WO2012031418A1

WO2012031418A1 - Multi-bank wavelet transform method and application for image and video compression coding and decoding

Info

Publication number: WO2012031418A1
Application number: PCT/CN2010/078008
Authority: WO
Inventors: 王国秋
Original assignee: 湖南华冠数码科技有限公司
Priority date: 2010-09-09
Filing date: 2010-10-22
Publication date: 2012-03-15
Also published as: CN101984664A; CN101984664B

Abstract

The present invention provides a multi-bank wavelet transform method for image and video compression coding and decoding. The r-bank discrete biothonormal wavelet with the bank number r greater than or equal to 16 is applied to perform forward or inverse transform on image compression or decompression. Above-mentioned multi-bank wavelet transform method can be applied to computer software, DSP software, ASIC chip or FPGA chip. The present invention provides a new multi-bank wavelet transform method. It has the advantages that images haven't blocking effect after wavelet transform, and avoids complicated iterative calculation in wavelet transform. And such multi-bank wavelet transform can be translated into the product of wavelet transform and block transform. Wavelet transform and block transform are integrated dynamically，thus enabling seamless downward compatibility of new and old technology, that is, the old technology is a standard subset of the new one. The images or videos coded with the old technology can be decoded smoothly using the new technology, which is favorable to parallel calculation.

Description

Multi-inlet wavelet transform method and application for image and video compression coding and decoding

[Technical Field]

The present invention relates to the field of information technology, and in particular, to a digital image and digital video compression coding conversion method. 【Background technique】

With the rapid development of technologies such as computers, microelectronics, signal processing, communications, and lasers, multimedia technologies that integrate sound, image, and video have rapidly penetrated into computers, communications, broadcast television, and consumer entertainment industries. Digital devices that transmit over digital signals are increasingly being used.

Digital signals have many advantages, but when the analog signals are digitized, their frequency bands will be greatly widened. For example, when a 6MHz ordinary TV signal is digitized, its digital rate will be as high as 167Mbps, which requires a large amount of memory capacity and transmission bandwidth. Digital signals lose their practical value. The digital compression technique solves the above difficulties well, and the frequency band occupied by the compressed signal is much lower than that of the original analog signal. Therefore, it can be said that digital compression coding technology is one of the key technologies for practical use of digital signals. A key factor in the transmission and preservation of digital images and digital video is the compressibility of digital images and digital video. This compression is based on the premise of reducing the quality of the image or video, at the expense of the quality of the image or video in exchange for valuable storage or transmission bandwidth. Of course, this compression cannot be excessive, so that the visual effect of the image or video becomes unacceptable, which requires continuous improvement of compression efficiency under certain quality conditions. In addition, the compression behavior should be standardized, which will facilitate the transmission and sharing of information.

In order to standardize this compression coding behavior, many international standards have been introduced, such as the image compression standard JPEG (international standard ISO/ICE 10918, which is widely used in digital cameras and the Internet), and the image compression standard JPEG2000 (ISO/IEC 15444-1). :2000), video compression standard MPEG-1 (international standard ISO/ICE 11172, used in VCD), MPEG-2 (international standard ISO/ICE 13818, used in DVD and digital TV) and MPEG-4 (international standard) ISO/ICE 14496, used in streaming media technology). In addition to standardizing compression behavior, these standards continue to improve compression efficiency. For example, MPEG-2 has higher compression efficiency than MPEG-1, and MPEG-4 has higher compression efficiency than MPEG-2.

In compression coding standards and techniques, transformation techniques must be used. At present, in JPEG, MPEG-MPEG-2 and MPEG-4, the orthogonal transform method used is Discrete Cosine Transform (DCT); in JPEG2000, Wavelet Transform Technology (Discrete Wavelet Transform) is used. Referred to as DWT).

Wavelet Transform (Wavelet Transform) has a good performance in image compression coding, so people have high hopes for it, and hope to create a new era of image and video compression coding. But for 20 years, the role of wavelet transform in image and video compression has not been as great as imagined. Although DWT is used in JPEG2000, JPEG2000 is very difficult to implement on the chip, which is determined by the characteristics of DWT. In fact, DWT is an iterative algorithm (iterative) The algorithm, that is, the input value of the second processing is the output value of the first processing), iteratively iteratively multiple times in the chip, resulting in a large amount of memory in the chip, and the structure is complicated. Therefore, the wavelet transform chip can only implement a limited image block transform, which is generally 128x128 or 256x256. This allows large-format images to be divided into smaller blocks in order to be compression-coded with the chip. This is one of the reasons why JPEG2000 has been available for more than a decade, and it is still not available for handheld devices such as digital cameras.

Relatively speaking, video compression coding is more complicated, and DWT is currently more difficult to use in video. This is not difficult to understand, because DWT is completely different from the form, structure and characteristics of block transforms such as DCT currently in large use. Therefore, a good transformation should not be iterative, that is, a small block of image data should be immediately connected to the next step after the transformation. In the image and video compression coding, after a small piece of data is transformed, To start the quantization and subsequent steps immediately, this is the advantage of block transforms such as DCT, and DWT does not have this advantage.

In the existing technical standards, although the compression coding efficiency of the new technology is improved, the compatibility of the old and new technologies is a big problem. If JPEG2000 is not compatible with JPEG at all, MPEG-4 is not compatible with MPEG-2 at all, which greatly limits the industrialization of new technologies.

[Summary of the Invention]

The object of the present invention is to overcome the above drawbacks of the prior art, and to provide a multi-inlet wavelet transform method in image and video compression coding and decoding, which can be compatible with existing JPEG and MPEG technologies at zero cost on the basis of improving coding efficiency. To make the new technology and the existing industry can be smoothly connected.

In order to achieve the above object, the technical solution proposed by the present invention is:

A multi-inlet wavelet transform method for image and video compression encoding and decoding, which uses a r-input bi-orthogonal wavelet with a radix r higher than or equal to 16 for image compression or decompression of a positive or Reverse transformation.

Another object of the present invention is to provide a computer software, DSP software, ASIC chip or FPGA chip implementation method having the above-described multi-inlet wavelet transform method.

The invention provides a novel multi-inlet wavelet transform, which has the advantage that the image of the wavelet transform has no blocking effect, and avoids the complex iterative algorithm of the wavelet transform, and such multi-inlet wavelet can be converted into wavelet transform and block transform. The product of this, through the multi-inlet wavelet, the wavelet transform and the block transform are organically linked, which can realize the seamless backward compatibility of the old and new technologies, that is, the old technology is a standard subset of the new technology, and the new technology can be successfully decoded. Technically encoded images or video, and facilitate the implementation of parallel computing.

[Description of the Drawings]

1 is a block diagram of a compression encoding process for compressing an image or a video according to the present invention;

2 is a block diagram showing an equivalent encoding process for compressing an image or a video according to the present invention;

3 is a block diagram of a decoding process for compressing an image or video according to the present invention. 【Detailed ways】

In the field of image and video compression technology, image compression is the core of the transformation technology, which is an indispensable technology in image and video compression coding. In the field of image and video compression coding, block conversion technology has always been the leader. The emergence of wavelet transform (wavelet transform means 2-inlet wavelet transform) has changed this situation, and wavelet transform has begun to be used in the new international technical standards. However, the current block transform and wavelet transform are completely incompatible, and there are two technologies that are not intrinsically linked. The lack of compatibility leads to a complete disconnect between new technologies and industries. The above-mentioned compatibility can be achieved by introducing a Multi-bank Discrete Wavelet Transform (MBDWT) into the transformation of image and video compression coding and decoding. When the multi-bank Wavelet has a high hexadecimal number, completing a transformation is equivalent to multiple iterations of the DWT. If the 8-letter wavelet is decomposed once, it is equivalent to DWT completing 3 iterations; 16-wave wavelet is decomposed once and equivalent DWT completes 4 iterations; 32-in wavelet transform is equivalent to once Completed 5 iterations and so on at DWT. The ensuing problem is that there are hundreds of variables in the multi-wavelet, and its construction is a big challenge. The invention provides a multi-inlet wavelet transform method for transforming in image and video compression encoding and decoding, which uses r-into-discrete bio-orthogonal wavelet with a radix r higher than or equal to 16 for image compression. Or decompressed forward or reverse transform.

It is assumed that { h _t } and { h _t } are two low-pass filters, { } and { g^ ^r> } (j=0, l,..., r-1 ) For r-1 high-pass filters, the dual is satisfied

∑1⁄2 = 0,

Here is a pulse signal, ie =1 (j=0), or =0 (} ≠0 o is defined by { , &( ^; ') } and { , 8^ ^r> } defines an r-incremental double R-bank discrete biorthogonal wavelet.

In particular, when r = 2, this is the usual bi-orthogonal wavelet, which is used in JPEG2000. Therefore, the so-called wavelet is also called 2-inlet wavelet. When r>2, it is called multi-inlet wavelet. In the present invention, "wavelet" or "DWT" is often referred to as a 2-inlet wavelet, and when ambiguity occurs, we will specifically explain it.

If ∑g! ⁰⁾ = 0 , ∑ ^> = 0, (j=0,l,..., r-1 ), then { } and { } are called vanishing moments (Vanishing

Moment). If hi = h,, g ^j) = g ^j) , then the bi-orthogonal wavelet at this time is called an orthogonal wavelet. Therefore, orthogonal wavelets are a special case of biorthogonal wavelets.

If {^} is a filter, i=l, 2,..., 2N+l, that is, the length of the filter is odd. If = , i = l, 2, ... N, the filter is said to be symmetric; if _; = , i = l, 2, ... N, the filter is called antisymmetric (anti-symmetric). The following formula (5) defines the forward transform of a one-dimensional r-incremental bi-orthogonal wavelet:

The following formula (6) defines the inverse transform of one-dimensional r-into-discrete bi-orthogonal wavelets (Inverse Transform):

^H ^+^ ). (6) For image or video compression coding, a two-dimensional transformation is required. The two-dimensional forward transform refers to a discrete multi-wavelet transform on a matrix, which is composed of a one-dimensional wavelet transform, that is, first, all the columns of the matrix are sequentially subjected to column transformation, and the transformed data is substituted for the column. Then, all rows of this matrix are sequentially transformed. It can be seen that the two-dimensional forward transformation is the process of repeated use (5). Reverse the above process to obtain a two-dimensional inverse transformation. The two-dimensional inverse transformation is the process of repeated use (6).

Forward conversion is used for image or video compression encoding, and inverse transformation is used for image or video decoding. When the radix of the multi-inlet wavelet is sufficiently high (r ≥ 16), only one forward transform or reverse transform is required, that is, in (5) and (6), j=-l is taken. At this time, { _Ci ( ^Q ) } is the original data.

When r-in has the following matrix form,

(W2)

₇ ₈ (rr/2+i) ₈ Π2+Ϊ) (7/ 2+1)

, 1 62

H = (8)

(r-1) (7-1)

8i 82

Here, >r is the maximum length of the filter bank, and assuming r is an even number. A remarkable feature of the present invention is that (7)~(10) can be decomposed into the following forms (11)~(14):

3⁄4 0 .. 0 0

0 0 .. 0 0

(13)

0 0 0 0

Here, _/2 is any normative orthogonal matrix of r/2-dimensional, which is characterized by a first behavior of 1//^7Ϊ, and the sum of elements of the remaining rows is 0, that is, having a vanishing moment. And {sj and {?;} are low-pass filters of any bi-orthogonal DWT, and

{ } This bi-orthogonal DWT high-pass filter.

Use the r-in wavelet with the structure of (11), (12), (13), (14) for the transform of image and video compression encoding and decoding, regardless of _{/2 which} is the norm orthogonal to satisfy the condition The matrix and { , ?·, , } form what kind of 2-into-double In particular, if r=16, the corresponding _/2 takes an 8-dimensional discrete cosine transform, then what kind of biorthogonal wavelet is formed by { s _; , s _t , t , with equation (11) , (12), (13), (14) The structure of the r-inlet wavelet is compatible with DCT. Therefore, the 16-inlet wavelet transform in the present invention can be compatible with DCT-based image and video compression coding and decoding algorithms.

Below is a concrete example of a 16-input bi-orthogonal wavelet (ie r=16). This filter bank is 23 or 21 in length and is symmetrical or antisymmetric. Except for the low pass filter, all high pass filters have vanishing moments.

1) Its forward low-pass filter is:

{ h _t }={ 9/640,-(3/320),-(3/128), 1/8,35/128,83/320, 151/640,

1/4,1/4,1/4,1/4,1/4,1/4,1/4,1/4,1/4,151/640,83/320,35/128,1/8, -(3/128),-(3/320),9/640},

2) 15 forward high-pass filters are:

{ _l?! ⁽¹⁾ }=c{27/64,-(9/32),-(63/80),609/160,1317/160,1137/160,351/64,403/80,317/80,223/80,

243/160,0,-(243/160),-(223/80),-(317/80),-(403/80),-(351/64),-(1137/160),

-(1317/160),-(609/160),63/80,9/32,-(27/64)},

{ _l?! ⁽²⁾ }=c{63/160,-(21/80),-(291/320),587/160,499/64,26/5,19/10,0,-(367/160 ),-(79/16), -(551/80),-(587/80),-(551/80),-(79/16),-(367/160),0,19/10, 26/5,499/64,587/160, -(291/320), -(21/80),63/160},

{ g! ⁽³⁾ }=c{27/80,-(9/40),-(63/64),105/32,2217/320,27/10,-(57/32),-(393 /80),-(1203/160),

-(251/40),-(311/80),0,311/80,251/40,1203/160,393/80,57/32,-(27/10),-(2217/320), -(105/32) , 63/64, 9/40,-(27/80)},

{ g ' }={9/640,-(3/320),-(33/640),23/160,41/128,3/320,-(181/640),-(23/80), -(43/160), 0,

43/160,23/80,43/160,0,-(43/160),-(23/80),-(181/640),3/320,41/128,23/160,-(33 /640),

-(3/320), 9/640},

{ g }=c{9/40,-(3/20),-(327/320),389/160,1907/320,-(31/16),-(1503/160),-(18/ 5), 303/160,

363/80,1167/160,0,-(1167/160),-(363/80),-(303/160),18/5,1503/160,31/16,-(1907/320),

-(389/160), 327/320, 3/20,-(9/40)},

{ _l?! ⁽⁶⁾ }=c{9/64,-(3/32),-(123/160),257/160,353/80,-(429/160),-(3161/320),0,779 /80,lll/40,

-(583/160),-(257/80),-(583/160),111/40,779/80,0,-(3161/320),-(429/160),353/80, 257/160 ,

-(123/160),-(3/32),9/64}, 3⁄4e/is^)-'3⁄4e/ee^)-'3⁄4e/A9i)-'3⁄4e/i8)-Ote/i8'8/At73⁄4e/At7 w/is (9i/A)-'3⁄4e/^)-} 3={ _(z i }

'{w/st7te/sr(w/61⁄2)-'(9i/6^i)-'(w/68t7)-'3⁄4e/e6i)-'3⁄4e/£9i)-'3⁄4e/6^i)- '3⁄4e/i6)-'3⁄4e/6t7)- ζζ '0te/6t7te/i6te/6^ite/e9ite/e6i 9/68t7'9i/6^i 9/6t7 3⁄4e/si)-'(w/st7) -}3={ ₍₁ ) }

'{(8n/£)-'(W/I)-'8/I' // '8^ΐ/5ε /ΐ /ΐ /ΐ /ΐ /ΐ /ΐ /ΐ /ΐ /ΐ /ΐ /ΐ '8^ΐ/5ε 9/Δΐ'8/ΐ'(^9/ΐ)-'(8^ΐ/ε)-}={ }

Ote/A6^'3⁄4e/6e)-'3⁄4e/6e^)-' Ate/6sr(w/iei)-'(9i/ie)-'w/i8te/e'(w/6)-}3= {

'{(w/si)-te/s'w/Aer( ei)-'(w/e^)-te/ ^'o'3⁄4e/ ^)-'9i/ASte/66 '3⁄4e/Aei)- Te/66'9i/AS'3⁄4e/ ^)-Ote/ ^'(w/e^)-'( ei)-'w/A£ite/s'(w/si)-}3={ }

' { 8/e'( i )-'(w/A6 \ z£/6i\ 'z L z szyz/e'z /Li'iz / s ΐ yz /ξζζ Ό'3⁄4ε/ς^^)-3⁄4ε /ε8ΐ'3⁄4ε/Δς)-'3⁄4/6)-3⁄4ε/ΐ8^'3⁄4ε/ΐΔ)-'3⁄4ε/6ςΐ)- 9/Δ6ΐ /ΐ'(8/ε)-}3={ _(ει }

'{(8^i/e)-'w/rw/n'(w/6i)-'8^i/ete/6'3⁄4e/n)- £/6'0' £/6) £/n '£/6)-'0t£/6' £/n) £/6'8n/£'(W/6I)-'/n'/I'(8n/£H={ _i) }

'{9ΐ/6'(8/ε)-'( 9/Δεζ) ε/6κ'(8// )-' ε/ΐς)-3⁄4ε/ΔΔΐ' ε/6ςζ)-'9ΐ/εΐΐ' ε/ Δεΐ)- 'ο3⁄4ε/Δεΐ'(9ΐ/εΐΐ) ε/6^(ζε/ΔΔΐ) ε/ΐς'8// ' ε/6κ)- 9/Δεζ'8/ε'(9ΐ/6)-} 3={ („ } οτ

'{3⁄4ε/ΐ^)-'9ΐ/Δ 9/ΐ5^'3⁄4ε/Δ1⁄2)-'8/Δ^'3⁄4ε/ΐ8)-Ό3⁄4ε/ΐ8'3⁄4ε/Δ9ΐ)-3⁄4ε/εε^

'{w/st7'3⁄4e/si)-'(w/61⁄2)-'9i/6^r(w/68t7)-te/e6r3⁄4e/£9i)-te/6^r3⁄4e/i6)- 3⁄4ε/6 ^Ό '3⁄4e/6t7)-te/i6'3⁄4e/6^i)-te/e9r3⁄4e/£6i)-'w/68t7'(9i/6^i)-'w/61⁄2te/sr(w/st7 )-}3={( ₆ ^ } /ii)- /i t7/i)-'r(t/i)-'t7/r(t7/i)-'†7/r(†7/i)-'8^i/se'(w/Ai)-'8/rw/r(8^i/e)-}={ ₍₈ ^ }

'{(0Ζε// )-'09ΐ/6'0Ζ/6

'(09i/esi)-'3⁄4e/A8)-O9i/is^'w/eot7'(oi/ei)-'(09i/A6t7i)-'9i/sro9i/6e8ro'(09i/6e8i)-'( 9i/si)- 'θ9ΐ/Δ6Μ'θΐ/εΐ'(ΐ79/εοΐ7)-'(ο9ΐ/ΐςζ) ε/Δ8'θ9ΐ/εςΐ'(οζ/6)-'(θ9ΐ/6)-'οζε/ / }3={ _ω ^ }

- L-

8008.0/0T0ZN3/X3d 8I £0/ZI0Z OAV ((}),,, 389/603/303/09/0127224-- (((((,,,,,,,,,,,,,,,,,,,,,,,,,,,,, -- - { }{(((,,,,,,59/03/03/30389/6090/303/6503/608/5303/60 2c422721172111111=---s

0 2

0 1

I { }{(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((( ,,,,,5/383/35/39/8/3/359/39/6/3/8222127222127121217414 ----- { }{((((,,,,,,,,,,,,, /659/3/38/39/5/383/35/30cl41741271221227212222=----- ((((}),,,, 9/3/39/33/89/6/6/63/82112212141141412 ----- }{(((((,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, ((},,,,,,,, 03/33/659/3/35/3/89/33/63/89/617211122177212272122741- - -

}{((((()) 职// O 800 sosld 8msiAV /In08/6s0£09I/6y08/£s//£nt£/r 9/6}A/;A)-

o

The remaining unwritten elements are also 0, and ^=-9^/16;

The forms of (13) and (14) are similar:

20. Here{

} constitutes a 9-7 type of bi-orthogonal 2-inlet wavelet. The invention converts a multi-inlet wavelet with a high hexadecimal number into a product of a lower-order 2-inlet wavelet and an orthogonal matrix, which simultaneously solves three major problems: First, the design of the multi-inlet wavelet is changed into Possiblely; the second is to make the computational complexity of multi-inlet wavelet transform effectively controlled, such as 2-inletted wavelet with efficient lift algorithm; thirdly, make multi-inlet wavelet and block transform establish an organic connection, making the new transform compatible Traditional block transformation. For example, if / ^ is taken as an 8-dimensional DCT, SP P ₈ =DCT=

353553, 0.353553, 0.353553, 0.353553, 0.353553, 0.35

{0.490393, 0.415735, 0.277785, 0.0975452, -0.0975452, -0.277785, -0.415735, -0.490393},

{0.461940, 0.191342, -0.191342, -0.461940, -0.461940, -0.191342, 0.191342, 0.461940},

{0.415735, -0.0975452, -0.490393, -0.277785, 0.277785, 0.490393, 0.0975452, -0.415735},

{0.353553, -0.353553, -0.353553, 0.353553, 0.353553, -0.353553, -0.353553, 0.353553},

{0.277785,-0.490393,0.0975452,0.415735,-0.415735,-0.0975452,0.490393,-0.277785},

{0.191342, -0.461940, 0.461940, -0.191342, -0.191342, 0.461940, -0.461940, 0.191342},

{0.0975452, -0.277785, 0.415735, -0.490393, 0.490393, -0.415735, 0.277785, -0.0975452} };

The invention is then compatible with DCT. In fact, the DCT is now part of our 16-input bi-orthogonal wavelet.

The transforming link of the present invention uses a multi-inlet wavelet structure, so the selection of the multi-inlet wavelet is large. It is within the scope of the invention to comply with such a structure, and it is not necessary to define a specific DWT and a specific /^ ₂ . The present invention does not limit the radix of the multi-inlet wavelet, but the application note is mainly on the 2 ^d -inlet wavelet, such as 16-in and 32-in, and only the hexadecimal number is high enough to avoid the iterative algorithm.

If our DWT is chosen to be bi-orthogonal, / ^ has a particularly good structure (such as (15)), then this multi-wavelet has a very efficient fast calculation method, whether it is software or chip implementation algorithm, the efficiency is very High.

Equation (15) has a special advantage. Although equation (15) itself is an orthogonal matrix, which is completely different from DCT, for DCT encoded images or video, equation (15) can be decoded without difficulty. This means that we are compatible with DCT in the chip or software. We don't need to design a DCT unit. We only need to design (15) to be compatible with DCT, which greatly saves the economic cost of compatibility. Compared with DCT, the computational cost of equation (15) is very economical. Of course, the coding performance of equation (15) is also higher than that of DCT.

From the features of the present invention, it can be seen that since the multi-wavelet of the present invention can be decomposed into two parts, as long as the performance of the two parts is excellent, the performance of the entire multi-inlet wavelet can be ensured to be excellent. We know that the performance of 2-input bi-orthogonal wavelets is very good, and whether it is DCT or (15), they are very good as block transforms, so the excellent performance of the multi-inlet wavelet designed is guaranteed. Referring to Figure 1, the present invention still follows the flow of compression coding when used for multi-stream wavelet compression of images or video. As can be seen from equations (11) and (12), the transformation here can be divided into two parts. The first is to make a DWT and divide the image into four, which is the usual DWT. Unlike the usual DWT, we will not break it down again, but divide the four-part "image" (three high-frequency subgraphs and one low-frequency subgraph) into (r/2) x (r /2) block, then use _/2 for each block for 2D Block transformation. Such a two-stage transform algorithm is essentially equivalent to the direct calculation method of (5) or (6) (see FIG. 2), and the process of decoding an image can be seen in FIG.

Of course, the algorithms in Figures 2 and 3 are much more efficient than direct calculations. DWT retains the advantages of wavelet transforms, such as eliminating block effects. The block transform can give a "direction" to the importance of the data, just like the DCT in JPEG, which makes the energy of the data orderable, so that it can absorb and be compatible with the excellent algorithms of JPEG and MPEG. The present invention is mainly applied to a transform technique in compression coding of images and video. In mathematics, these things are attributed to the operation of the matrix. In the image, the Y, U, and V components are operated separately; in the video, for the residual frame (B frame or P frame) and the reference frame (I frame), we regard it as "image".

Therefore, all of the products using compression coding of images and video, such as computer software, DSP software, ASIC chips or FPGA chips, can adopt the multi-inlet wavelet transform method of the present invention.

The above-described embodiments are merely illustrative of several preferred embodiments of the present invention, and the description thereof is not to be construed as limiting the scope of the invention. It should be noted that a number of variations and modifications may be made by those skilled in the art without departing from the spirit and scope of the invention. Therefore, the scope of the invention should be determined by the appended claims.

Claims

^ ^

A multi-inlet wavelet transform method for image and video compression encoding and decoding, characterized in that: image compression or decompression is performed by using r-into-discrete bi-orthogonal wavelet with a number r greater than or equal to 16. Forward or reverse transformation.

2. The multi-inlet wavelet transform method for image and video compression encoding and decoding according to claim 1, wherein: said r-incremental bi-orthogonal wavelet having a radix r higher than or equal to 16. Forward transformation to:

, ( ) , ( +! ) d ( ) J + i ) , Z = l, ... r r - Inverse discrete bi-orthogonal wavelet transform is:

Where: {^} and { } are low-pass filter pairs, { )} and (k=l,...,r-l) are r-1 high-pass filters dual, ) are transform coefficients.

The multi-inlet wavelet transform method for image and video compression encoding and decoding according to claim 1 or 2, wherein: the filter bank using the r-input bi-orthogonal wavelet has the following matrix form ,

. ₈ (7r/2+1) ₀ ₈ (r/2+l) - - ₈ r "

61 62 · ·· 01

H, = (2)

Where > is the maximum length of the filter bank, and sets r to an even number, and { } is the low-pass filter pair, and (k=l,...,rl) is the r-1 high-pass filter dual, then the above (1)~(4) expressions have the following (5)~(8) decomposition forms:

Where: { s _; } and { s _t } are any low-pass filters of bi-orthogonal 2-inlet wavelets, { t _t } and { I } are high-pass filters of the 2-input bi-orthogonal wavelets , _/2 is any r/2-dimensional canonical orthogonal matrix whose elements in the first row are both 1/2, and the sum of the elements of the remaining rows is 0.

4. The wavelet transform method for image and video compression encoding and decoding according to claim 3, wherein: when r=16, the filter bank is composed of 32 filters, 16 of which are used for Forward transform, 16 for inverse transform, the filter bank is:

1) Forward low pass filter:

{ h _t }={9/640,-(3/320),-(3/128),1/8,35/128,83/320,151/640,1/4,1/4,1/4, 1/4, 1/4, 1/4, 1/4, 1/4, 1/4,

151/640, 83/320, 35/128, 1/8, -(3/128), -(3/320), 9/640},

2) 15 forward high-pass filters:

{ }=c{27/64,-(9/32),-(63/80),609/160,1317/160,1137/160,351/64,403/80,317/80,223/80,

243/160,0,-(243/160),-(223/80),-(317/80),-(403/80),-(351/64),-(1137/160),-( 1317/160),-(609/160) /3/:/〇8008/-ososil£ 8ΪΗεθίϊΟίΑν 9ΐ/6)09ΐ/9£)0ΐ/6Γς/9909ΐ/8ς0£/ΐ6)08/ΐ3⁄409ΐ/£9}{ }Δ(ΔΔ.=”--” 0£/ΐ63⁄409ΐ/8ς9ς/90ΐ/6309ΐ/9£)9ΐ/608/ΐςς)08/8ς)08/ΐςς)Δ(Δ/Δ”---- 09ΐ3⁄408§(- (eο9ΐ/£οπ08/£6 £)3⁄4£/ς)οΐ/ΤΟ/6ο8/}{ } χ(Δ//.=”” 3⁄4£/SOI)O£/)OI/)t£/^08/£6ro9I/SrowIsro8/nrso8/ n£)OWIS3⁄4/(//-"--- 0 mesh) 0 inch / 6 ("

)o8/3⁄4)ol9/I8IO£/8n/£/££)O7---

09ΐ/£ο£ς/8ΐ)ο9ΐ/£οςΐ9ΐ/ΐ£Ο£/06Γ09ΐ/68£Ο£/£)Ο/£ο1/6}{ }(Δ/7.=--

WIWI)/nwI)/nwI)wrWIWrWI)/s/)/rs/r((/--"""

3⁄4£/ςΐ)9ΐ)3⁄4£/£6ΐ3⁄4£/£9ΐ)3⁄4£/6π3⁄4£/ΐ60(""-- 3⁄4£/ΐ)9ΐ/ΐ3⁄4£/ΐ8)03⁄4£/ΐ83⁄4£/9ΐ)3⁄4 £/£3⁄4Δ ^"""- { g ^12> }={ -(3/128), 1/64, 1 l/64,-(19/64),3/128,9/32,-(ll/32),9/32,0 ,-(9/32), 11/32,-(9/32),0, 9/32,-(ll/32),9/32,3/128,-(19/64),ll/64 ,l/64,-(3/128)},

{ }=c{ -(3/8), 1/4, 197/64,-( 159/32), -(71/32),281/32,-(9/2),-(57/32 ), 183/32,-(225/32),0,

225/32,-(183/32),57/32,9/2,-(281/32),71/32,159/32,-(197/64),-(l/4),3/8} ,

{ _i?! ⁽¹⁴⁾ }=c{-(15/64),5/32,137/64,-(13/4),-(213/64),271/32,0,-(271/32) , 57/16, 99/32,-(137/32),

99/32, 57/16,-(271/32), 0,271/32,-(213/64),-(13/4),137/64,5/32,-(15/64)},

{ g! ⁽¹⁵⁾ }=c{-(9/64),3/32,81/64,-(31/16),-(131/64),159/32,7/4,-(239 /32),-(39/32),297/32,0,

-(297/32),39/32,239/32,-(7/4),-(159/32),131/64,31/16,-(81/64),-(3/32),9 /64};

3) Reverse low pass filter:

{ 3⁄4 }={-(3/128),-(1/64),1/8,17/64,35/128,1/4,1/4,1/4,1/4,1/4 , 1/4, 1/4, 1/4, 1/4, 1/4, 1/4, 35/128,

17/64, 1/8, -(1/64),-(3/128)},

4) 15 reverse high-pass filters:

{ }=c{-(45/64),-(15/32),249/64,129/16,489/64,193/32,163/32,129/32,91/32,49/32,0,-(49/32), -(91/32),-(129/32),-(163/32),-(193/32),-(489/64),-(129/16),-(249/64),15 /32,45/64},

{ 5· ²⁾ }=c{-(21/32),-(7/16),251/64,247/32,47/8,81/32,0,-(81/32),-(167/ 32),-(233/32),

-(251/32),-(233/32), -( 167/32),-(81/32),0,81/32,47/8,247/32,251/64,-(7/16),- (21/32) } ,

{ g > }=c{-(9/16),-(3/8),237/64,219/32,27/8,-(51/32),-(177/32),-(259/32 ),-(113/16),-(137/32) 0,137/32, 113/16,259/32,177/32,51/32,-(27/8),-(219/32),-(237/64 ), 3/8, 9/16},

{ 5· ⁴⁾ }={-(3/128),-(1/64), 11/64, 19/64,3/128,-(9/32),-( 11/32),-( 9/32), 0, 9/32, 11/32, 9/32, 0, -(9/32), -(11/32), -(9/32), 3/128, 19/64, 11/64,-(1/64),-(3/128)},

{ 5· ⁵⁾ }=c{-(3/8),-( 1/4), 197/64, 159/32,-(71/32),-(281/32),-(9/2 ), 57/32, 183/32, 225/32, 0, -(225/32), -(183/32), -(57/32), 9/2,281/32,71/32,-(159/32 ),-(197/64),1/4,3/8},

{ 5· ⁶⁾ }=c{-(15/64),-(5/32), 137/64, 13/4,-(213/64),-(271/32),0,271/32,57 /16,-(99/32),

-(137/32),-(99/32), 57/16,271/32,0,-(271/32),-(213/64),13/4,137/64,-(5/32),- (15/64)},

{ ^ ⁽⁷⁾ }= _c {-(9/64),-(3/32),81/64,31/16,-(131/64),-(159/32),7/4,239/32 ,-(39/32),-(297/32),0,

297/32,39/32,-(239/32),-(7/4),159/32,131/64,-(31/16),-(81/64),3/32,9/64} , { g " }={ 9/640,3/320,-(3/128),-(l/8),35/128,-(83/320), 151/640,-(l/4), l/4,-(l/4), l/4,-(l/4), l/4

-(1/4), 1/4, -(1/4),151/640,-(83/320),35/128,-(1/8),-(3/128),3/320 , 9/640},

{ gf }=c{27/64,9/32,-(63/80),-(609/160), 1317/160,-(1137/160),351/64,-(403/80), 317/80,

-(223/80),243/160,0,-(243/160),223/80,-(317/80),403/80,-(351/64), 1137/160,-(1317/ 160), 609/160, 63/80,-(9/32),-(27/64) },

{ ^ ⁽¹⁰⁾ }=c{ 63/160,21/80,-(291/320),-(587/160),499/64,-(26/5),19/10,0,-( 367/160), 79/16,

-(551/80),587/80,-(551/80),79/16,-(367/160),0, 19/10,-(26/5),499/64,-(587/ 160),-(291/320), 21/80, 63/160},

^ ⁽¹¹⁾ }=c{27/80,9/40,-(63/64),-(105/32),2217/320,-(27/10),-(57/32),393/ 80,-(1203/160) 251/40,-(311/80),0,311/80,-(251/40), 1203/160,-(393/80),57/32,27/10,- (2217/320), 105/32, 63/64, -(9/40),-(27/80)},

{ ^ ⁽¹²⁾ }={ 9/640,3/320,-(33/640),-(23/160),41/128,-(3/320),-(181/640),23/ 80,-(43/160), 0,

43/160,-(23/80),43/160,0,-(43/160),23/80,-(181/640),-(3/320),41/128,-(23/ 160),-(33/640), 3/320, 9/640},

{ ^ ⁽¹³⁾ }=c{ 9/40,3/20,-(327/320),-(389/160),1907/320,31/16,-(1503/160), 18/5,303/ 160,

-(363/80), 1167/160,0,-(1167/160),363/80,-(303/160),-(18/5),1503/160,-(31/16),- (1907/320), 389/160, 327/320,-(3/20),-(9/40)},

{ ^ ⁽¹⁴⁾ }=c{ 9/64,3/32,-(123/160),-(257/160),353/80,429/160,-(3161/320),0,779/80,-( l H/40),

-(583/160),257/80,-(583/160),-(lll/40),779/80,0,-(3161/320),429/160,353/80,-(257/160) , -(123/160), 3/32, 9/64},

{ ^ ⁽¹⁵⁾ }=c{27/320,9/160,-(9/20),-(153/160),87/32,251/160,-(403/64),-(13/10) , 1497/160,

15/16,-(1839/160),0, 1839/160,-(15/16),-(1497/160),13/10,403/64,-(251/160),-(87/32) ,

153/160, 9/20, -(9/160), -(27/320) }; In the above filter, all c=l/^.

The multi-inlet wavelet transform method for image and video compression encoding and decoding according to claim 4, wherein: generating a 2-inlet wavelet of said 16-input bi-orthogonal wavelet filter bank is a 9 Type -7 biorthogonal wavelet, the filter bank is:

Dsa ^ 3⁄4, "/3⁄4 3⁄43⁄41⁄2 (3⁄4 s-i ^ m^ ^-, L

q/s q/zi- q/ςι q/ςι- q/zi q/s- q/z

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q/s- q/ςι q/£- q/zi- q/zi qii q/ςι- q/s

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q/z\- q/£ q/ςι q/ςι- q/£- q/z\

q/vi q/ς q/ς- qm— q/p\- q/ς- q/vi

q/ςι- q/z\- q/s- q/£- q/z\ q/ςι

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