JP2001285643A - Image converting apparatus and method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an image converting apparatus and its method that can reduce the capacity of a memory storing a wavelet coefficient and conduct the conversion processing with a small scale of the hardware at a high-speed. SOLUTION: Storage devices 901 and 902 store pixel data required by an adder 903 and a subtractor 904 to generate a wavelet coefficient with a 1st frequency band among pixel data of an input image, the wavelet coefficient with the 1st frequency band is generated on the basis of the pixel data of the input image and the pixel data stored in the storage devices 901 and 902, a storage device 905 stores a wavelet coefficient required by an adder 906 to generate a wavelet coefficient with a 2nd frequency band in the generated wavelet coefficients, and the wavelet coefficient with the 2nd frequency band is generated on the basis of the wavelet coefficient with the 1st frequency band that is generated and the wavelet coefficient stored in the storage device 905.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an image conversion apparatus and method for converting an input image into wavelet coefficients by wavelet transform or in the reverse direction.

[0002]

2. Description of the Related Art An image, particularly a multi-valued image, contains a great deal of information, and there is a problem that the amount of data becomes enormous when storing and transmitting the image. For this reason,
When storing and transmitting an image, high-efficiency coding is used to reduce the amount of data by removing the redundancy of the image or changing the content of the image to such an extent that the deterioration of the image quality is difficult to visually recognize. ing.

For example, JPEG recommended by the ISO and ITU-T as an international standard encoding method for still images.
In this method, after the image data is converted into DCT coefficients by discrete cosine transform (DCT) for each block (8 pixels × 8 pixels), each coefficient is quantized and further entropy-coded to compress the image data. . Since DCT and quantization are performed for each block, so-called block distortion may be seen at the boundary of each block of the decoded image.

Also, JPEG2000 is being studied as a new international standard encoding method for still images.
PEG2000 proposes a wavelet transform as one of preprocessing performed before quantization. The wavelet transform does not perform processing in units of blocks as in the current JPEG, but continuously processes input data, and thus has a feature that deterioration of a decoded image is hardly visually recognized.

Here, a conventional wavelet transform will be described with reference to the drawings.

FIG. 1 is a diagram for explaining a wavelet transform according to a conventional example. In FIG. 1, reference numeral 101 denotes a conversion memory which temporarily stores a wavelet coefficient being converted. Reference numeral 102 denotes a discrete wavelet transform unit, which converts an input image into wavelet coefficients by predetermined filtering and outputs the wavelet coefficients.

FIG. 2 shows a discrete wavelet transform unit 102.
FIG. 2 is a block diagram showing a basic configuration of FIG. FIG. 2A shows the basic configuration in the forward direction, where H0 is a filter having low-pass characteristics, and H1 is a filter having high-pass characteristics. FIG. 2B is a diagram showing a basic configuration in the reverse direction.

FIG. 3 is a diagram showing an example of coefficients of the filter shown in FIG. In order to simplify the explanation, the filter coefficients of the forward filters H0 and H1 shown in FIG. 2A (5 × 3 configuration in the example of FIG. 3) will be described as an example.

FIG. 4 is a diagram showing filtering of wavelet transform. An example in which an input image is sequentially input (raster order) from the upper left in the main scanning direction as shown in FIG. The image size is N
* M

As shown in FIG. 2A, image data input from the left side is a filter H0 having low-pass characteristics.
After being filtered by a filter H1 having high-pass characteristics, each result is down-sampled by 2: 1 and finally output as the same number (N * M) of wavelet coefficients as the input.

[0011] More specifically, FIG.
, By sequentially filtering the input image data in the horizontal direction, the wavelet coefficient L ((N / 2) * M) on the low frequency side and the wavelet coefficient H ((N / 2) on the high frequency side ) * M).

The above-mentioned wavelet coefficients L and H are all once stored in the conversion memory 101 shown in FIG. 1 in order to further divide them into subbands and obtain wavelet coefficients in the vertical direction.

Next, the wavelet coefficients stored in the conversion memory 101 are read out in the vertical direction, and as shown in FIG.
, Filtering is performed in the vertical direction by filters H0 and H1, and the result is down-sampled 2: 1. LL and H1 obtained by applying H0 to the low-frequency wavelet coefficient L are LH, and HL and HH are obtained by applying the high-frequency wavelet coefficient H to H0 and H1. . LL, LH, HL, HH
Are ((N / 2) * (M / 2)).

In addition, the lifting method of Sweldens (Lift
It is also known that the above-described discrete wavelet transform is performed by a method referred to as an “ing scheme”.

FIG. 5 is a diagram showing a basic configuration of a forward lifting method. FIG. 6 is a diagram showing a basic configuration of a lifting method in the reverse direction. In FIGS. 5 and 6, p and u are called lifting coefficients.
Shows an example of a lifting coefficient for generating the same output as that of the 5 × 3 filter.

Here, based on the lifting coefficients p = (-1, -1) / 2 and u = (1,1) / 4 shown in FIG. 7, the operation in the forward lifting method shown in FIG. 5 is performed. Will be described.

In FIG. 5, X is an input image, and (X
_{0, X 1, X 2,} X 3, X 4, X 5, a ...). The input images are classified into even and odd numbers, respectively. After the classified images are multiplied by lifting coefficients, they are subjected to an addition process, and are converted into low-frequency coefficients and high-frequency coefficients. Specifically, it is as follows.

[0018] (high coefficient of frequency _{side) X 'o = X o +} ( coefficients of the low frequency _{side) pX e X' e = X} e + uX 'e Incidentally, k shown in FIG. 5, which normalizes the wavelet coefficients However, in describing the essence of the present invention, there is no particular relevance, so the description is omitted.

Similarly, the generation of a pixel which is an output in the reverse direction shown in FIG. 6 is specifically expressed by the following equation.

[0020] (even-numbered _{pixels) X e = X 'e -uX} ' o ( odd-numbered _{pixel) X o = X 'o -pX} e if configuration of the filter is Kaware, lifting factor, as well as a target pixel to be processed Are different, but the conversion to the forward and backward coefficients can be performed in the same manner.

Even when the conversion is performed by the above-described lifting method, when the coefficients are generated by the procedures (A), (B), and (C) shown in FIG. 4, the coefficients are generated by (c). After all the coefficients thus obtained are once stored in the conversion memory 101 shown in FIG. 1, they must be read out in the vertical direction, converted again by the lifting method, and generate the coefficients by the procedure (C).

[0022]

In the above-mentioned conventional example,
In order to convert input image data into wavelet coefficients of a plurality of frequency bands by discrete wavelet transform, after filtering all the images of interest in the horizontal direction, all of them are temporarily stored in a storage device, and then temporarily stored again in the vertical direction from the storage device. It was necessary to perform reading and filtering processing. Similarly, after all the target images are subjected to the filtering process in the vertical direction, all the images are temporarily stored in the storage device,
It was necessary to read the data from the storage device again in the horizontal direction and perform the filtering process.

For this reason, a memory capacity for storing the coefficients generated by the first filtering processing is required depending on the image size, and a large-scale memory is required for converting a large image. There was a problem that would.

In addition, there is another problem that a large-scale memory is required to obtain a transform coefficient by further dividing into sub-bands.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems, and provides an image conversion apparatus and method capable of reducing the capacity of a memory for storing wavelet coefficients and performing high-speed conversion processing with a small hardware scale. The purpose is to:

[0026]

In order to achieve the above object, the present invention provides an image conversion apparatus for converting an input image into wavelet coefficients by a wavelet transform. First holding means for holding pixel data required by the first filter operation means for generating a wavelet coefficient of a band, pixel data of the input image, and pixel data held by the first holding means A first filter calculating means for generating a wavelet coefficient of the first frequency band, and a wavelet coefficient of a second frequency band among the wavelet coefficients generated by the first filter calculating means. Second holding means for holding wavelet coefficients required by second filter calculating means for performing A second filter operation unit configured to generate a wavelet coefficient of the second frequency band based on the wavelet coefficient generated by the filter operation unit and the wavelet coefficient stored in the second storage unit. And

According to another aspect of the present invention, there is provided an image conversion apparatus for converting an input wavelet coefficient into a coefficient in a reverse direction. First holding means for holding a wavelet coefficient required by the first filter operation means for conversion, and the first wavelet coefficient based on the input wavelet coefficient and the wavelet coefficient held in the first holding means. A first filter computing means for inversely transforming the wavelet coefficients into the wavelet coefficients of the frequency band, and a wavelet coefficient for inversely transforming the wavelet coefficients of the second frequency band among the wavelet coefficients inversely transformed by the first filter computing means. Second holding means for holding wavelet coefficients required by the second filter operation means; Based on the wavelet coefficients inversely transformed by the filter arithmetic means and the wavelet coefficients held by the second holding means, and a second filter arithmetic means for inversely converting the wavelet coefficients into the second frequency band based on the wavelet coefficients held by the second holding means. It is characterized by the following.

[0028]

Embodiments of the present invention will be described below in detail with reference to the drawings.

[First Embodiment] First, in describing the first embodiment, a description will be given using a forward filter coefficient of a 5 × 3 configuration shown in FIG. 7 as an example.

FIG. 8 is a diagram showing how the wavelet coefficients in the horizontal direction are generated, which is the first processing. In the figure, (X ₀ , X ₁ , X ₂ , X ₃ ,...) Is an input image. H, which is a coefficient on the high frequency side, is X _n−1 , X _n , X
It is calculated by performing an operation on three input images of _{n + 1} . L, which is a low-frequency coefficient, is calculated by performing an operation on one input image and two high-frequency coefficients L.

FIG. 9 is a block diagram showing a configuration of a converter for obtaining wavelet coefficients in the horizontal direction. As shown in the figure, the input image (X ₀ , X ₁ , X ₂ , X ₃ ,...)
Are horizontally delayed by storage devices (delay elements) 901 and 902. For example, if b is the output of the storage device 901 is assumed to be X _1, next to c is X ₀ is the output of the storage device 902, an input image a is the X _2. Then, the adder 903 and the subtractor 904 calculate the coefficients on the high frequency side using the values of a, b, and c.

The content of this operation is shown by the following equation.

D = X ₁ -1/2 (X ₂ + X ₀ ) Specifically, first, the values of the pixel a and the pixel c are added to the adder 903.
And the subtracter 904 subtracts the bit-shifted result of the addition result of the adder 903 from the value of the pixel b.
The value d generated by the above operation is H, which is the wavelet coefficient on the high frequency side.

Next, the low-frequency side coefficient L is calculated by the adder 906.
Is calculated. The output d of the subtractor 904 is horizontally delayed by the storage device 905. For example, c, d,
f corresponds to X ₂ , H ₃ , and H ₁ shown in FIG. 8, respectively.

More specifically, the coefficient L on the low frequency side can be calculated by adding a value obtained by bit-shifting the values of d and f to the value of the pixel c.

FIG. 10 is a horizontal timing chart for obtaining wavelet coefficients. As shown in the figure, the wavelet coefficient can be obtained in synchronization with the clock by the storage device for delay and the adder / subtractor. Note that the storage device 907 shown in FIG. 9 is inserted in the first embodiment to adjust the timing of the output coefficient H and the output coefficient L.

Next, referring to FIG. 11, a description will be given of a process for further generating wavelet coefficients in the horizontal direction. The wavelet coefficient converter shown in FIG. 9 generates wavelet coefficients line by line. That is, the images X _{0 (1)} , X _{1 (1)} , X _{2 (1)} , X _{3 (1)} ,... Of the _first row are processed in order, and the X _{0 (2)} , X _{1 (2)} ,
X _{2 (2)} , X _{3 (2)} ,... Are sequentially processed, and then sequentially processed.

A process of vertically transforming the wavelet coefficients H and L thus generated in order to perform sub-band processing will now be described. The coefficients H and L are continuously generated in synchronization with the clock, as shown in FIG. In order to simplify the description, a case will be described where the wavelet coefficient H on the high frequency side is wavelet-transformed in the vertical direction.

The coefficients in the first column are, as shown in FIG.
H1 ₍₁₎ , H1 ₍₂₎ , H1 ₍₃₎ , H1 ₍₄₎ , H1 ₍₅₎ , H1 ₍₆₎ , ...
It is. In order to obtain the coefficients in the vertical direction in the order of the coefficients, a line buffer corresponding to the number of taps of the filter is required.

FIG. 12 is a block diagram showing a configuration of a converter for obtaining wavelet coefficients in the vertical direction. Also,
FIG. 13 is a vertical timing chart for obtaining a wavelet coefficient.

As the input coefficients a ', b', and c 'shown in FIG. 12, the coefficient H on the high frequency side is input. In the first clock cycle shown in FIG. 13, the coefficients H _{1 (5)} , H _{1
1 (4)} and H _{1 (3)} are input to a ′, b ′, and c ′, and the adder 1
201 and the subtractor 1202, the coefficient HH _{1 (4)} on the high frequency side
And outputs it to d ′. In the next clock cycle, the coefficients in the second column, H _{3 (5)} , H _{3 (4)} , and H _{3 (3)} are a ′,
bH and c 'are input to obtain HH3 ₍₄₎ . Hereinafter, similarly, the coefficient H obtained by the horizontal wavelet transformer is continuously converted into HH.

Next, a method of obtaining a wavelet coefficient in the vertical direction of the coefficient L on the low frequency side will be described. As shown in FIG. 12, the high frequency side coefficient d ′ output from the subtractor 1202 is a line memory 12 that delays by one line.
03 is stored. In the first clock cycle shown in FIG. 13, when the wavelet coefficient HH _{1 (4)} is output from the subtractor 1202, in order to obtain the low-frequency wavelet coefficient HL, H ′ _{1 (4)} which is d ′ is used. , C ′ H
_{1 (3)} and HH _{1 (2)} obtained as the HL coefficient in the front row are required. Here, HH _{1 (2)} is extracted from the line memory 503 which can delay the coefficient calculated in the front row by one line. An adder 1204 adds bit shifts of d 'and f' to c 'to obtain a wavelet coefficient HL on the low frequency side.

Also, the coefficient L on the low frequency side obtained by performing the wavelet transform on the image data can be similarly converted into LH and LL.

FIG. 14 shows wavelet coefficients HH, H
It is a figure showing the whole discrete wavelet coefficient converter which asks for L, LH, and LL continuously. In the figure, 1
Reference numeral 401 denotes a converter for obtaining a horizontal wavelet coefficient shown in FIG. Reference numerals 1404 and 1407 denote converters for calculating the vertical wavelet coefficients shown in FIG.
Reference numerals 1402, 1403, 1405, and 1406 denote line memories required to delay the coefficients calculated by the horizontal wavelet coefficient converter 1401 in the vertical direction. The depth of each line memory is N / 2, as shown in FIG. The depth of the line memory 1203 shown in FIG. 12 is N / 4.

The above description has been made by taking a 5 × 3 filter as an example. However, the same effect can be obtained by increasing or decreasing the configuration and capacity of a storage device or a line buffer, or by performing an arithmetic operation using other arithmetic expressions according to the configuration of the filter. Needless to say, this is obtained.

As described above, according to the first embodiment, it is not necessary to store all the wavelet coefficients output from the first filtering process, and at least the second filtering process is required. Wavelet coefficients can be generated at high speed using only a line memory that stores only wavelet coefficients.

[Second Embodiment] Next, a second embodiment according to the present invention will be described with reference to the drawings.

FIG. 15 is a diagram showing a discrete wavelet coefficient converter according to the second embodiment. 14, 1501, 1502 and 1503 are wavelet coefficient converters in FIG. However, the number of input data of 1502 is ４ of the number of input data of 1501, and
3 is 1/4 of the input data number of 1502
Therefore, the storage capacities of the line memories in each wavelet transformer are different.

With this configuration, wavelet coefficients of a plurality of frequency bands can be generated without a large-scale memory.

As described above, according to the first and second embodiments, when converting image data into wavelet coefficients of a plurality of frequency bands, the image data and the wavelet coefficients are converted into a frame of one image data. Since there is no need to store the information in the memory, the storage capacity can be reduced as compared with the related art.

Further, since the wavelet coefficients of a plurality of frequency bands can be simultaneously generated and only the necessary band wavelet coefficients can be easily extracted, a system using the wavelet coefficients can be easily configured.

Further, since the present invention can be realized with simple hardware, it can be constructed not only with small-scale hardware as compared with the conventional one but also at high speed.

The present invention can be applied to a system including a plurality of devices (for example, a host computer, an interface device, a reader, a printer, etc.), but can be applied to a single device (for example, a copier, a facsimile). apparatus,
Digital camera).

An object of the present invention is to supply a storage medium storing a program code of software for realizing the functions of the above-described embodiments to a system or an apparatus, and to provide a computer (CPU or MP) of the system or apparatus.
It goes without saying that U) can also be achieved by reading and executing the program code stored in the storage medium.

In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiment, and the storage medium storing the program code constitutes the present invention.

As a storage medium for supplying the program code, for example, a floppy (registered trademark) disk,
Hard disk, optical disk, magneto-optical disk, CD-
A ROM, a CD-R, a magnetic tape, a nonvolatile memory card, a ROM, and the like can be used.

When the computer executes the readout program code, not only the functions of the above-described embodiment are realized, but also the OS (Operating System) running on the computer based on the instructions of the program code. ) May perform some or all of the actual processing, and the processing may realize the functions of the above-described embodiments.

Further, after the program code read from the storage medium is written in a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer, based on the instruction of the program code, It goes without saying that the CPU included in the function expansion board or the function expansion unit performs part or all of the actual processing, and the functions of the above-described embodiments are realized by the processing.

[0059]

As described above, according to the present invention,
The capacity of the memory for storing the wavelet coefficients can be reduced, and the conversion processing can be performed at a high speed with a small hardware scale.

[Brief description of the drawings]

FIG. 1 is a diagram for explaining a wavelet transform according to a conventional example.

FIG. 2 is a block diagram illustrating a basic configuration of a discrete wavelet transform unit 102.

FIG. 3 is a diagram illustrating an example of coefficients of the filter illustrated in FIG. 2;

FIG. 4 is a diagram illustrating filtering of a wavelet transform.

FIG. 5 is a diagram showing a basic configuration of a forward lifting method.

FIG. 6 is a diagram showing a basic configuration of a lifting method in the reverse direction.

FIG. 7 is a diagram illustrating an example of a lifting coefficient for generating the same output as a 5 × 3 filter.

FIG. 8 is a diagram illustrating a state where a wavelet coefficient in the horizontal direction is generated as the first processing.

FIG. 9 is a block diagram illustrating a configuration of a horizontal wavelet coefficient transformer.

FIG. 10 is a horizontal timing chart for obtaining a wavelet coefficient.

FIG. 11 is a diagram illustrating a process of generating a wavelet coefficient in the horizontal direction.

FIG. 12 is a block diagram showing a configuration of a vertical wavelet coefficient transformer.

FIG. 13 is a vertical timing chart for obtaining a wavelet coefficient.

FIG. 14 is a diagram illustrating an overall configuration of a discrete wavelet coefficient converter according to the first embodiment.

FIG. 15 is a diagram illustrating an overall configuration of a discrete wavelet coefficient converter according to a second embodiment.

Continued on front page F-term (reference) 5C059 KK08 LB05 MA00 MA24 PP01 SS06 SS15 SS26 SS28 TA31 TC04 TC41 TC42 TD00 UA06 UA11 UA15 UA33 UA34 5C078 BA12 BA53 CA27 DA01 EA01 5J064 AA04 BA16 BC01 BC08 BC12 BD03 9A001 EE

Claims (14)

[Claims] 1. An image conversion apparatus for converting an input image into wavelet coefficients by a wavelet transform, wherein a first filter operation means for generating a wavelet coefficient of a first frequency band among pixel data of the input image is provided. A first holding unit for holding required pixel data; and a wavelet coefficient of the first frequency band is generated based on the pixel data of the input image and the pixel data held by the first holding unit. A first filter operation means, and a wavelet coefficient required by the second filter operation means for generating a wavelet coefficient of a second frequency band among the wavelet coefficients generated by the first filter operation means. Second holding means for holding, and a wavelet generated by the first filter operation means Based on the wavelet coefficients held in the several second holding means, an image conversion device and having a second filtering unit for generating a wavelet coefficient of the second frequency band. 2. A wavelet required by a third filter calculating means for generating a wavelet coefficient of a third frequency band among the wavelet coefficients generated by the first or second filter calculating means. A third holding unit for holding a coefficient, the third frequency band based on the wavelet coefficient generated by the first or second filter operation unit and the wavelet coefficient held by the third holding unit. A third filter calculating means for generating a wavelet coefficient of the following, and a fourth filter calculating means for generating a wavelet coefficient of a fourth frequency band among the wavelet coefficients generated by the third filter calculating means. A fourth holding unit for holding a required wavelet coefficient; and a third filter operation unit. And a fourth filter calculating means for generating a wavelet coefficient of the fourth frequency band based on the wavelet coefficient generated by the above and the wavelet coefficient held by the fourth holding means. Item 2. The image conversion device according to Item 1. 3. The first filter operation means and the third filter operation means.
And the fourth filter operation means are connected in cascade,
3. The image according to claim 2, wherein wavelet coefficients of a plurality of frequency bands are generated by cascading the second filter operation means and the third and fourth filter operation means. Conversion device. 4. The image conversion apparatus according to claim 2, wherein the first to fourth holding units have different holding capacities. 5. The image conversion apparatus according to claim 2, wherein only the wavelet coefficients in a part of the frequency band are output. 6. The first to fourth filter operation means respectively comprise the first to fourth filter operation means by a lifting method.
The image conversion apparatus according to claim 2, wherein wavelet coefficients of a frequency band of? 7. An image conversion apparatus for converting an input wavelet coefficient into a coefficient in a reverse direction, wherein a first filter operation means for inversely converting a wavelet coefficient in a first frequency band among the input wavelet coefficients is required. First holding means for holding a wavelet coefficient to be used, and first wavelet coefficient for inversely converting to the wavelet coefficient of the first frequency band based on the input wavelet coefficient and the wavelet coefficient held by the first holding means. Of the wavelet coefficients inversely transformed by the first filter arithmetic means, and the wavelet coefficients required by the second filter arithmetic means for inversely transforming the wavelet coefficients into the wavelet coefficients of the second frequency band. Second holding means for holding, and inversely converted by the first filter operation means Based on the wavelet coefficients held in the second holding means and Eburetto coefficients, the image conversion device and having a second filtering unit inversely transforming the wavelet coefficients of the second frequency band. 8. The wavelet coefficients inversely transformed by the first or second filter operation means,
A third holding unit for holding a wavelet coefficient required by a third filter operation unit for inversely converting the wavelet coefficient into a wavelet coefficient of a third frequency band, and an inverse conversion by the first or second filter operation unit. A third filter operation unit that performs an inverse conversion to a wavelet coefficient of the third frequency band based on the obtained wavelet coefficient and the wavelet coefficient stored in the third storage unit; A fourth holding unit for holding a wavelet coefficient required by a fourth filter operation unit for inversely converting the converted wavelet coefficient into pixel data of an output image, and an inverse operation by the third filter operation unit. Based on the transformed wavelet coefficients and the wavelet coefficients held in the fourth holding means, the output Image converter according to claim 7, characterized in that it comprises a fourth filtering unit inversely converts the image pixel data. 9. The first filter operation means and the third filter operation means
And the fourth filter operation means are connected in cascade,
9. The wavelet coefficient of a plurality of frequency bands is inversely transformed by connecting the second filter operation means and the third and fourth filter operation means in a cascade. Image conversion device. 10. The image conversion apparatus according to claim 8, wherein the first to fourth holding units have different holding capacities. 11. The image conversion apparatus according to claim 8, wherein only the wavelet coefficients in a part of the frequency band are output. 12. The first to fourth filter operation means respectively comprise the first to fourth filter operation means by a lifting method.
9. The image conversion apparatus according to claim 8, wherein the wavelet coefficients in the frequency band of the following are inversely transformed. 13. An image conversion method for converting an input image into wavelet coefficients by a wavelet transform, wherein a first filter operation step for generating a wavelet coefficient of a first frequency band among pixel data of the input image. A first holding step of holding required pixel data; and generating a wavelet coefficient of the first frequency band based on the pixel data of the input image and the pixel data held in the first holding step. Holding a wavelet coefficient required in a second filter operation step for generating a wavelet coefficient in a second frequency band among the wavelet coefficients generated in the first filter operation step and the first filter operation step A second holding step, and the wavelet coefficient generated in the first filter operation step Image conversion method characterized in that it comprises a second filter operation process based on the wavelet coefficients held by the second holding step, to generate a wavelet coefficient of the second frequency band. 14. An image transformation method for transforming an input wavelet coefficient into a coefficient in a reverse direction, wherein the input wavelet coefficient is required in a first filter operation step for inversely transforming the input wavelet coefficient into a wavelet coefficient in a first frequency band. A first holding step of holding a wavelet coefficient to be used, and a first step of inversely converting the wavelet coefficient of the first frequency band based on the input wavelet coefficient and the wavelet coefficient held in the first holding step. Holding a wavelet coefficient required in the second filter operation step for inversely converting to a wavelet coefficient in a second frequency band among the wavelet coefficients inversely transformed in the filter operation step and the first filter operation step A second holding step, and a wavelet inversely transformed in the first filter operation step. Based on the wavelet coefficients held by the coefficient second holding step, an image conversion method characterized in that it comprises a second filter operation step of inverse transform to the wavelet coefficients of the second frequency band.