CN106131575A - The method for compressing image combined with Chinese remainder theorem based on wavelet transformation - Google Patents
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- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/60—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding
- H04N19/63—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using sub-band based transform, e.g. wavelets
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- H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
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- H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
- H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
- H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
- H04N19/13—Adaptive entropy coding, e.g. adaptive variable length coding [AVLC] or context adaptive binary arithmetic coding [CABAC]
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- H04N19/169—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding
- H04N19/17—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object
- H04N19/176—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the coding unit, i.e. the structural portion or semantic portion of the video signal being the object or the subject of the adaptive coding the unit being an image region, e.g. an object the region being a block, e.g. a macroblock
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- H04N19/60—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding
- H04N19/625—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using transform coding using discrete cosine transform [DCT]
Abstract
A kind of method for compressing image combined with Chinese remainder theorem based on wavelet transformation, including following process: first, after original image two-dimensional wavelet transformation, the wavelet coefficient being converted in wavelet field, next the wavelet coefficient in wavelet field is carried out quantization encoding, only retain bigger wavelet coefficient, remaining zero setting；Data after wavelet transformation are carried out zero RLE, and the data set after zero RLE exists positive and negative, needs to add a constant value and makes data set be all the number not less than zero, and constant value fetches data the absolute value of minima in group；Judge the maximum bit wide of the new data set obtained again, select to carry out the grouping number N of Chinese remainder theorem coding by bit wideC, carry out Chinese remainder theorem compression；Then, utilizing classical entropy code that data are carried out statistical coding, the output after statistical coding is the compression data to original image.The present invention is ensureing that decompressed image reaches certain signal to noise ratio, meets the image quality demand after decompressing, and can increase again compression factor simultaneously.
Description
Technical field
The present invention relates to a kind of method for compressing image, the compression method that still image can be compressed fast and effectively.
Background technology
Along with developing rapidly with universal of network technology, video information occupies considerable ratio in people's sphere of life
Weight, if being transmitted image information by network, needs bigger quantity of information.Therefore computer and multimedia are allowed in the information age
Network provides for us and services more easily, it is necessary to effectively process image.Its solution need to ensure digitized map
On the premise of picture element amount, reduce the data volume of digital picture so that it is the data volume in storage and transmitting procedure is as far as possible as far as possible
Ground is little, i.e. digital picture must be effectively compressed process.Image compression algorithm is i.e. used to reduce image file as far as possible
Memory space.Existing image compression algorithm is divided into lossless compress and lossy compression method.
Wavelet transformation is just to start in the later stage eighties to rise, owing to it has good time-frequency domain localization property,
It is widely used in signal processing field at random, and is successfully incorporated among the compression algorithm of image, achieve well
Compression effectiveness, causes the extensive attention of the scientific research personnel being engaged in compression of images research.It is embedding that particularly Shaprio et al. proposes
Enter formula zerotrees wavelet algorithm (EZW), be one of the most generally acknowledged the best way of image change compression code.Small echo parameter is
A kind of analysis method of variable resolution, it is to high-frequency signal employing hour window, and when using big to low frequency signal, window is analyzed, this
Just short with nature high frequency signal general persistence, and low frequency signal long-term video distribution characteristic kissing
Close, be very suitable for image procossing, have more preferably than compression methods such as JPEG based on DCT based on wavelet-transform image compression method
Implementation effect, particularly in the case of high compression ratio.
In some cases, in order to ensure the signal to noise ratio of image, reducing the distortion factor, such compression of images ratio can not mistake
Height, also increases the band bandwidth of memory space and transmission.This is accomplished by the premise of not losing picture quality, further
Improve the compression ratio of image.
Summary of the invention
In order to overcome the deficiency that cannot take into account signal to noise ratio and compression factor of existing method for compressing image, the present invention provides one
Plant the method for compressing image combined with Chinese remainder theorem based on wavelet transformation taking into account signal to noise ratio and compression factor, ensure decompression
Image reaches certain signal to noise ratio, meets the image quality demand after decompressing, and can increase again compression factor simultaneously.
The technical solution adopted for the present invention to solve the technical problems is:
A kind of method for compressing image combined with Chinese remainder theorem based on wavelet transformation, described method for compressing image include as
Lower process:
First, after original image two-dimensional wavelet transformation, the wavelet coefficient being converted in wavelet field, next to wavelet field
On wavelet coefficient carry out quantization encoding, only retain bigger wavelet coefficient, remaining zero setting；
Data after wavelet transformation are carried out zero RLE, and the data set after zero RLE exists positive and negative, needs to add
One constant value makes data set be all the number not less than zero, and constant value fetches data the absolute value of minima in group；
Judge the maximum bit wide of the new data set obtained again, select to carry out the grouping number of Chinese remainder theorem coding by bit wide
NC, carry out Chinese remainder theorem compression；
Then, utilizing classical entropy code that data are carried out statistical coding, the output after statistical coding is to original image
Compression data.
The technology of the present invention is contemplated that: use wavelet transformation, zero RLE and Chinese remainder theorem compressed encoding.Due to grandson
Theorem compressed encoding has the characteristic of lossless compress, therefore this coded method is entered with image compression encoding methods such as wavelet transformations
Row combines, and serves the effect improving compression multiple further, and whole scheme realizes simple, is transmitting compression image both sides
In the case of knowing code table, compression effectiveness is the most notable.Described Chinese remainder theorem is also called Chinese remainder theorem.
Chinese remainder theorem coding with a bigger integer, can play one multiple less integers by certain conversion
Fixed compression.Chinese remainder theorem compression algorithm, then be the algorithm that combines with entropy code of Chinese remainder theorem.Entropy code is utilized to make
Big integer after Chinese remainder theorem compression can represent with less number, reaches compression effectiveness.Whole compression process does not lose letter
Breath amount, belongs to lossless data compression.
The algorithm that the present invention relates to utilizes this advantage of Chinese remainder theorem to combine with wavelet image compression algorithm, enters
One step improves wavelet image compression efficiency.
Wavelet transformation-Chinese remainder theorem compression method (WT-CRT), utilizes Encoder Advantage and the Chinese remainder theorem of wavelet transformation
Lossless coding advantage, compresses efficiently to image, and wherein wavelet transform is identical with JPEG2000 Standard of image compression.
The procedure of the present invention is as it is shown in figure 1, first algorithm carries out wavelet transform, then warp to the image of input
Cross zero RLE, then encode through Chinese remainder theorem, finally utilize the entropy code such as Huffman encoding or arithmetic coding to data
Carry out statistical coding.Output after statistical coding is the compression data to original image.During decompression, first pass through known code
Table carries out entropy decoding, then needs Chinese remainder theorem decoding and zero run-length to decode, obtains original image finally by wavelet inverse transformation.
Beneficial effects of the present invention is mainly manifested in: in the feelings ensureing that signal noise ratio (snr) of image is identical with wavelet transformation compression algorithm
Under condition, further increase the compression effectiveness of wavelet transformation compression algorithm, save memory space, also act as certain encryption effect
Really.
Accompanying drawing explanation
Fig. 1 is the flow chart of the method for compressing image of the present invention.
Fig. 2 is original image " lena " figure before carrying out wavelet transformation-Chinese remainder theorem compression.
Fig. 3 is original image " tire " figure before carrying out wavelet transformation-Chinese remainder theorem compression.
Fig. 4 compresses for " lena " figure is carried out wavelet transformation-Chinese remainder theorem using Huffman encoding as entropy code and decompresses
The image of contracting.
Fig. 5 compresses for " lena " figure is carried out wavelet transformation-Chinese remainder theorem using arithmetic coding as entropy code and decompresses
Image.
Fig. 6 uses Huffman encoding and arithmetic coding as the wavelet transformation Chinese remainder theorem of entropy code for contrast " lena " figure
The compression multiple that coding obtains.Transverse axis is K value, and the longitudinal axis is compression ratio.
Fig. 7 uses Huffman encoding and arithmetic coding as the wavelet transformation Chinese remainder theorem of entropy code for contrast " tire " figure
The compression multiple that coding obtains.Transverse axis is K value, and the longitudinal axis is compression ratio.
The decompressing image obtained after changing first key when Fig. 8 decompresses for " lena " figure.
The decompressing image that Fig. 9 obtains after changing all keys when decompressing for " lena " figure.
Figure 10 is the decompression flow chart of the present invention.
Detailed description of the invention
The invention will be further described below in conjunction with the accompanying drawings.
With reference to Fig. 1～Figure 10, a kind of method for compressing image combined with Chinese remainder theorem based on wavelet transformation, first to former
After beginning two-dimensional image wavelet transformation, the wavelet coefficient being converted in wavelet field, next the wavelet coefficient in wavelet field is carried out
Quantization encoding, only retains bigger wavelet coefficient, remaining zero setting.Small echo processes identical with JPEG2000 standard, repeats no more.Right
Data after wavelet transformation carry out zero RLE, and the data set after zero RLE exists positive and negative, need to add a constant value
Making data set is all the number not less than zero, and constant value fetches data the absolute value of minima in group.Judge the new data obtained again
The maximum bit wide of group, selects to carry out the grouping number N of Chinese remainder theorem coding by bit wideC, it is specifically defined such as formula (2) institute
Show.Carry out Chinese remainder theorem compression by the process of formula (3)～(10), then utilize classical entropy code (Huffman encoding or
Arithmetic coding) data are carried out statistical coding.Owing to arithmetic coding exists patent problem, actual application is proposed with Huffman
Coding calculates.Output after statistical coding is the compression data to original image.
During decompression, first pass through known code table and carry out entropy decoding, then need Chinese remainder theorem to decode (formula (11))
Decode with zero run-length, obtain original image finally by wavelet inverse transformation.
Further, it is considered to the when of Chinese remainder theorem reduction length K, need to consider complexity and compression ratio.Work as compression
When length K is the biggest, complexity is the highest, and compression ratio is the highest.General K span is 2～12.Additionally Chinese remainder theorem compression is close
Key { m1,…,mKTo take relatively prime positive integer, the present invention is for randomly selecting.But the key value chosen is the least, computer can be made
Complexity reduces.
Wavelet transformation-Chinese remainder theorem compression algorithm obtains data c after wavelet transformation with zero RLE, and zero run-length is compiled
Value after Ma has just to be had negative, needs through below equation before entropy code:
C'=c+ | min (c) | (1)
Value after c represents zero RLE in formula, | min (c) | expression takes the absolute value of minima in c sequence.Through being somebody's turn to do
After formula manipulation so that c sequence only exist on the occasion of or zero, i.e. c'.Then determine that Chinese remainder theorem encodes according to the size of c'
Grouping number NC, it is defined as follows:
Max represents the maximum taking out c',Expression rounds up.Such as assume that the bit wide of c' maximum has 11bits,
Then needing c' to be divided into and be cut into three tunnels, every road is 4bits, does Chinese remainder theorem coding and entropy code the most respectively.
Next with NCStating Chinese remainder theorem coding step as a example by=2, corresponding image pixel data bit wide is 8 bits,
Pixel span 0～255.First the data after zero RLE are carried out piecemeal, be divided into the data block of a length of 1 × K.K
Represent Chinese remainder theorem coding piecemeal size, carry out Chinese remainder theorem coding owing to needs are divided into 2 tunnels, remove each in block with 16
Data, are divided into 2 4bit data sets it, and this process is referred to as threshold values conversion [document S..Mallat.A Wavelet Tour
Of Signal Processing (small echo in signal processing guides) .Academic Press, NewYork, NY, 1998.]:
A'[i]=r [i] mod16, i=1,2 ..., K (4)
In formula, mod is modulus operator, and r [i] is i-th data in Chinese remainder theorem coding piecemeal, and a [i] represents front half data
Group, a ' [i] represents later half data set,Represent and round downwards.And the group key needed for Chinese remainder theorem to meet:
mi＞ max (a [i], a'[i]) (5) ma x represents and takes maximum, miFor Chinese remainder theorem key.Formula (5) represents
All of key have to be larger than maximum in data set.We can try to achieve all key products according to Chinese remainder theorem
Value, then by formula below obtain Chinese remainder theorem coefficient:
Mi=m/mi(6) recycling formula below generation congruence expression:
Mi'Mi≡1(modmi), i=1,2 ..., K (7)
Try to achieve Mi', and make
Ci=Mi'Mi(8) above step is to perform before encoding.
From formula (8) it will be seen that one group of CiDetermined by a group key and generate.After user selects a group key, just
One group of C can be obtained with calculated in advancei, it is then store in system.During compression image, this process that prestores can reduce whole pressure
The operand of compression process.Then we can take following coded system, the value after wherein Ta and Ta ' represents coding:
The encoding block of one group of 1 × K finally produces two compressed encoding values, the number after wherein Ta represents the compression of first half data set
According to, Ta ' represents the data after the compression of later half data set.
Obtaining data (Ta and Ta ') by Chinese remainder theorem coding, finally by entropy code, (arithmetic coding or Huffman are compiled
Code) obtain the output valve of whole compression algorithm.If the data after compression to be transmitted, it is only necessary to the data after entropy code
It is transmitted.When receiving terminal is to image decompressor, it is necessary first to logarithm row entropy factually decodes, and is then given extensive by formula below
Multiple:
Ar [i]=Ta (modmi), i=1,2 ..., K
Ar'[i]=Ta'(modmi), i=1,2 ..., K (11)
In formula, ar [i] and ar ' [i] is the data after solving Chinese remainder theorem compressed encoding, decodes for zero run-length.After zero run-length decoding
The reconstruct of data is completed by following formula:
S [i]=ar [i] × 16+ar'[i] (12)
In formula, s [i] is the final data recovered.
Chinese remainder theorem coding in the present invention can also play certain cipher round results, and reason is that Chinese remainder theorem encodes needs
The key m that one ergin array becomesiCalculate Ci, the quantity of a group key is equal to piecemeal size K value.Compression and decompression use not
The data of decoding can be impacted with key value, influence whether the display of view picture figure.As long as therefore Chinese remainder theorem coding is close
Key is not disclosed, the data secrecy of present invention compression.
Further, it is considered to the when of Chinese remainder theorem reduction length K, need to consider complexity and compression ratio.Work as compression
When length K is the biggest, complexity is the highest, and compression ratio is the highest, and general K span is 2～12.Additionally Chinese remainder theorem compression is close
Key { m1,…,mKTo take relatively prime positive integer, the present invention is for randomly selecting.But the key value chosen is the least, computer can be made
Complexity reduces.
The compression effectiveness of WT-CRT algorithm is carried out simulation analysis.Fig. 2 illustrates the original image " lena " needing compression,
Fig. 3 illustrates the original image " tire " needing compression, uses arithmetic coding to carry out WT-CRT as entropy code in figure " lena "
Compress and decompress and obtain Fig. 4, use Huffman encoding carry out WT-CRT compression as entropy code and decompress in figure " lena "
Obtain Fig. 5.Fig. 6 provides WT-CRT algorithm compression ratio (CR) performance when " lena " figure uses different entropy code.Fig. 7 is given right
" tire " figure uses WT-CRT algorithm compression ratio (CR) performance during different entropy code.
Finally WT-CRT algorithm for encryption performance is carried out simulation analysis, use as original image, original image using Fig. 2
Key group: key=[17,18,19,23,29,31,37,41,43,47], K=10.Change first key so that key (1)=
67, decompressing image shows such as Fig. 8.Change all keys to show such as Fig. 9.As long as result shows that key the most all leaks, pressure
Data after contracting can not correctly be decompressed, and the present invention serves encryption effect.
Fig. 2 is the image " lena " needing to be compressed, and belongs to rgb format, and size is 256 × 256 × 3, memory space
It is 196608 bytes
Fig. 3 is the image " tire " needing to be compressed, and belongs to rgb format, and size is 256 × 256, and memory space is
65536 bytes
Fig. 4 compresses for " lena " figure is carried out wavelet transformation-Chinese remainder theorem using arithmetic coding as entropy code and decompresses
Image, recovery effects is good.The Y-PSNR (PSNR) that can be calculated decompressed image is 26.3477 and structural similarity
(SSIM) it is 0.77626.
Fig. 5 compresses for " lena " figure is carried out wavelet transformation-Chinese remainder theorem using Huffman encoding as entropy code and decompresses
The image of contracting, recovery effects is good.The Y-PSNR that can be calculated decompressed image is 26.3477, and structural similarity is
0.77626。
Fig. 6 is to using Huffman encoding and arithmetic coding as the wavelet transformation grandson of entropy code under " lena " figure different K values
Sub-theorem encodes the compression multiple obtained.When using arithmetic coding, during K=2, compression multiple is 26.936；During K=10, compression
Multiple is 55.870.When using Huffman encoding, during K=2, compression multiple is 26.203；During K=10, compression multiple is
55.026.Visible compression effectiveness is preferable.
Fig. 7 is to using Huffman encoding and arithmetic coding as the wavelet transformation grandson of entropy code under " tire " figure different K values
Sub-theorem encodes the compression multiple obtained.When using arithmetic coding, during K=2, compression multiple is 14.658；During K=10, compression
Multiple is 30.681.When using Huffman encoding, during K=2, compression multiple is 14.29；During K=10, compression multiple is
30.397.Visible compression effectiveness is preferable.
The decompressing image obtained after changing first key when " lena " figure is decompressed by Fig. 8.Decompressed image now
Y-PSNR be 5.9194, and structural similarity is 0.06341, recovers index poor, simultaneously basic in terms of visual effect
Cannot find out artwork, cipher round results is preferable.
The decompressing image that Fig. 9 obtains after changing all keys when decompressing " lena " figure.The now peak of decompressed image
Value signal to noise ratio is 5.3926, and structural similarity is 0.01492, recover index poor, finish watching completely without method from visual effect simultaneously
Finding out artwork, cipher round results is preferable.
Claims (3)
1. the method for compressing image combined with Chinese remainder theorem based on wavelet transformation, it is characterised in that: described compression of images
Method includes following process:
First, after original image two-dimensional wavelet transformation, the wavelet coefficient being converted in wavelet field, next in wavelet field
Wavelet coefficient carries out quantization encoding, only retains bigger wavelet coefficient, remaining zero setting；
Data after wavelet transformation are carried out zero RLE, and the data set after zero RLE exists positive and negative, needs to add one
Constant value makes data set be all the number not less than zero, and constant value fetches data the absolute value of minima in group；
Judge the maximum bit wide of the new data set obtained again, select to carry out the grouping number N of Chinese remainder theorem coding by bit wideC, enter
Row Chinese remainder theorem is compressed；
Then, utilizing classical entropy code that data are carried out statistical coding, the output after statistical coding is the compression to original image
Data.
2. the method for compressing image combined with Chinese remainder theorem based on wavelet transformation as claimed in claim 1, it is characterised in that:
The process of described Chinese remainder theorem compression is as follows:
Obtaining data c after wavelet transformation and zero RLE, the value after zero RLE has just to be had negative, needs before entropy code
Will be through below equation:
C'=c+ | min (c) | (1)
Value after c represents zero RLE in formula, | min (c) | expression takes the absolute value of minima in c sequence, through this formula
After process so that c sequence only exist on the occasion of or zero, i.e. c'；Then according to the size of c' determine that Chinese remainder theorem encodes point
Group number NC, it is defined as follows:
Max represents the maximum taking out c',Expression rounds up.
3. the method for compressing image combined with Chinese remainder theorem based on wavelet transformation as claimed in claim 2, it is characterised in that:
The process of described Chinese remainder theorem compression is as follows:
First the data after zero RLE are carried out piecemeal, be divided into the data block of a length of 1 × K.K represents that Chinese remainder theorem encodes
Piecemeal size, carries out Chinese remainder theorem coding owing to needs are divided into 2 tunnels, removes each data in block with 16, it is divided into 2
4bit data set, this process is referred to as threshold values and changes:
A'[i]=r [i] mod16, i=1,2 ..., K (4)
In formula, mod is modulus operator, and r [i] is i-th data in Chinese remainder theorem coding piecemeal, and a [i] represents first half data set, a '
[i] represents later half data set,Represent and round downwards.And the group key needed for Chinese remainder theorem to meet:
mi＞ max (a [i], a'[i]) (5) max represents and takes maximum, miFor Chinese remainder theorem key.
Formula (5) represents that all of key have to be larger than maximum in data set；All key products are tried to achieve according to Chinese remainder theoremValue, then by formula (60 obtain Chinese remainder theorems coefficient:
Mi=m/mi(6) recycling formula (7) generation congruence expression:
M′iMi≡1(modmi), i=1,2 ..., K (7)
Try to achieve M 'i, and make
Ci=M 'iMi(8) above step is to perform before encoding；
See from formula (8), one group of CiDetermined by a group key and generate, after user selects a group key, just can count in advance
Calculate and obtain one group of Ci, it is then store in system；Taking formula (9) and the coded system of (10), wherein Ta and Ta ' represents coding
After value:
One group of 1 × K
Encoding block finally produce two compressed encoding values, wherein, Ta represents the data after the compression of first half data set, and Ta ' represents later half
Data after data set compression；
Obtain data Ta and Ta ' by Chinese remainder theorem coding, obtain the output valve of whole compression method finally by entropy code.
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| 孙健，任国强，吴钦章: "基于自适应指数哥伦布编码的图像压缩算法", 《光学精密工程》 * |
| 徐勇，徐智勇，张启衡，赵汝进: "适于硬件实现的低复杂度图像压缩", 《光学精密工程》 * |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109716658A (en) * | 2016-12-15 | 2019-05-03 | 华为技术有限公司 | A kind of data de-duplication method and system based on similitude |
| US11514666B2 (en) | 2016-12-15 | 2022-11-29 | Huawei Technologies Co., Ltd. | Method and system of similarity-based deduplication |
| CN110113505A (en) * | 2019-04-24 | 2019-08-09 | 湖北工业大学 | A kind of safe steganography coding method of low disturbance information based on Chinese remainder theorem |
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