + λ‖Ψ ^-1 y−x‖ ₂ ² (4)
Here, ‖ · ‖ ₁ is an L ¹ norm, and represents the sum of absolute values of vector elements.

  As a technique for giving a sub-optimal solution of the minimization problem of Equation (4), a technique called noise shaping processing shown in FIG. 7 has been proposed (see Non-Patent Document 1).

  Organize the symbols used. The conversion coefficient after forward conversion for the input signal x (N pixels) is defined as follows.

y ₀ = Ψx
Using I as a unit matrix, two types of projections P ^s ≡ΨΨ ⁻¹ and P ， ≡I−ΨΨ ¹ are defined (note that ⊥ is a subscript attached to the right shoulder of P).

The output obtained by the former projection is called the effective component, and the output obtained by the latter projection is called the invalid component. An index indicating the number of repetitions in the noise shaping process is represented by i, and the i-th output in the noise shaping process is represented by y _i . For y _i , a clipping process is performed in which the coefficient whose absolute value is equal to or smaller than the threshold θ _i is rounded down to zero. The output after clipping processing for y _i is represented as ｙy _i (＾ is a symbol on y) as follows:

^ Y _i (θ _i ) = y _i + ε _i (θ _i )
Here, ε _i (θ _i ) is an error to be superimposed with clipping processing. When the weighting factor k in noise shaping is k = 1, w _i in FIG. 7 is a correction signal in noise shaping processing and is given by the following equation.

w _i (θ _i ) = y ₀ −ΨΨ ⁻¹ ^ y _i (θ _i )
Using this ^ y _i (θ _i ) and w _i (θ _i ), y _{i + 1} (θ _i ) can be expressed as y _{i + 1} (θ _i , ^ y _i (θ _i )) It is expressed in

y _{i + 1} (θ _i , ^ y _i (θ _i )) = ^ y _i (θ _i ) + w _i (θ _i )
The clipping threshold θ _i is set to θ _{i + 1} = θ _i −Δ _i (5) using Δ _i (> 0).
And Δ _i is set smaller as the number of repetitions increases. However, the conventional method does not show a specific setting policy. For this reason, the setting of the threshold value, that is, the setting of Δ _i has to be done by trial and error.

The operation of the noise shaping processing apparatus 200 shown in FIG. 7 will be briefly described. The conversion unit 201 performs conversion using a redundant conversion basis on the input signal x to calculate a conversion coefficient y ₀ . The clipping processing unit 202, transform coefficients y _i (initial value i = 0) performs a comparison between a predetermined threshold theta _i, if y _i is less than theta _i, replacing y _i to zero. Assume that the output after this clipping process is y _i . The inverse transform unit 203, ^ inversely convert y _i seek ^ x _i of the inverse transform results. The difference between the input signal x and ^ x _i is the error e _i in the pixel region.

The weight coefficient multiplication unit 204 multiplies e _i by a predetermined weight coefficient k, and forward-converts the multiplication result in the conversion unit 205 to calculate a correction signal w _i . An update conversion coefficient y _{i + 1} is calculated by adding the correction signal w _i to the output ^ y _i of the clipping processing unit 202. After being delayed for a certain time by the delay unit 206, the update conversion coefficient y _{i + 1} is input to the clipping processing unit 202 and the process is repeated in the same manner for the update conversion coefficient y _{i + 1} . The end condition judging unit 207 checks whether or not the difference between e _{i + 1} and e _i is smaller than a certain minute value, and when the difference becomes smaller than the minute value, the ^ y _i is output as a conversion result.

T. Reeves and N. Kingsbury, “Overcomplete image coding using iterative projection-based noise shaping”, Proc. IEEE Conf. On Image Processing, vol.3, pp.597-600, 2002.

The performance of the noise shaping process depends on the threshold value θ _i in the clipping process. Conventionally, however, there is no clear standard for setting the threshold value, and there is room for improvement in improving energy compaction, which is the purpose of the original iterative processing.

  The present invention has been made in view of such circumstances, and a threshold value setting method that realizes an improvement in energy compaction in a noise shaping process for removing redundancy between transform coefficients in a redundant transform using an overcomplete basis. The purpose is to establish an image coding method based on the above.

  In order to solve the above-mentioned problems, the present invention performs a conversion using a redundant conversion base for an input video signal, and narrows down the coefficients used for encoding with respect to the obtained conversion coefficients. In image coding, an adaptive threshold process is used to select a transform coefficient that maximizes energy compaction.

  Further, according to the present invention, when selecting a threshold value in the adaptive threshold processing, a threshold value that maximizes an evaluation scale related to energy compaction is selected.

  Specifically, the present invention solves the above problem by a method as described below.

[Parameter selection (part 1)]
In the following, for each element of y _{i + 1} (θ _i ), the negative element is inverted in sign, and then normalized so that the sum of all elements becomes 1, y ′ _{i + 1} Let (θ _i ).

As the parameter Δ _i , an optimal value is selected from U candidates of Δ _i = uΔ (u = 1, 2,..., U). Δ is a predetermined fixed setting value. As a parameter selection criterion, a parameter selection criterion (part 1) or a parameter selection criterion (part 2) described later is used. For example, when the Cullback library information amount (KLI) shown in Expression (10) is used, u ^* satisfying the following expression is an optimal value.

Here, “arg max” represents a parameter that maximizes the cost below max.

  The KLI shown in equation (10) as an example of the evaluation scale represents the degree of deviation from the uniform distribution, and when the value of KLI is large, the coefficient indicates that the energy is biased to a specific component. . Therefore, selecting a parameter having a large KLI value leads to a clipping process that concentrates energy on a specific component, which meets the object of the present invention.

[Parameter selection (part 2)]
As the parameter Δ _i , an optimal value is selected from U candidates of Δ _i = uΔ (u = 1, 2,..., U). As a parameter selection criterion, a parameter selection criterion (part 1) or a parameter selection criterion (part 2) described later is used. For example, when KLI shown in Expression (10) is used, the following processing is performed. First, the following two values are obtained.

The above D ^* sets a new threshold θ _i −uΔ (u = 1, 2,..., U−1) between θ _i and θ _{i + 1} = θ _i −UΔ as a clipping threshold. This is the maximum value of KLI when clipping is performed in two stages using θ _i and θ _i −uΔ (u = 1, 2,..., U−1).

Next, the KLI for the output of one clipping process using the threshold value θ _{i + 1} = θ _i −UΔ is obtained as follows.

Finally, the comparison between D ^* and D _0, the larger the better of D ^*, performs a two-stage clipping process using the threshold value θ _i -uΔ and θ _i -UΔ. In other cases, clipping processing using a threshold θ _{i + 1} = θ _i −UΔ is performed.

  Here, an example of multi-stage clipping processing is shown in two stages. However, multi-stage multi-stages of three or more stages can be similarly performed.

[Parameter selection criteria (1)]
The Cullback library information amount (KLI) for the uniform distribution of y ′ _{i + 1} (θ _i ) is as follows.

Here, y ′ _{i + 1} (θ _i ) [m] is the m-th element of y ′ _{i + 1} (θ _i ).

[Parameter selection criteria (2)]
For each element of y _{i + 1} (θ _i ), the negative element is inverted in sign, and then normalized so that the sum of all elements becomes 1, y ′ _{i + 1} (θ _i )far. The coding gain of y ′ _{i + 1} (θ _i ) is expressed by the following equation.

Here, y ′ _{i + 1} (θ _i ) [m] is the m-th element of y ′ _{i + 1} (θ _i ).

  According to the present invention, it is possible to improve encoding efficiency by improving energy compaction in noise shaping processing and consolidating information into specific components.

It is a figure which shows the structural example of the principal part of this invention. It is a flowchart of the conversion coefficient selection process (the 1). It is a flowchart of the conversion coefficient selection process (the 2). It is a flowchart of the calculation process of an update conversion coefficient. It is a system block diagram when implement | achieving by a software program. It is a block diagram of a general encoding apparatus. It is a figure which shows the example of the conventional noise shaping processing apparatus.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 1 is a diagram showing a configuration example of an encoding apparatus according to an embodiment of the present invention.

  The encoding apparatus according to the embodiment of the present invention is such that, for example, in the encoding apparatus 100 as shown in FIG. 6, the conversion unit 101 is replaced with the conversion coefficient selection unit 1 shown in FIG. The conversion coefficient selection unit 1 includes a redundant conversion unit 10 that performs conversion using a redundant conversion basis. The output of the transform coefficient selecting unit 1 is quantized by the quantizing unit 20, variable-length coded by the entropy coding unit 30, and output as an encoded stream.

  The parts other than the transform coefficient selection unit 1 may be the same as those of the conventional coding apparatus 100 shown in FIG. 6, for example, and the configuration of the parts other than the transform coefficient selection unit 1 is well known. Description is omitted. Note that the present invention is not limited to the encoding apparatus 100 as shown in FIG. 6, and the present invention can be similarly applied to an apparatus having a conversion unit for compressing a signal to be encoded. Is clear. For example, the present invention can be similarly applied to a still image encoding apparatus.

  In addition to the redundant conversion unit 10, the conversion coefficient selection unit 1 stores an update conversion coefficient calculation unit 12 having a clipping processing unit 19, an evaluation information calculation unit 13 that calculates evaluation information that serves as an evaluation measure, such as KLI, and stores the evaluation information The evaluation information storage unit 14, the evaluation unit 16 that evaluates the update conversion coefficient based on the evaluation information, the threshold setting unit 11 for adaptively determining the clipping threshold, the threshold update processing unit 15, and the evaluation unit 16 A differential signal fluctuation check unit 17 for checking whether or not the fluctuation of the difference signal between the original signal and the decoded signal has become sufficiently small with respect to the selected update transformation coefficient, and the update transformation when the fluctuation of the difference signal becomes a sufficiently small value And an update conversion coefficient output unit 18 that outputs the coefficient as a conversion coefficient of the conversion result.

  The operation of the conversion coefficient selector 1 is as follows. Here, the operation at the time of “parameter selection (part 1)” will be mainly described. However, the operation at the time of “parameter selection (part 2)” can be easily inferred from the following explanation.

  The redundant conversion unit 10 receives an encoding target signal such as an image signal, a video signal, or a prediction residual signal, performs conversion using a redundant conversion base, and outputs a conversion coefficient. The conversion coefficient is input to the update conversion coefficient calculation unit 12, and the clipping processing unit 19 performs clipping processing using the threshold set by the threshold setting unit 11. That is, the clipping processing unit 19 replaces a conversion coefficient smaller than the threshold with a zero value and outputs it as an updated conversion coefficient.

  The evaluation information calculation unit 13 calculates evaluation information according to a predetermined evaluation scale for the calculated update conversion coefficient. As the evaluation scale, a scale that increases as the degree of concentration of energy on a specific component increases. As an example of the evaluation scale, KLI as shown in Equation (10) or coding gain as shown in Equation (11) can be used. The evaluation information storage unit 14 stores the calculated evaluation information.

  The threshold update processing unit 15 updates the threshold according to a predetermined threshold update parameter candidate and notifies the threshold setting unit 11 of the threshold. In the update conversion coefficient calculation unit 12, the clipping processing unit 19 similarly performs the clipping process of the conversion coefficient using the updated threshold value, and calculates the update conversion coefficient.

  When the calculation of the update conversion coefficient and the calculation of the evaluation information for all candidates for the update parameter of the threshold are completed, the evaluation unit 16 selects evaluation information that maximizes the evaluation scale related to energy compaction.

  The difference signal fluctuation check unit 17 determines whether the difference signal between the decoded signal and the original signal obtained by inversely transforming the update conversion coefficient when the threshold corresponding to the evaluation information selected by the evaluation unit 16 is large is large. If the fluctuation is large, the update conversion coefficient is input to the update conversion coefficient calculation unit 12 and the same update conversion coefficient calculation process is repeated again while updating the threshold value. That is, in the difference signal fluctuation check unit 17, the difference between the difference signal (initial value 0) obtained from the previous update conversion coefficient and the difference signal obtained from the update conversion coefficient obtained in the current evaluation is a certain value. Control is performed to repeat the update conversion coefficient calculation process until the value becomes smaller. When the fluctuation becomes a sufficiently small value, the update conversion coefficient output unit 18 outputs the update conversion coefficient at that time as a conversion coefficient selection result.

  Here, an example has been described in which the differential signal fluctuation check unit 17 determines the end condition of the iterative process in which the fluctuation of the differential signal has become a sufficiently small value. The conversion coefficient narrowing down may be terminated by determining other termination conditions.

  Hereinafter, the processing by the conversion coefficient selection unit 1 is performed by selecting a conversion coefficient selection process corresponding to the above “parameter selection (part 1)” (part 1) and a conversion coefficient selection corresponding to the above “parameter selection (part 2)”. This will be described in more detail by dividing it into the processing flow (part 2).

[Flow of conversion coefficient selection process (1)]
The following is processing corresponding to parameter selection (part 1). FIG. 2 is a flowchart of the conversion coefficient selection process (part 1). The parameter Δ _i = uΔ (u = 1, 2,..., U) is called a threshold update parameter.

First, an image to be encoded is input, conversion using a redundant base is performed, and a conversion coefficient is obtained (step S1). Next, the conversion coefficient of the conversion result is read (step S2). Subsequently, the following steps S4 to S5 are repeated for each candidate of the threshold update parameter Δ _i = uΔ (u = 1, 2,..., U).

  An update conversion coefficient calculation process (described later) shown in FIG. 4 is performed using the conversion coefficient and the clipping threshold as arguments, and an update conversion coefficient corresponding to the clipping threshold is obtained (step S4). As evaluation information, the KLI for the updated conversion coefficient obtained in step S4 is calculated (step S5).

  The above processing is repeated for all update parameter candidates while updating the threshold value according to the threshold update parameter (step S6).

When the above processing is completed, an update parameter that maximizes the KLI is selected from the KLI when the U clipping thresholds are used, and stored in Δ ^* _i (step S7). The difference signal between the decoded signal and the original signal obtained by inversely converting the update conversion coefficient obtained by the clipping process using the threshold when Δ ^* _i is used (the update conversion coefficient in step S4) (Calculated in step S8).

  By comparing with the previous difference signal, it is determined whether or not the variation of the difference signal is sufficiently small (step S9). If the fluctuation of the difference signal is sufficiently small, the update conversion coefficient is written as an output, and the process is terminated (step S10). Otherwise, the update conversion coefficient is written out as a conversion coefficient which is an input of the “update conversion coefficient calculation process (FIG. 4)” (step S11), and the process proceeds to step S2.

[Transformation coefficient selection process flow (2)]
The following is processing corresponding to parameter selection (part 2). FIG. 3 is a flowchart of the conversion coefficient selection process (part 2). The parameter Δ _i = uΔ (u = 1, 2,..., U−1) is referred to as a threshold update parameter.

First, an image to be encoded is input, conversion using a redundant base is performed, and a conversion coefficient is obtained (step S20). Next, the conversion coefficient of the conversion result is read (step S21). Subsequently, with the clipping threshold set to θ _i −UΔ, an update conversion coefficient calculation process (described later) shown in FIG. 4 is performed on the conversion coefficient, and an update conversion coefficient corresponding to the clipping threshold is written (step S22). The KLI for the calculated update conversion coefficient is calculated and stored as D1 (step S23).

Next, the following steps S25 to S27 are repeated for each candidate of the threshold update parameter Δ _i = uΔ (u = 1, 2,..., U).

The update conversion coefficient calculation process (described later) shown in FIG. 4 is performed using the conversion coefficient and the clipping threshold θ _i −uΔ as arguments, and the update conversion coefficient corresponding to the clipping threshold θ _i −uΔ is calculated (step S25). ). Subsequently, the update conversion coefficient calculation process shown in FIG. 4 (described later) is performed using the update conversion coefficient obtained in step S25 and the clipping threshold θ _i −UΔ as arguments, and the clipping conversion coefficient θ _i −UΔ is supported. The updated conversion coefficient is calculated (step S26). After that, as evaluation information, KLI for the update conversion coefficient obtained in step S26 is calculated (step S27).

  The above processing is repeated for all update parameter candidates while updating the threshold value according to the threshold update parameter (step S28).

When the above processing is completed, the maximum value is selected from the KLI when U−1 clipping thresholds are used, stored as D2, and an update parameter for maximizing the KLI is Δ ^*. Store as _i (step S29).

  Next, the magnitudes of D1 and D2 are compared (step S30), and if D1 is equal to or greater than D2, the update conversion coefficient corresponding to D1 and the difference signal corresponding to the update conversion coefficient are written (step S31). On the other hand, when D1 is smaller than D2, the update conversion coefficient corresponding to D2 and the difference signal corresponding to the update conversion coefficient are written (step S32). Thereafter, it is determined whether or not the variation of the difference signal obtained by the above processing is sufficiently small (step S33). If the variation is sufficiently small, the update conversion coefficient is written as an output, and the processing is terminated (step S34). Otherwise, the update conversion coefficient is written out as a conversion coefficient which is an input of the “update conversion coefficient calculation process (FIG. 4)” (step S35), and the process proceeds to step S21.

[Flow of update conversion coefficient calculation process]
FIG. 4 shows the flow of update conversion coefficient calculation processing in step S4 shown in FIG. 2 and steps S22, S25, and S26 shown in FIG. The input is a conversion coefficient and a clipping threshold.

  First, the conversion coefficient to be clipped is read (step S40). Also, the designated clipping threshold is read (step S41). Next, a clipping process is performed in which the value of the conversion coefficient equal to or less than the threshold is set to zero to obtain a corrected conversion coefficient (step S42). The modified transform coefficient obtained by the clipping process is inversely transformed to obtain a decoded signal (step S43). Next, a differential signal between the decoded signal and the original signal is calculated (step S44). This difference signal is stored in a register. The calculated difference signal is forward-converted to obtain a correction coefficient (step S45). Finally, the correction signal is added to the modified conversion coefficient, and the updated conversion coefficient is written (step S46).

  The above image encoding processing can be realized by a computer and a software program, and the program can be recorded on a computer-readable recording medium or provided through a network.

  FIG. 5 shows an example of a system configuration when the present invention is implemented using a software program. The memory 52 stores an image encoding program 53 for performing the image encoding process of the present invention. The CPU 50 sequentially fetches and executes the instructions of the image encoding program 53 stored in the memory 52. The video storage device 51 is a device that stores a video signal to be encoded. The video signal may be input from a camera or the like (not shown). The encoded stream generated by the image encoding program 53 is stored in the encoded stream storage device 54. Alternatively, the encoded stream may be output to an external device via an interface such as a network adapter. The system bus 55 is a bus that connects the CPU 50, the video storage device 51, the memory 52, and the encoded stream storage device 54.

DESCRIPTION OF SYMBOLS 1 Conversion coefficient selection part 10 Redundant conversion part 11 Threshold setting part 12 Update conversion coefficient calculation part 13 Evaluation information calculation part 14 Evaluation information memory | storage part 15 Threshold update process part 16 Evaluation part 17 Difference signal fluctuation check part 18 Update conversion coefficient output part 19 Clipping processing unit 20 Quantization unit 30 Entropy coding unit

Claims (5)

An image in which the input signal to be encoded is converted using a redundant conversion basis, the conversion coefficients used for encoding are narrowed down for the obtained conversion coefficients, and the result is encoded An encoding device comprising:
A redundant conversion unit that performs conversion using a redundant conversion basis on the input encoding target signal;
An update conversion coefficient calculation unit that performs clipping processing according to a set threshold and calculates an update conversion coefficient by replacing a conversion coefficient smaller than the threshold with a zero value;
An evaluation information calculation unit for calculating an evaluation value indicating the degree of energy compaction with respect to the calculated update conversion coefficient;
A threshold update processing unit that updates the threshold and repeatedly calculates the update conversion coefficient by the update conversion coefficient calculation unit for the threshold candidates;
An evaluation unit that selects an update conversion coefficient having a maximum evaluation value among the update conversion coefficients;
Until the predetermined end condition is satisfied, the update conversion coefficient selected by the evaluation unit is re-input as a conversion coefficient to be input to the update conversion coefficient calculation unit, and the update conversion coefficient calculation unit and the evaluation information calculation unit are input. , An end condition check unit for narrowing down conversion coefficients by the processes of the threshold update processing unit and the evaluation unit;
An update conversion coefficient output unit that outputs an update conversion coefficient that maximizes the evaluation value when the termination condition is satisfied;
An image encoding apparatus comprising: an encoding unit that encodes the update transform coefficient output by the update transform coefficient output unit. The image encoding device according to claim 1,
The evaluation value indicating the degree of energy compaction is a Cullback library information amount for the uniform distribution of the update transform coefficients or a coding gain calculated from a value obtained by normalizing the update transform coefficients. Encoding device. Image coding that transforms the input image signal using the transform base of the redundant system, narrows down the transform coefficient used for encoding, and encodes the result. In the method,
A redundant transform process for transforming the input signal to be encoded using a transform base of a redundant system;
An update conversion coefficient calculation process that performs clipping processing according to a set threshold and calculates an update conversion coefficient by replacing a conversion coefficient smaller than the threshold with a zero value;
An evaluation information calculation process for calculating an evaluation value indicating the degree of energy compaction with respect to the calculated update conversion coefficient;
A threshold update process for updating the threshold and repeatedly processing the update conversion coefficient in the update conversion coefficient calculation process for threshold candidates;
An evaluation process for selecting an update conversion coefficient having the maximum evaluation value among the update conversion coefficients;
Until the predetermined end condition is satisfied, the update conversion coefficient selected by the evaluation process is re-input as a conversion coefficient to be an input of the update conversion coefficient calculation process, and the update conversion coefficient calculation process and the evaluation information calculation process are input. , An end condition check process for narrowing down transform coefficients by the threshold update process and the evaluation process;
An updated transform coefficient output process for outputting an updated transform coefficient that maximizes the evaluation value when the termination condition is satisfied;
An image encoding method comprising: an encoding process for encoding the update transform coefficient output by the update transform coefficient output process. The image encoding method according to claim 3, wherein
The evaluation value indicating the degree of energy compaction is a Cullback library information amount for the uniform distribution of the update transform coefficients or a coding gain calculated from a value obtained by normalizing the update transform coefficients. Encoding method.   An image encoding program for causing a computer to execute the image encoding method according to claim 3 or 4.

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