CN1568005A - A method of 8 input/output integer transformation/reverse transformation for coding processing - Google Patents

Abstract

The invention discloses an integer transform and inverse transform of 8 inputs and outputs in code process. The method includes: receives image parameter X=(x1, x2, ...., x8) outputted by predicting model; carries on special setting to the universal transform matrix, acquires the transform matrix T; decomposes the transform matrix T, each decomposed matrix is convenient to convert the multiply operation into addition and shifting operation; carries quick calculating matrix to Y=TX using above mentioned matrix decomposing result, and acquires the result Y= (y1, y2, ...., y8) of transform, namely the frequency domain parameter, which represents the signal intensity of each frequency segment of inputting image. The invention decomposes the transform matrix into several simple matrixes with 1 or 2 power, which can be realized through addition and shifting operation, it is convenient to design hardware, reduces the hardware design cost. And the invention guarantees the high efficiency of code.

Description

A kind of integer transform/inverse transform method that is used for 8 I/O of encoding process

Technical field

The present invention relates to digital image processing techniques, relate in particular to the integer transform in the image encoding and decoding technique, be specifically related to a kind of integer transform/inverse transform method that is used for 8 I/O of encoding process.

Background technology

Comprise high definition digital television, EVD, broadband network, WiMAX multimedia communication etc. these with information household appliances, communication equipment, industry that multimedia equipment is relevant, its common technology is to be the multimedia messages treatment technology of main contents with the digital video-audio encoding and decoding technique.Video coding and decoding technology is to realize high-quality, storage of low-cost multi-medium data and transmission key efficiently.In recent years, broadcasting, communication, development of computer network have also proposed more and more higher requirement for video coding and treatment technology.Coding method at present commonly used has predictive coding, orthogonal transform coding, vector quantization coding or the like, and these methods all are based on signal processing theory, are also referred to as first generation coding techniques usually.Popular image encoding international standard all is based on this coding theory now, the coding method that the motion compensation strategy, discrete cosine transform and the quantification that are based on the image block coupling of employing combines.

A complete video coding system generally includes: four main modular such as prediction, conversion, quantification and comentropy coding.Utilize the encoded image of building of laying equal stress on that the current image encoded of wanting is predicted (inter prediction) during the major function of prediction module, perhaps utilize in the image the encoded image block of building (or macro block) of laying equal stress on that the current image encoded piece (or macro block) of wanting is predicted (infra-frame prediction); The major function of conversion module is that the image block that will import transforms to the another one space, the energy of input signal is concentrated on the low frequency transform coefficient as much as possible, and then reduce the correlation between the image block interior element, helps compression; The major function of quantization modules is that the coefficient with conversion is mapped on the finite element collection that helps encoding; The major function of comentropy coding module is according to statistical law, and the conversion coefficient after quantizing is represented with variable length code.Similarly, video decoding system comprises similar module, mainly is the code stream of input is rebuild decoded picture by processes such as entropy decoding, inverse quantization, inverse transformations.Except above-mentioned module, also comprise some auxiliary coding toolses in the video coding and decoding system usually, these instruments equally also can contribute to the coding efficiency (compression ratio) of whole system.

Obviously, conversion/inverse transformation is the important component part of video coding and decoding system, the falling relevant effect and will directly influence the coding efficiency of encoder of conversion/inverse transformation.At present, Xian Jin video/audio encoding and decoding technology exists with the form of standard usually.Typically look at present (the Moving Picture Expert Group of Motion Picture Experts Group that audio compress standard has International Organization for Standardization to divide into, abbreviation MPEG) the MPEG series international standard of releasing, the H.26x series video compression recommendation that International Telecommunication Union proposes.In these video encoding standards, conversion commonly used has discrete cosine transform (DCT), wavelet transformation etc.Dct transform and wavelet transformation all have good encoding compression effect, but owing to need the computing of floating-point multiplication and addition, so complexity is than higher.Recent discovers that can use conversion coefficient all is the conversion of integer, as long as tie in quantized segment, under the situation that code efficiency does not reduce, still can reduce computational complexity greatly.

Joint video team (the Joint Video Team that ISO and ITU set up, abbreviation JVT) AVC (the Advanced Video Coding) video encoding standard of formulating is the video encoding standard of a new generation, it has adopted a series of novel coding techniquess, than all high many of the compression efficiency of existing any coding standard.The formal title of AVC standard in ISO is the tenth part of MPEG-4 standard, and the formal title in ITU is a standard H.264.The AVC standard has adopted a kind of integer transform of 4 I/O, shown in following matrixing.Because coefficient is very simple, only need just can realize that 4 * 4 two-dimensional transform only needs 16 displacements, 64 sub-additions altogether with addition and displacement.

$Y=\left[\begin{array}{cccc}1& 1& 1& 1\\ 2& 1& -1& -2\\ 1& -1& -1& 1\\ 1& -2& 2& -1\end{array}\right]\left[\begin{array}{cccc}{x}_{00}& x_{01}& x_{02}& x_{03}\\ x_{10}& x_{11}& x_{12}& x_{13}\\ x_{20}& x_{21}& x_{22}& x_{23}\\ x_{30}& x_{31}& x_{32}& x_{33}\end{array}\right]\left[\begin{array}{cccc}1& 2& 1& 1\\ 1& 1& -1& -2\\ 1& -1& -1& 2\\ 1& -2& 1& -1\end{array}\right]$

In brief, integer transform has following characteristics:

Algorithm is simple and clear, is easy to hardware designs; The operation result precision is high and can not overflow fast operation.When traditional dct transform is realized, different transformation results can be obtained in the device with nonidentity operation precision, therefore when carrying out video coding, not matching of direct transform and inverse transformation can be formed.And the integer transform coding can be combined closely with quantizing process, obtains the result of calculation of maximal accuracy under the prerequisite that data are not overflowed.

Therefore, in the design Video Codec, adopt integer transform to become a kind of inexorable trend.There have been some integer orthogonal transforms to be used for video coding at present, but still can have designed new more efficiently integer transform.For example, although the integer transform of 4 I/O that the AVC standard adopts is very simple, but when the input block that is applied to 8 * 8, can only be divided into 8 * 8 piece 44 * 4 sub-piece earlier, and then make the integer transform of 4 I/O respectively, therefore can't directly remove the correlation of all elements in the piece by conversion, code efficiency is undesirable.Particularly when handling high-definition digital video, because the resolution of image is very high, so the details in each 4 * 4 (content that promptly comprises) seldom.In this case, adopt minimum to be input as 8 * 8 piece and carry out motion compensated prediction and also can obtain very high precision of prediction, adopt minimum to be input as 4 * 4 piece and then can waste considerable bit and be used for additional informations such as encoding motion vector and pattern.In the digital audio/video encoding and decoding standard (AVS standard) that China is formulating, towards high-definition digital video coding, the minimum input block of employing is exactly 8 * 8.As previously mentioned, the integer transform of 4 I/O is 8 * 8 o'clock in input block, the coding effect is unsatisfactory, although in AVC standard formulation process, the integer transform that 8 I/O also once occurred, but need multiplication of integers during this transformation calculations, and the complexity of multiplication of integers is far above operations such as the addition and subtraction of integer and displacements.Therefore its computational complexity is higher, haves much room for improvement.

Summary of the invention

The technical problem to be solved in the present invention is, towards application such as high-definition digital video encoding and decoding, propose a kind of integer transform/inverse transform method and device thereof that is used for 8 I/O of encoding process, the present invention can also guarantee code efficiency efficiently when reducing complexity.

The integer transform method that is used for 8 I/O of encoding process of the present invention: comprise following step:

The first step receives the image parameter X=(x that prediction module is exported ₁, x ₂..., x ₈) ';

Second step is to universal transformation matrix

$W=\left[\begin{array}{cccccccc}z4,& z4,& z4,& z4,& z4,& z4,& z4,& z4\\ z1,& z3,& z5,& z7,& -z7,& -z5,& -z3,& -z1\\ z2,& z6,& -z6,& -z2,& -z2,& -z6,& z6,& z2\\ z5,& z7,& -z1,& -z3,& z3,& z1,& -z7,& -z5\\ z4,& -z4,& -z4,& z4,& z4,& -z4,& -z4,& z4\\ z3,& -z1,& -z7,& z5,& -z5,& z7,& z1,& -z3\\ z6,& -z2,& z2,& -z6,& -z6,& z2,& -z2,& z6\\ z7,& -z5,& z3,& -z1,& z1,& -z3,& z5,& -z7\end{array}\right],$ Make among the W coefficient satisfy: z1: z3: z5: z7=5: 4: 3: 1, obtain:

$T=\left[\begin{array}{cccccccc}a& a& a& a& a& a& a& a\\ 5b& 4b& 3b& b& -b& -3b& -4b& -5b\\ \mathrm{cd}& \mathrm{ce}& -\mathrm{ce}& -\mathrm{cd}& -\mathrm{cd}& -\mathrm{ce}& \mathrm{ce}& \mathrm{cd}\\ 3b& b& -5b& -4b& 4b& 5b& -b& -3b\\ a& -a& -a& a& a& -a& -a& a\\ 4b& -5b& -b& 3b& -3b& b& 5b& -4b\\ \mathrm{ce}& -\mathrm{cd}& \mathrm{cd}& -\mathrm{ce}& -\mathrm{ce}& \mathrm{cd}& -\mathrm{cd}& \mathrm{ce}\\ b& -3b& 4b& -5b& 5b& -4b& 3b& -b\end{array}\right],$ Wherein, a, b, c, d, e are integer;

In the 3rd step, T decomposes to transformation matrix, and the matrix after each is decomposed is convenient to the multiplication of matrices computing is converted into addition and shift operation;

The 4th step, utilize the result of above-mentioned matrix decomposition, carry out quick compute matrix Y=TX, obtained conversion Y=as a result (y1, y2 ..., y8) ', promptly frequency coefficient has been represented each frequency range signal intensity of input picture.

The integral inverse transform method that is used for 8 I/O of encoding process of the present invention comprises following step:

The first step, the coefficient Y=(y behind the reception inverse quantization ₁, y ₂..., y ₈) ';

Second step is by the transformation matrix of integer direct transform $T=\left[\begin{array}{cccccccc}a& a& a& a& a& a& a& a\\ 5b& 4b& 3b& b& -b& -3b& -4b& -5b\\ \mathrm{cd}& \mathrm{ce}& -\mathrm{ce}& -\mathrm{cd}& -\mathrm{cd}& -\mathrm{ce}& \mathrm{ce}& \mathrm{cd}\\ 3b& b& -5b& -4b& 4b& 5b& -b& -3b\\ a& -a& -a& a& a& -a& -a& a\\ 4b& -5b& -b& 3b& -3b& b& 5b& -4b\\ \mathrm{ce}& -\mathrm{cd}& \mathrm{cd}& -\mathrm{ce}& -\mathrm{ce}& \mathrm{cd}& -\mathrm{cd}& \mathrm{ce}\\ b& -3b& 4b& -5b& 5b& -4b& 3b& -b\end{array}\right],$

Obtaining its inverse transformation matrix is T ';

The 3rd step was that T ' decomposes to the inverse transformation matrix, and the matrix after each is decomposed is convenient to the multiplication of matrices computing is converted into addition and shift operation;

The 4th goes on foot, and utilizes the result of above-mentioned matrix decomposition, carries out quick compute matrix X=T ' Y, and the result who obtains conversion is: X=(x1, x2 ..., x8) ', the image of expression reconstruct or the residual image of reconstruct.

The present invention has following characteristics:

In this conversion/inverse transform method, because transformation matrix is resolved into the simple matrix that several contain the number of 1 or 2 power time, so integer transform can realize by addition and shifting function, be easy to hardware designs, reduces cost of hardware design.

The operational precision of this conversion and inverse transformation is high and can not overflow, and does not have the unmatched phenomenon of direct transform and inverse transformation.

This conversion/inverse transformation meets the statistical property of high-definition digital video, and it is good to fall relevant effect.

In brief, the present invention can also guarantee code efficiency efficiently when reducing complexity.

Description of drawings

Fig. 1 is the computing block diagram by the direct transform fast algorithm of the integer transform of satisfying of butterfly computation decomposition predetermined coefficients relation of the present invention;

Fig. 2 is the calculating schematic diagram by the inverse transformation fast algorithm of the integer transform of satisfying of butterfly computation decomposition predetermined coefficients relation of the present invention;

Fig. 3 is the realization schematic diagram of the fast algorithm of G4;

Fig. 4 is the realization schematic diagram of the fast algorithm of G4 ';

Fig. 5 is the video coding and decoding system structure chart that adopts integer transform method of the present invention.

Embodiment

Describe integer direct transform method of the present invention and direct transform method in detail below in conjunction with accompanying drawing.

Be shown below, W can regard a kind of general formula of 8 * 8 integer transforms as.Z1 wherein, z2 ... z7 is an integer.For the input X=(x1, x2 ..., x8) ', the output Y=WX of conversion.For inverse transformation, transformation matrix is W ', promptly for the input Y=(y1, y2 ...., y8) ', the output X=W ' Y of conversion.

$W=\left[\begin{array}{cccccccc}z4,& z4,& z4,& z4,& z4,& z4,& z4,& z4\\ z1,& z3,& z5,& z7,& -z7,& -z5,& -z3,& -z1\\ z2,& z6,& -z6,& -z2,& -z2,& -z6,& z6,& z2\\ z5,& z7,& -z1,& -z3,& z3,& z1,& -z7,& -z5\\ z4,& -z4,& -z4,& z4,& z4,& -z4,& -z4,& z4\\ z3,& -z1,& -z7,& z5,& -z5,& z7,& z1,& -z3\\ z6,& -z2,& z2,& -z6,& -z6,& z2,& -z2,& z6\\ z7,& -z5,& z3,& -z1,& z1,& -z3,& z5,& -z7\end{array}\right]$

The present invention adopts the combination of numbers meet certain rule to realize 8 I/O integer transform and inverse transformations, and its key is to make that coefficient satisfies among the W: z1: z3: z5: z7=5: 4: 3: 1.Be that transformation matrix T can write following form:

$T=\left[\begin{array}{cccccccc}a& a& a& a& a& a& a& a\\ 5b& 4b& 3b& b& -b& -3b& -4b& -5b\\ \mathrm{cd}& \mathrm{ce}& -\mathrm{ce}& -\mathrm{cd}& -\mathrm{cd}& -\mathrm{ce}& \mathrm{ce}& \mathrm{cd}\\ 3b& b& -5b& -4b& 4b& 5b& -b& -3b\\ a& -a& -a& a& a& -a& -a& a\\ 4b& -5b& -b& 3b& -3b& b& 5b& -4b\\ \mathrm{ce}& -\mathrm{cd}& \mathrm{cd}& -\mathrm{ce}& -\mathrm{ce}& \mathrm{cd}& -\mathrm{cd}& \mathrm{ce}\\ b& -3b& 4b& -5b& 5b& -4b& 3b& -b\end{array}\right]$

The inverse transformation matrix is T '.

A wherein, b, c, d, e are integer.The benefit of doing like this is, z1, and z3, z5, z7 satisfies certain proportion, has promptly guaranteed the compression effectiveness of conversion, can further implement effective fast algorithm again.A in addition, b, c are the equal of the scale factor that can extract from T, multiply by a, b, c can merge in the quantification and carry out.

In order to improve conversion efficiency, thereby improving the efficient of encoding and decoding, mainly is to start with from the butterfly computation of using DCT, therefore need decompose transformation matrix, so that adopt fast algorithm.

T is decomposed into:

T＝PKB，

Wherein

B=B1B2B3, P wherein, B1, B2, B3 is as follows:

$P=\left[\begin{array}{cccccccc}a& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& b& 0& 0& 0\\ 0& 0& c& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& b& 0& 0\\ 0& a& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& b& 0\\ 0& 0& 0& c& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& b\end{array}\right]$

$B1=\left[\begin{array}{cccccccc}1& 1& 0& 0& 0& 0& 0& 0\\ 1& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right]$ $B2=\left[\begin{array}{cccccccc}1& 0& 0& 1& 0& 0& 0& 0\\ 0& 1& 1& 0& 0& 0& 0& 0\\ 1& 0& 0& -1& 0& 0& 0& 0\\ 0& 1& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right],$ $B3=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 1\\ 0& 1& 0& 0& 0& 0& 1& 0\\ 0& 0& 1& 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 1& 0& 0& 0\\ 1& 0& 0& 0& 0& 0& 0& -1\\ 0& 1& 0& 0& 0& 0& -1& 0\\ 0& 0& 1& 0& 0& -1& 0& 0\\ 0& 0& 0& 1& -1& 0& 0& 0\end{array}\right]$

, can get like this:

$K=\left[\begin{array}{cccc}{G}_1& & & \\ & G_1& & \\ & & G_2& \\ & & & G_4\end{array}\right]$

Wherein,

G1＝[1]，

$G_2=\left[\begin{array}{cc}d& e\\ e& -d\end{array}\right]$ $G4=\left[\begin{array}{cccc}5& 4& 3& 1\\ 3& 1& -5& -4\\ 4& -5& -1& 3\\ 1& -3& 4& -5\end{array}\right]$

More than be the decomposable process of T, certainly, the matrix decomposition form of multiple equivalence can be arranged also.

Can further decompose as follows to G4:

G4=g4+g3*g2*g1; Promptly calculate G4X and can be converted into calculating: g4X+g3*g2*g1 X wherein:

$g_1=\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 0\\ 1& 0& -1& 0\\ 0& 0& 0& 1\\ 0& -1& 0& -1\\ 0& 0& 1& 0\\ 0& 1& 0& -1\\ 1& 0& 0& 0\end{array}\right],$ $g_2=\left[\begin{array}{cc}1000& 0000\\ 1100& 0000\\ 0010& 0000\\ 001-1& 0000\\ 0000& 1000\\ 0000& 1100\\ 0000& 0010\\ 0000& 001-1\end{array}\right]$ $g_3=\left[\begin{array}{cc}0410& 0000\\ -1004& 0000\\ 0000& 100-4\\ 0000& 0410\end{array}\right]$

$g_4=\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 1& 0& 0& 0\end{array}\right]$

The computing block diagram of the direct transform fast algorithm of the integer transform that satisfies predetermined coefficients relation of the present invention that decomposes by butterfly computation that Fig. 1 provides; The left side is input X, and the right side is output as Y.In conjunction with Fig. 1, as can be seen:

1. at first through 8 butterfly computation, calculate 4 and with 4 differences.

2. after 4 processing of difference in the 1st step, multiply by b again and just obtained output Y2, Y4, Y6, Y8 through the G4 module.

3. 4 of the 1st step and through 4 butterfly computation, calculate 2 and with 2 differences.

4. after 2 processing of difference in the 3rd step, multiply by c again and just obtained output Y3, Y7 through the G2 module.

5. 2 of the 3rd step and through 2 butterfly computation, calculate 1 and with 1 difference.Multiply by a respectively and just obtained output Y1, Y5.

6, to the wherein calculating of G4, carry out according to Fig. 3.

Among the present invention, to fast algorithm such as Fig. 3 of G4, wherein taking advantage of 4 operation in fact is exactly to move to left 2, and as can be seen: output one is:

out1＝(input1+input3+input2)*4+(input1-input3+input4)。

The following describes the matrix form of integral inverse transform method of the present invention.

The fast algorithm of inverse transformation can be pushed away by direct transform, and the inverse transformation matrix is T ', and T ' can resolve into:

T’＝B’K’P’，

B’＝B3’B2’B1’，

Definition by K can get:

$K^{\′}=\left[\begin{array}{cccc}{G_1}^{\′}& & & \\ & {G_1}^{\′}& & \\ & & {G_2}^{\′}& \\ & & & {G_4}^{\′}\end{array}\right],$

By G1, the definition of G2 as can be known:

G1’＝G1，G2’＝G2，

Definition by G4 can get:

${G_4}^{\′}=\left[\begin{array}{cccc}5& 3& 4& 1\\ 4& 1& -5& -3\\ 3& -5& -1& 4\\ 1& -4& 3& -5\end{array}\right]$

G4 ' can be decomposed into: G4 '=4*h1+h2*h1, wherein:

$h_1=\left[\begin{array}{cccc}1& 1& 1& 0\\ 1& 0& -1& -1\\ 1& -1& 0& 1\\ 0& -1& 1& -1\end{array}\right],$ $h_2=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& -1\\ -1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]$

Promptly calculate G4 ' Y and can be converted into calculating in two steps:

V＝h1Y

G4’Y＝4*V+h2*V

Wherein take advantage of 4 in fact to be exactly to move to left two.

The data flow diagram formal description of the method for integral inverse transform of the present invention is adopted butterfly computation to decompose and is seen Fig. 2, and the left side is input Y, and the right side is output as X.

1. at first Y1 and Y5 multiply by a respectively, then through 2 butterfly computation, calculate and with poor.

2.Y3 Y7 multiply by b respectively, pass through the processing of G2 ' module then after, two values of two values of output and first step output are through 4 butterfly computation, calculate 2 and with 2 differences.

3.Y2, Y4, Y6, Y8 multiply by c respectively, pass through the processing of G4 ' module then after, 4 values of 4 values of output and the output of second step are through 8 butterfly computation, calculate 4 and with 4 differences.

4. the output in the 3rd step is exactly X1, X2 ..., X8.

Wherein the calculating of G4 ' can be undertaken by Fig. 4.Among Fig. 4,

out1＝(input1+input2+input3)*4+(input1-input2+input4)。

As shown in Figure 5, based on the thinking of conversion/inverse transform method of the present invention, can realize being used for video encoder converting means and inverse transformation device in the general video coding and decoding system by hardware module.

Specify as follows:

Coded portion is estimated the motion of decoded picture in present image and the buffer memory, and obtains predicted picture according to movable information, subtracts the residual image that current input image obtains motion compensation;

The residual image that obtains is input to conversion module, adopts the inventive method, obtain conversion coefficient;

Conversion coefficient is quantized;

Adopt the conversion coefficient after the output of comentropy encoder quantizes, the bit stream after obtaining to compress.

Decoded portion utilizes the comentropy decoder that the bit stream of input is converted to conversion coefficient after the quantification;

Utilize inverse quantization module, obtain the conversion coefficient of reconstruct;

Conversion coefficient is input to inverse transform block, adopts the inventive method, obtain the error image of rebuilding;

Obtain predicted picture according to the image of having decoded in movable information and the buffer memory, add the error image of reconstruction, obtain the decoded picture of rebuilding.

It should be noted last that: above embodiment is the unrestricted technical scheme of the present invention in order to explanation only, although the present invention is had been described in detail with reference to the foregoing description, those of ordinary skill in the art is to be understood that: still can make amendment or be equal to replacement the present invention, and not breaking away from any modification or partial replacement of the spirit and scope of the present invention, it all should be encompassed in the middle of the claim scope of the present invention.

Claims (6)

1, a kind of integer transform method that is used for 8 I/O of encoding process is characterized in that, comprises the steps:

The first step receives the image parameter X=(x that prediction module is exported ₁, x ₂..., x ₈) ';

Second step is to universal transformation matrix

$W=\left[\begin{array}{cccccccc}z4,& z4,& z4,& z4,& z4,& z4,& z4,& z4\\ z1,& z3,& z5,& z7,& -z7,& -z5,& -z3,& -z1\\ z2,& z6,& -z6,& -z2,& -z2,& -z6,& z6& z2\\ z5,& z7,& -z1,& -z3& z3,& z1,& -z7,& -z5\\ z4,& -z4& -z4,& z4& z4,& -z4,& -z4,& z4\\ z3,& -z1,& -z7,& z5& -z5,& z7,& z1& -z3\\ z6,& -z2,& z2,& -z6,& -z6,& z2,& -z2,& z6\\ z7,& -z5,& z3,& -z1,& z1& -z3,& z5,& -z7\end{array}\right],$ Make among the W coefficient satisfy: z1: z3: z5: z7=5: 4: 3: 1, obtain:

$T=\left[\begin{array}{cccccccc}a& a& a& a& a& a& a& a\\ 5b& 4b& 3b& b& -b& -3b& -4b& -5b\\ \mathrm{cd}& b& -\mathrm{ce}& -\mathrm{cd}& -\mathrm{cd}& -\mathrm{ce}& \mathrm{ce}& \mathrm{cd}\\ 3b& b& -5b& -4b& 4b& 5b& -b& -3b\\ a& -a& -a& a& a& -a& -a& a\\ 4b& -5b& -b& 3b& -3b& b& 5b& -4b\\ \mathrm{ce}& -\mathrm{cd}& \mathrm{cd}& -\mathrm{ce}& -\mathrm{ce}& \mathrm{cd}& -\mathrm{cd}& \mathrm{ce}\\ b& -3b& 4b& -5b& 5b& -4b& 3b& -b\end{array}\right],$ Wherein, a, b, c, d, e are integer;

In the 3rd step, T decomposes to transformation matrix, and the matrix after each is decomposed is convenient to the multiplication of matrices computing is converted into addition and shift operation;

The 4th step, utilize the result of above-mentioned matrix decomposition, carry out quick compute matrix Y=TX, obtained conversion Y=as a result (y1, y2 ..., y8) ', promptly frequency coefficient has been represented each frequency range signal intensity of input picture.

2, the integer transform method that is used for 8 I/O of encoding process according to claim 1 is characterized in that, described the 3rd step decomposes transformation matrix T, comprising:

Make T=PKB, B=B1B2B3, wherein,

$P=\left[\begin{array}{cccccccc}a& 0& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& b& 0& 0& 0\\ 0& 0& c& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& b& 0& 0\\ 0& a& 0& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& b& 0\\ 0& 0& 0& c& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 0& 0& b\end{array}\right],$

$B1=\left[\begin{array}{cccccccc}1& 1& 0& 0& 0& 0& 0& 0\\ 1& -1& 0& 0& 0& 0& 0& 0\\ 0& 0& 1& 0& 0& 0& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right],$ $B2=\left[\begin{array}{cccccccc}1& 0& 0& 1& 0& 0& 0& 0\\ 0& 1& 1& 0& 0& 0& 0& 0\\ 1& 0& 0& -1& 0& 0& 0& 0\\ 0& 1& -1& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 1& 0& 0& 0\\ 0& 0& 0& 0& 0& 1& 0& 0\\ 0& 0& 0& 0& 0& 0& 1& 0\\ 0& 0& 0& 0& 0& 0& 0& 1\end{array}\right],$ $B3=\left[\begin{array}{cccccccc}1& 0& 0& 0& 0& 0& 0& 1\\ 0& 1& 0& 0& 0& 0& 1& 0\\ 0& 0& 1& 0& 0& 1& 0& 0\\ 0& 0& 0& 1& 0& 0& 0& 0\\ 1& 0& 0& 0& 1& 0& 0& -1\\ 0& 1& 0& 0& 0& 0& -1& 0\\ 0& 0& 1& 0& 0& -1& 0& 0\\ 0& 0& 0& 1& -1& 0& 0& 0\end{array}\right];$

Can get thus:

$K=\left[\begin{array}{cccc}{G}_1& & & \\ & G_1& & \\ & & G_2& \\ & & & G_4\end{array}\right];$

Wherein,

G1＝[1]， $G_2=\left[\begin{array}{cc}d& e\\ e& -d\end{array}\right],$ $G_4=\left[\begin{array}{cccc}5& 4& 3& 1\\ 3& 1& -5& -4\\ 4& -5& -1& 3\\ 1& -3& 4& -5\end{array}\right];$

G ₄Can further decompose as follows:

Make G4=g ₄+ g ₃* g ₂* g ₁, wherein,

$g_1=\left[\begin{array}{cccc}1& 0& 1& 0\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 0& 0& 0& 1\\ 0& -1& 0& -1\\ 0& 0& 1& 0\\ 0& 1& 0& -1\\ 1& 0& 0& 0\end{array}\right],$ $g_2=\left[\begin{array}{cc}1000& 0000\\ 1100& 0000\\ 0010& 0000\\ 001-1& 0000\\ 0000& 1000\\ 0000& 1100\\ 0000& 0010\\ 0000& 001-1\end{array}\right],$ $g_3=\left[\begin{array}{cc}0410& 0000\\ -1001& 0000\\ 0000& 100-4\\ 0000& 0410\end{array}\right],$ $g_4=\left[\begin{array}{cccc}0& 0& 0& 1\\ 0& 1& 0& 0\\ 0& 0& -1& 0\\ 1& 0& 0& 0\end{array}\right].$

3, the integer transform method that is used for 8 I/O of encoding process according to claim 2 is characterized in that, comprising: calculate G4X and be converted into calculating g4X+g3*g2*g1X; Promptly use matrix g1, g2, g3 be premultiplication X successively, promptly calculates g1X successively, g2 (g1X), and g3 (g2 (g1X)) adds with g4 premultiplication X.

4, a kind of integral inverse transform method that is used for 8 I/O of encoding process is characterized in that, comprises the steps:

The first step, the coefficient Y=(y behind the reception inverse quantization ₁, y ₂..., y ₈) ';

Second step is by the transformation matrix of integer direct transform $T=\left[\begin{array}{cccccccc}a& a& a& a& a& a& a& a\\ 5b& 4b& 3b& b& -b& -3b& -4b& -5b\\ \mathrm{cd}& \mathrm{ce}& -\mathrm{ce}& -\mathrm{cd}& -\mathrm{cd}& -\mathrm{ce}& \mathrm{ce}& \mathrm{cd}\\ 3b& b& -5b& -4b& 4b& 5b& -b& -3b\\ a& -a& -a& a& a& -a& -a& a\\ 4b& -5b& -b& 3b& -3b& b& 5b& -4b\\ \mathrm{ce}& -\mathrm{cd}& \mathrm{cd}& -\mathrm{ce}& -\mathrm{ce}& \mathrm{cd}& -\mathrm{cd}& \mathrm{ce}\\ b& -3b& 4b& -5b& 5b& -4b& 3b& -b\end{array}\right],$

Obtaining its inverse transformation matrix is T ';

The 3rd step was that T ' decomposes to the inverse transformation matrix, and the matrix after each is decomposed is convenient to the multiplication of matrices computing is converted into addition and shift operation;

The 4th goes on foot, and utilizes the result of above-mentioned matrix decomposition, carries out quick compute matrix X=T ' Y, and the result who obtains conversion is: X=(x1, x2 ..., x8) ', the image of expression reconstruct or the residual image of reconstruct.

5, the integral inverse transform method that is used for 8 I/O of encoding process according to claim 4 is characterized in that, described the 3rd step is that T ' decomposes to the inverse transformation matrix, comprising:

Make T '=B ' K ' P ', B '=B3 ' B2 ' B1 ',

Can get:

$K^{\′}=\left[\begin{array}{cccc}{G_1}^{\′}& & & \\ & {G_1}^{\′}& & \\ & & {G_2}^{\′}& \\ & & & {G_4}^{\′}\end{array}\right],$

According to the characteristics of transposed matrix as can be known:

G1’＝G1，G2’＝G2；

Definition by G4 can get:

${G_4}^{\′}=\left[\begin{array}{cccc}5& 3& 4& 1\\ 4& 1& -5& -3\\ 3& -5& -1& 4\\ 1& -4& 3& -5\end{array}\right]$

G4 ' can further be decomposed into: G4 '=4*h1+h2*h1

Wherein:

$h_1=\left[\begin{array}{cccc}1& 1& 1& 0\\ 1& 0& -1& -1\\ 1& -1& 0& 1\\ 0& -1& 1& -1\end{array}\right],$ $h_2=\left[\begin{array}{cccc}0& 0& 1& 0\\ 0& 0& 0& -1\\ -1& 0& 0& 0\\ 0& 1& 0& 0\end{array}\right]$

6, the integral inverse transform method that is used for 8 I/O of encoding process according to claim 5 is characterized in that, calculates G4 ' Y and can be converted into calculating in two steps, that is:

With matrix h1 premultiplication Y, obtain V=h1Y earlier;

Calculate again: G4 ' Y=4*V+h2*V, wherein take advantage of 4 to be exactly to move to left two.

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