JPH01240074A - Picture encoder - Google Patents

Abstract

PURPOSE:To efficiently access compressed data in accordance with resolution by compressing original picture data efficiently and accumulating them hierarchically. CONSTITUTION:In a cosine conversion part 17-2, a consine conversion is performed to f(m, n)0<=m<=N-1, 0<=n<=N-1 which is the partial picture data (density value) of NXN picture elements. In a hierarchization part 17-3, cosine conversion data F(u, v) are divided into four classes of classes 1-4 in sequence from the one whose space frequency, that is, resolution is low. In a restoration part 9, the cosine conversion data F(u, v) accumulated in an accumulation part 18 are successively read out and the pictures are restored. Here, when retrieving what the accumulated pictures are, the picture of low resolution is first displayed in a short time, and when the picture is identified, the processing is stopped at that time, therefore, they can be retrieved very efficiently.

Description

[Detailed Description of the Invention] [Summary] This invention relates to an image encoding device using orthogonal transformation, and in particular to an image encoding device that can restore images in stages according to a desired resolution. With the aim of enabling step-by-step restoration in as short a time as possible, 1st 2
In an image encoding device for restoring image data from a power of 2 x a first power of 2 orthogonal transformed data, desired second 2 of the orthogonal transformed data not more than the first power of 2 From the power x second power of 2, the second power of 2 (1
and an inverse transform means for calculating the X second power of two thinned image data.

[Industrial application field]

The present invention relates to an image encoding device using orthogonal transformation,
In particular, the present invention relates to an image encoding device capable of restoring an image in stages according to a desired resolution.

[Conventional technology]

Since the amount of image data is much larger than text/numeric data, the challenge is to develop technology to efficiently store it and technology to access the stored data efficiently. be.

In order to efficiently store huge amounts of image data, it is necessary to compress the data through encoding. The requirements that this encoding method must meet include: 1) high compression rate, 2) high quality (there is almost no difference between the restored image and the original image), and 2) efficient access.

Various methods such as predictive coding, vector quantization, block coding, and transform coding have been proposed as coding technologies that satisfy the conditions ① and ② above. Among these, transform coding has a high compression ratio and In terms of image quality, it is inferior compared to other methods. In this method, original image data is converted into spatial frequency spectrum parameters by orthogonal transformation, and then quantized, and restoration is performed by performing the reverse process. This method takes advantage of the fact that the data after orthogonal transformation is statistically biased, and also takes into consideration the visual characteristics of humans regarding spatial frequencies when encoding, resulting in a high compression rate and high quality. This makes it possible to perform three-dimensional image encoding.

FIG. 10 shows the configuration of an image encoding device when cosine transformation is used as one of the orthogonal transformations. For example, the original image data 1 sampled into 256 x 256 pixels (one pixel represents a density value) is first divided into, for example, 256 pieces of 16 x 166 pixel partial image data in the block dividing section 2 . Note that this division process may or may not necessarily be performed when the size of the original image data 1 is small.

Then, compression is performed in the compression unit 3 for each partial image data. First, assuming N -16, each partial image data (density value) of the NxN pixels is f (m).

n), 0≦m≦N-1, 0≦n≦N-1, and cosine transformation based on the following equation is performed in the cosine transformation unit 3-1.

However, 0≦U≦N-1, O≦■≦N-1■ c (u, v) = stone (u=v=o)=1 (others) N X N ([ The two-dimensional cosine transformation data F (u, v) of lil becomes data indicating the two-dimensional spatial frequency spectrum distribution for the partial image data f (m, n), and the distribution has statistical bias depending on the type of image. has.

Next, in the quantization unit 3-2 of FIG. 10, each of the NXN pieces of cosine transformed data F (u
, v) are allocated an appropriate number of quantization bits, and are quantized (encoded) and data compressed.

Cosine transform data F quantized as above
(u, V) is stored in a means not particularly shown, transferred as necessary (FIG. 10, 4), and then input to the restoring unit 5.

In the restoring unit 5, the inverse quantizing unit 5-1 performs a process opposite to that of the quantizing unit 3-2, and decodes the NXN pieces of cosine transform data F (u, v).

Subsequently, the inverse cosine transform unit 5-2 performs inverse cosine transform on this data based on the following equation to calculate restored partial image data f' (m, n).

However, 0≦m≦N-1. O≦n≦N-1 Restored partial image data f' of N×N pixels calculated as above
(m, rl) is the original partial image data' (m
+ n), and by obtaining, for example, 256 pieces of such restored partial image data, a restored image data of 256 x 256 pixels (Figure 10) that corresponds well to the original original image data 1 can be restored. can do.

Next, in addition to the above-mentioned encoding techniques, a technique is required that enables efficient access to the stored compressed data, as described in section (2) above. In order to efficiently access compressed data, it is essential to have a hierarchical data structure when storing data. In other words, it is essential to first present an image with a low resolution and gradually increase the resolution so that it can be determined at an early stage whether the image is the desired one. By doing so, unnecessary data access and transfer can be avoided. In addition, by having a hierarchical data structure according to the resolution, data can be adjusted according to the resolution of the image display device.
This can be done by simply transferring the data. This allows for example 51
1024X 1 to 2X 512 pixel resolution display device
To enable efficient transfer by eliminating waste such as transferring data of 0.24 pixels.

In order to meet the above requirements, as shown in FIG.
It is necessary to have a hierarchical restoring unit 10 that hierarchically restores the compressed data of the seed portion 9 and the compressed data hierarchically and displays it on the display unit 11.

Applying the concept of FIG. 11 above to the cosine transform image encoding device of FIG. 10, we find that the quantization unit 3-2
Cosine transformation data F (u, v) output from
O≦U≦N-1, 0≦V≦N-1 may be stored hierarchically in order from data corresponding to a portion with a low spatial frequency, that is, data with a low order (values of u, v).

At the time of restoration, first, using only the low-order cosine transform data F (u, v), the restoration unit 10 (FIG. 10) uses the low-resolution restored partial image data f.
' (m, n) is restored and restored image data 6 is presented. Subsequently, the restoration operation in the restoration unit 5 may be repeated while gradually increasing the order to gradually increase the resolution and display.

Here, when calculating the above equation (2) in the inverse cosine transform unit 5-2 in FIG. An algorithm has been proposed to calculate quickly. Such a high-speed calculation algorithm is generally configured such that restored partial image data f'(m, n) of NXN pixels is always calculated from NXN pieces of cosine transform data F (u, V).

Therefore, in order to restore an image with low resolution as described above, for example, O≦U ≦3,0
If only the range ≦■≦3 was transferred,
Conventionally, the value of cosine transform data F (u, v) in the range of 4≦U≦N-1, 4≦V≦N-1 is set to O, and NXN pieces of data are created, and then a high-speed calculation algorithm is applied. As a result, restored partial image data f' (m, n) of NxN@element with low resolution was obtained.

(Problem to be Solved by the Invention) However, in the case of the above conventional example, even when high-speed inverse cosine transform is performed on a small number of cosine transform data in order to restore an image with low resolution, NXN (11 cosine This method always requires the same amount of calculation as performing a high-speed inverse cosine transform on the converted data, and has the problem that it cannot meet the demand for quickly restoring low-resolution data and performing early discrimination. .

An object of the present invention is to enable gradual restoration of low-resolution images in a short period of time.

[Means to solve the problem]

FIG. 1 is a block diagram of the present invention. In the same figure,
First, let 2″ be the first power of 2, 24 × 24
The original image data f(m, n), 96
Figure 12 for m; 2”-1, Q≦fi≦2A-1
Orthogonal transformation is performed as follows, 2″×22 orthogonal transformed data F (u, v), O≦U≦2″−1,0≦■≦21
-1 is obtained and stored, for example, in a storage means not particularly shown. Here, the orthogonal transformation 12 is, for example, a cosine transformation,
The orthogonal transformation data F (u, v) is the original image data f (
The two-dimensional spatial frequency spectrum for fn, n) is shown.

The inverse transform unit 13 converts the 2′×2” orthogonal transform data F
Among (u, v), the desired second power of 2 number less than or equal to 21 (first power of 2 number) is 2i, and 2tx2
From the orthogonal transformation data F (u, v) of j, 2'×2' thinned image data is calculated according to a high-speed inverse transformation algorithm. Here, the fast inverse transform algorithm is, for example, a fast inverse cosine transform algorithm.

Next, the image rearrangement means 14 rearranges the thinned-out image data of 2'×2', and the original image data f (m
, n) is restored.

[For production]

In the above means, for example, as shown in FIG.
”, the original image sampled on a 22×21 grid (elephant data f (m, n) = f (0,0) ~ f
For (3, 3), 22 × 22 orthogonal transformation data F (u, v) = F (0, 0) ~ F (3, 3)
Assume that bonds have been accumulated in advance.

Here, depending on the resolution required for the restored image,
Among the 2 × 22 orthogonal transformation data F (u, v), for example, as shown in FIG.
Select only 1).

When the inverse transform means 13 performs an operation according to the high-speed inverse transform algorithm on the orthogonal transform data F (u, v), the same number of thinned image data as the selected number 2' × 21 is obtained. It will be done.

Next, the size of the restored image data r' (m, n) is set to, for example, the size of the original image data f (m, n), 2' x 22
If the image relocation means 14 is the same as the above 2'
The thinned image data of X2' is rearranged on the 2' x 2' restored image, and the 22 x 22 restored image data
(m, n>=f' (0,O) ~f' (3,
3) is obtained.

In the above rearrangement, for example, the desired 22 × 22 restored image area is calculated as 2' (first power of 2) ÷ 2' (second power of 2) as shown by the thick line in FIG. 4 pieces with a grid of size 2 as one side (second power of 2 squared)
into square divided areas, and each divided area has 2'
This is executed by selecting the thinned image data of X2' one by one and arranging the same data obtained. That is,
For example, the restored image data f' (0, O), M
(1,O), M (0,1) and f' (1,1)
All the same thinned image data is arranged in one divided area consisting of.

Through the above operations, restored image data f' (m, n) of the previously requested resolution can be obtained.

If it is desired to increase the IW image quality, the same calculation as above can be performed by increasing the value of the number 2'X2' selected from the 2-1×27 orthogonal transformation data F (u, v). As a result, by first acquiring a restored image with a low resolution and gradually increasing the resolution, it is possible to quickly determine whether the restored image is a desired one. Here, the lower the resolution, the smaller the value of 2j x 27, so the calculation in the inverse transformation means 13 is executed faster, and the lower the resolution, the more efficiently the image can be converted in a short time.

In addition, a plurality of 2' below 2' (first power of 2)
By arranging a plurality of inverse transformation means 13 and image rearrangement means 14 in parallel corresponding to the value of (second power of 2) and selecting according to the resolution of the image to be restored, more efficient processing becomes possible.

In addition, 2'X2'' orthogonal transformation data F stored in advance
(u, v) is first 2°×26, then 2′×2
', 22 x 22, etc. If the data are stored hierarchically so that they can be accessed sequentially, efficient access becomes possible.

〔Example〕

Hereinafter, embodiments of the present invention will be explained in detail.

FIG. 2 is a block diagram of an image encoding device according to the present invention. The original image 15 is sampled by an input section 16 consisting of a television camera and an AD converter as density data of, for example, 256 x 256 pixels, and is input to a compression section 17 .

In the compression unit 17, first, the block division unit 17-1 divides the image into partial image data f (m, n) of, for example, N×N pixels (for example, N=8 or 16, etc.).

Next, the partial image data f (m.

n) is cosine-transformed in the cosine-transforming unit 17-2, and NXN two-dimensional cosine-transformed data F (u
, v) are calculated.

Subsequently, F (u, V) is 4 in the hierarchization unit 17-3.
The quantization unit 17-4
After being sequentially quantized in the storage section 18, the signals are stored in a four-layered structure.

The cosine transform data F (
u, v) are sequentially read out from desired layers and restored at a desired resolution in the restoration unit 19, resulting in a restored image 21
is displayed on the display unit 20 as follows.

In the restoring unit 19, first, an inverse quantizing unit 19-1 performs processing opposite to that of the quantizing unit 17-4, and the cosine transform data F (u, v) of a desired layer is decoded.

The above cosine transform data F (u, v) is inputted to a cosine inverse transform unit 19-4 corresponding to each layer in a multiplexer (MPX, the same applies hereinafter) 19-2 according to a layer selection signal 19-3 having a value of 1 to 4. .

Here, an inverse cosine transform calculation is performed according to a fast inverse cosine transform algorithm, and thinned image data corresponding to each layer is calculated.

Then, this data is input to the redistribution unit 19-5 corresponding to each layer, and the partial image data r (m,
NxN pixel restored partial image data f corresponding to n)
'(m, n) is restored.

Then, the restored partial image data f' (m, n)
By obtaining a plurality of images and displaying them on the display unit 20, a restored image 21 corresponding to the original original image 15 is restored.

Next, the operation of the image encoding apparatus having the above configuration will be explained.

First, in the cosine transformation unit 17-2, f (m, n)0≦m≦ which is partial image data (density value) of N×N pixels.
For N-1.0≦n≦N-1, (cosine transformation is performed based on the formula t1> shown in the conventional example section. As a result, the partial image data f (m.

NXN two-dimensional cosine transform data F(u, v) representing a two-dimensional spatial frequency spectral distribution for n) are obtained.

In F (u, v), 11 and ■ are each 05U≦
It can take each value of N-1, O≦V≦N-1, but here,
A smaller value of U or ■ represents a spectral component with a lower spatial frequency and a lower resolution, and a larger value represents a spectral component with a higher spatial frequency and a higher resolution.

Therefore, the hierarchization unit 17-3 divides the cosine transform data F (u, v) into four hierarchies, hierarchies 1 to 4, in descending order of spatial frequency, ie, resolution. Therefore, after the above processing, the cosine transform data F (u, v) is quantized by the quantization unit 17-4 and stored in the storage unit 1B.
has a hierarchical structure as shown in FIG. In the figure, layer 1 represents the spatial frequency spectral component with the lowest IW image resolution, and as the layer goes up to 2, 3, and 4, the spatial frequency spectral component becomes higher in resolution.

At this time, in order to apply the fast inverse cosine transformation algorithm described later, the size of the partial image data "(m, n) is set so that the value of N is a power of 2, for example, 2' = 8, and , 2.3 is also a value of a power of 2 less than or equal to N, for example, when N = 8, 2 = 1. 2 =
2. It is determined to take a value such as 2'=4.

Next, in the restoration section 19 (Fig. 2), the cosine transformation data F(u, v
) are read out sequentially to restore the image.

Here, if you want to search for what each stored image is, you can first display the low-resolution images for a short time, and then stop processing once you know what the image is. If it is not available, you can increase the resolution even further and display it, which will allow you to perform a very efficient search.

Therefore, in the restoration section 19, the cosine transform data F stored hierarchically in the storage section 18 as shown in FIG.
(u, v) is restored for each floor while sequentially accessing 2°3.4 from floor N1.

That is, the hierarchical structure as shown in FIG. 3 is a data structure that facilitates efficient access during restoration.

As mentioned above, the cosine transform data F(u,
v) is read out, an inverse cosine transform operation is performed in the inverse cosine transform unit 19-4 corresponding to each layer.

Now, for the cosine transform data F (u, v) of NXN (N is a power of 2), the cosine transform data of a certain layer is F (u, v), O≦U≦2'-1゜O≦■ ≦2f
−1, 0≦j≦log2N, and the inverse cosine transform arithmetic expression of equation (2) shown in the conventional example section is changed as follows. However, the coefficient c (u.

However, m, n = 7 ・k, O≦≦21-1 Now, let N = 21 in the cosine transformation data F (u, v), and set the above j values in layers 1, 2, and 3.4 to 0. ．．
1. 2. 3, first, in layer 1, j−
0, and equation (3) becomes as follows.

f'(0,0)=7''F (u,v) ・-
−141 From the above equation (4), the cosine transformed data F (u, v) −F (0
.

In the case of layer 1 above, then redistribution section 1 of layer 1 in Figure 2.
9-5, for each r' (m, n) in the bold line other than the shaded part in Figure 4+a), f'(0
, 0), the restored partial image data f of NXN = 2°
' (m, n) can be made into fff element.

Next, at floor r52, j=1, and equation (3) becomes as follows.

F(u+ ■) ・cos "-""'-N However, m, n=o, 4 From the above equation (5), the cosine transform data F (u , v), u, v-0°1 is the thinned restored partial image data f, which is also indicated by diagonal lines.
' Converted to (m, n).

In the case of the above-mentioned floor 152, in the rearrangement section 19-5 of the floor 2 in FIG. By giving the same density value as , the restored partial image data r' (
m, n> can be restored.

Next, in layer 3, j=2, and equation (3) becomes as follows.

,. . 5'' νT αEL-, ---(61N However, m, n=o, 2, 4.6 From the above equation (6), the cosine transformation data r of layer 3 indicated by the diagonal line in FIG. 4(C) ;' (u, v) + u,
v=O+1.2.3 is converted into thinned restored partial image data f' (m, n), which is also indicated by diagonal lines.

In the case of the above hierarchy 3, the relocation unit 1 of the hierarchy 3 in FIG.
In 9-5, by giving each of the 16 divided areas surrounded by thick lines in FIG. 4(C) the same density value as the shaded area included in each divided area, the resolution is further improved than in the case of layer 2. Restored partial image data f' of 2" x 2" pixels with high
(m, n) can be restored.

Next, in layer 4, j=3, and equation (3) becomes as follows.

However, m, n=Q, l, . . . 7 From the above equation (7), the cosine transform data F (u, v) l u, v=O+1, ...
7 is restored partial image data f that is not thinned out as is.
' Converted to (m, n). Therefore, ζ in the rearrangement unit 19-5 of layer 4 in FIG. The restored partial image data f' (m, n) can be restored.

Next, the fast inverse cosine transform algorithm of layer 4 corresponding to the above equation (7) is shown in FIG. 5 for a one-dimensional case. Here, "." indicates a mere contact terminal, and "○" indicates an addition operation. Further, the sine function value or cosine function value or the negative sign "-" on each line indicates that those values are multiplied. For example, in FIG. 5, the output X is F
o-cos(π/4) + F a ・cos
(π/4), and the output y is F 2 ・cos
(7C/8) +F 6 ·cos (3π/8). And output 2 becomes xy.

According to the calculation algorithm J2 shown in FIG. 5, eight pieces of restored partial image data f'o=f't can be restored at high speed from eight pieces of cosine transformed data Fo=Ft. In addition, formula (7)
A two-dimensional operation corresponding to F (u.

v) To perform −+f′ (m, n),
The calculation algorithm shown in FIG. 5 may be repeated for u and m for each value of v and n. Note that the calculation algorithm for layer 4 is described in the document r IEEE TRANSACTION
S ON COM-MLINICATIONS, Vo
l, C0M-25, Nu9, SEPTEMBE
R.

1977, published in J.W., Il., CI.
IEN, C, 11, S)'I-ITII, and S
, C., FRALICK, J. et al.
Computational Algorithm f
or Discrete CoCo51neTrans
It corresponds to the algorithm disclosed in for.

Next, the fast inverse cosine transformation algorithms of layers 1 and 2°3 corresponding to the above equations (41, (5), and (6)) are as follows:
It can be realized as a subset of FIG. 5 and configured as shown in FIGS. 6, 7, and 8, respectively.

As described above, in the present invention, in the cosine inverse transform unit 19-4 of FIG. 2 for each layer, from 2j The extracted restored partial image data ('
(m, n), and for the thinned out part, the original part is restored by rearranging the density values that were not thinned out in the rearrangement section 19-5 in FIG. It is possible to obtain restored partial image data f' (m, n) of N×N pixels of the same size as the image data r (m, n>. By adopting such a configuration,
It is now possible to perform inverse cosine transform calculations for each floor 1a using the high-speed inverse cosine transform algorithm shown in Figures 5 to 8. It can be seen that the inverse cosine transform (low) requires a very small amount of calculation.

FIG. 9 shows the number of operations (addition and multiplication) required for two-dimensional inverse cosine transform of each layer when the above-described fast inverse cosine transform algorithm is used. As can be seen from the figure,
The amount of computation for layer 2 is about 1/1O smaller than that for layer 4, and the image restoration time is also reduced in proportion to this. Although the restored image of layer 2 has a lower resolution than that of layer 4, it is considered to be sufficiently useful for determining whether the image is a desired image in image searches and the like. If it is the desired image, the restoration can be continued further to obtain a high-resolution image, and if it is not the desired image, it can be stopped immediately and the next image can be accessed, which reduces the transfer time and processing time. can be significantly reduced and is extremely efficient.

In the embodiment shown in FIG. 2, the case where N=8 and the number of layers is 4 has been explained as an example, but the explanation is not limited thereto. , by configuring similarly to FIGS. 5 to 8,
A fast inverse cosine transform can be performed.

Note that the size of the restored partial image data f' (m, n) does not need to be the same as the original restored partial image data f (m, n), and the size of the restored partial image data f' (m, n) is not necessarily the same as that of the original restored partial image data f (m, n), and the size of the restored partial image data f' (m, n) is not necessarily the same as that of the original restored partial image data f (m, n). By changing the operation, for example, reduced restored partial image data r' (m, n) can be obtained,
This also makes it possible to display the restored image 21 in a reduced size on the display unit 20 in FIG. For example, 102.
IX 1024 pixel original image data, for example 512X
It is also possible to display on a display device with a low resolution of 512 pixels.

〔Effect of the invention〕

According to the present invention, by efficiently compressing original image data and storing it hierarchically, it is possible to efficiently access compressed data according to the W1 quadrant.

Further, when the hierarchical compressed data is hierarchically restored and displayed, it becomes possible to perform the restoration at a processing speed according to the resolution, and efficient restoration becomes possible.

In addition, even in systems where image display devices with different resolutions coexist, there is no need to have separate compressed data.
This is highly effective because it is only necessary to transfer and restore the data up to the layer corresponding to the resolution.

[Brief explanation of the drawing]

FIG. 1 is a block diagram of the present invention; FIG. 2 is a configuration diagram of an image encoding device according to the present invention; FIG. 3 is an explanatory diagram of the hierarchical storage structure of compressed data; (dl is an explanatory diagram of the hierarchical restoration operation according to this embodiment, Figure 5 is a diagram showing the signal flow graph of the one-dimensional fast inverse cosine transform of layer 4, and Figure 6 is a diagram showing the signal flow graph of the one-dimensional fast inverse cosine transform of layer 1. Figure 7 is a signal flow graph of inverse cosine transform. Figure 7 is a signal flow graph of one-dimensional fast inverse cosine transform of layer 2. Figure 8 is a signal flow of one-dimensional fast inverse cosine transform of layer 3. Figure 9 is a graph showing the number of calculations required for two-dimensional inverse cosine transformation of each layer. Figure 10 is a configuration diagram of a cosine transformation image encoding device. Figure 11 is an image This is a conceptual diagram of data compression and hierarchical restoration. 13... Inverse conversion means, 14... Image rearrangement means, f (m, n)... Original image data, F (u,
v3...Orthogonal transformation data, f' (m,
n) ...Restored image data. 1!1' Applicant: Fujitsu Limited f (m+'
1 F (u + v
January] "Hierarchy of Hakutenita's Hierarchical Ustsutomi, Yuri Structure" Encircle Figure 3 00V I:im. Calculation: 300i'. oro floor 7 adventure figure 9 cosine dead picture zango ichisen l no name 41 Shigeru figure 10

Claims (1)

[Claims] 1) First power of 2 x first power of 2 (2^i
The original image data (f(m
, n)) obtained by orthogonal transformation x
In an image encoding device that restores image data from a first power of 2 (2^i x 2^i) orthogonal transform data (F(u,v)), the orthogonal transform data (F(u,v) )), perform high-speed inverse transformation from the desired second power-of-two number (2^i) or less x second power-of-two number (2^j x 2^j) of the first power-of-two number (2^i). According to the algorithm, the second power of two ×
An image encoding device comprising: inverse transform means (13) for calculating second power-of-two (2^j x 2^j) thinned-out image data. 2) The thinned out image data is rearranged to obtain restored image data (f') corresponding to the original image data (f(m, n)).
The image encoding device according to claim 1, further comprising an image rearrangement means (14) for restoring (m, n)). 3) The image rearrangement means (14) divides the first power of 2 x first power of 2 (2^i x 2^i) area by dividing the first power of 2 by the first power of 2. The second power of 2 (
The second 2 whose side is the number determined by 2＾i÷2＾i)
In each of the divided areas divided into square divided areas, which are the squares of the power of 2 (2^j), the second power of 2 x the second
By arranging the same data obtained by selecting one by one from the power of 2 (2^j x 2^j) thinned image data, the first power of 2 x the first 2 A claim characterized in that restored image data (f'(m, n)) having the same size as a power number (2^i x 2^i) of original image data (f(m, n)) is restored. 2. The image encoding device according to 2. 4) The second power of 2 (2^j) is the first 2
The inverse transformation means (13) and the image rearrangement means (14) can be selected from a plurality of values equal to or less than the power of (2^i)
) are installed in parallel, each corresponding to the second power of 2 (2^j) values, and are selected according to the resolution of the image to be restored. , 2 or 3. 5) First power of 2 pieces x first power of 2 pieces (2
The orthogonal transformation data (F(u,v)) of ＾i×2＾i) is
hierarchically stored in the storage means such that the plurality of second power-of-two pieces (2^j) are sequentially accessed by second power-of-two pieces x second power-of-two pieces corresponding to the smallest value of the plurality of second power-of-two pieces (2^j); The image encoding device according to claim 1, 2, 3, or 4, wherein the image encoding device is stored. 6) The image encoding device according to claim 1, 2, 3, 4, or 5, wherein the orthogonal transformation is a discrete cosine transformation.