CN106131575B - The method for compressing image combined based on wavelet transformation with Chinese remainder theorem - 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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- H04N19/625—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 based on wavelet transformation with Chinese remainder theorem, it comprises the following processes: first, after original image two-dimensional wavelet transformation, the wavelet coefficient being converted into wavelet field, next quantization encoding is carried out to the wavelet coefficient in wavelet field, only retain biggish wavelet coefficient, remaining zero setting；Zero RLE is carried out to the data after wavelet transformation, the data group after zero RLE there are positive and negative, need plus a constant value to make data group all be not less than zero number, constant value takes the absolute value of minimum value in data group；The maximum bit wide of the new data set judged again selects the grouping number N for carrying out Chinese remainder theorem coding by bit wideC, carry out Chinese remainder theorem compression；Then, statistical coding is carried out to data using classical entropy coding, the output after statistical coding is the compressed data to original image.The present invention is guaranteeing that decompressed image reaches certain signal-to-noise ratio, the image quality demand after meeting decompression, while can increase compression factor again.
Description
Technical field
The present invention relates to a kind of method for compressing image, can be to the compression method that still image is quickly and effectively compressed.
Background technique
With the rapid development of network technology and universal, video information occupies considerable ratio in people's sphere of life
Weight needs bigger information content if passing through network transmission to image information.Therefore computer and multimedia are allowed in the information age
Network provides more convenient and fast service for us, it is necessary to effectively be handled image.Its solution need to guarantee digitized map
Under the premise of image quality amount, the data volume of digital picture is reduced as far as possible, makes its data volume during storing and transmitting as far as possible
Ground is small, i.e., must carry out being effectively compressed processing to digital picture.Reduce image file as far as possible using image compression algorithm
Memory space.Existing image compression algorithm is divided into lossless compression and lossy compression.
Wavelet transformation is just to start in the later period eighties to rise, since it has good time-frequency domain localization property,
It is widely used in field of signal processing at random, and is successfully incorporated among the compression algorithm of image, is achieved well
Compression effectiveness causes the extensive attention for the scientific research personnel for being engaged in compression of images research.Especially Shaprio et al. is proposed embedding
Enter formula zerotrees wavelet algorithm (EZW), is one of the best way of image change compression code generally acknowledged at present.Small echo parameter is
A kind of analysis method of variable resolution, it uses hour window to high-frequency signal, and window is analyzed when using big to low frequency signal, this
It is just short with nature high frequency signal general persistence, and the long-term video distribution characteristic kissing of low frequency signal
It closes, is very suitable for image procossing, had more preferably based on wavelet-transform image compression method than compression methods such as JPEG based on DCT
Implementation effect, especially in the case where high compression ratio.
In some cases, in order to guarantee the signal-to-noise ratio of image, the distortion factor is reduced, such compression of images ratio cannot mistake
Height also increases the band bandwidth of memory space and transmission.This is just needed under the premise of not losing picture quality, further
Improve the compression ratio of image.
Summary of the invention
In order to which overcome the shortcomings of existing method for compressing image cannot be considered in terms of signal-to-noise ratio and compression factor, the present invention provides one
Kind takes into account the method for compressing image of signal-to-noise ratio and compression factor combined based on wavelet transformation with Chinese remainder theorem, is guaranteeing to decompress
Image reaches certain signal-to-noise ratio, the image quality demand after meeting decompression, while can increase compression factor again.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of method for compressing image combined based on wavelet transformation with Chinese remainder theorem, described image compression method include such as
Lower process:
Firstly, after to original image two-dimensional wavelet transformation, the wavelet coefficient being converted into wavelet field, next to wavelet field
On wavelet coefficient carry out quantization encoding, only retain biggish wavelet coefficient, remaining zero setting；
Zero RLE is carried out to the data after wavelet transformation, the data group after zero RLE there are positive and negative, need plus
It is not less than zero number that one constant value, which makes data group all, and constant value takes the absolute value of minimum value in data group；
The maximum bit wide of the new data set judged again selects the grouping number for carrying out Chinese remainder theorem coding by bit wide
NC, carry out Chinese remainder theorem compression；
Then, statistical coding is carried out to data using classical entropy coding, the output after statistical coding is to original image
Compressed data.
Technical concept of the invention are as follows: use wavelet transformation, zero RLE and Chinese remainder theorem compressed encoding.Due to grandson
Theorem compressed encoding have lossless compression characteristic, therefore the image compression encoding methods such as the coding method and wavelet transformation into
Row combination plays the role of further increasing compression multiple, and entire scheme is realized simply, has compressed image both sides in transmission
In the case where knowing code table, compression effectiveness is very significant.The Chinese remainder theorem is also known as Chinese remainder theorem.
Multiple lesser integers can be played one with a biggish integer by certain transformation by Chinese remainder theorem coding
Fixed compression.Chinese remainder theorem compression algorithm is then the algorithm that Chinese remainder theorem is combined with entropy coding.Made using entropy coding
Chinese remainder theorem compressed big integer can be indicated with lesser number, reach compression effectiveness.Entire compression process does not lose letter
Breath amount, belongs to lossless data compression.
The present invention relates to algorithm combined using Chinese remainder theorem this advantage with wavelet image compression algorithm, into
One step improves wavelet image compression efficiency.
Wavelet transformation-Chinese remainder theorem compression method (WT-CRT) utilizes the Encoder Advantage and Chinese remainder theorem of wavelet transformation
Lossless coding advantage efficiently compresses image, and wherein wavelet transform is identical as JPEG2000 Standard of image compression.
Method process of the invention is as shown in Figure 1, then algorithm passes through first to the image progress wavelet transform of input
Zero RLE is crossed, is encoded using Chinese remainder theorem, finally using entropy codings such as Huffman encoding or arithmetic codings to data
Carry out statistical coding.Output after statistical coding is the compressed data to original image.When decompression, pass through known code first
Table carries out entropy decoding, then needs Chinese remainder theorem decoding and zero run-length decoding, obtains original image finally by wavelet inverse transformation.
Beneficial effects of the present invention are mainly manifested in: guaranteeing signal noise ratio (snr) of image feelings identical with wavelet transformation compression algorithm
Under condition, the compression effectiveness of wavelet transformation compression algorithm is further improved, saves memory space, also acts as certain encryption effect
Fruit.
Detailed description of the invention
Fig. 1 is the flow chart of method for compressing image of the invention.
Fig. 2 is original image " lena " figure carried out before wavelet transformation-Chinese remainder theorem compression.
Fig. 3 is original image " tire " figure carried out before wavelet transformation-Chinese remainder theorem compression.
Fig. 4 is to carry out wavelet transformation-Chinese remainder theorem using Huffman encoding as entropy coding to " lena " figure to compress and decompress
The image of contracting.
Fig. 5 is to carry out wavelet transformation-Chinese remainder theorem using arithmetic coding as entropy coding to " lena " figure to compress and decompress
Image.
Fig. 6 is comparison " lena " figure using Huffman encoding and wavelet transformation Chinese remainder theorem of the arithmetic coding as entropy coding
Encode obtained compression multiple.Horizontal axis is K value, and the longitudinal axis is compression ratio.
Fig. 7 is comparison " tire " figure using Huffman encoding and wavelet transformation Chinese remainder theorem of the arithmetic coding as entropy coding
Encode obtained compression multiple.Horizontal axis is K value, and the longitudinal axis is compression ratio.
Fig. 8 changes the decompressing image obtained after first key when being " lena " diagram compression.
Fig. 9 changes the decompressing image obtained after all keys when being " lena " diagram compression.
Figure 10 is decompression flow chart of the invention.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
Referring to Fig.1~Figure 10, a kind of method for compressing image combined based on wavelet transformation with Chinese remainder theorem, first to original
After beginning two-dimensional image wavelet transformation, next the wavelet coefficient being converted into wavelet field carries out the wavelet coefficient in wavelet field
Quantization encoding only retains biggish wavelet coefficient, remaining zero setting.Small echo processing is identical with JPEG2000 standard, repeats no more.It is right
Data after wavelet transformation carry out zero RLE, and the data group after zero RLE needs plus a constant value there are positive and negative
So that data group is all the number not less than zero, constant value takes the absolute value of minimum value in data group.The new data judged again
The maximum bit wide of group selects the grouping number N for carrying out Chinese remainder theorem coding by bit wideC, it is specifically defined such as formula (2) institute
Show.Carry out Chinese remainder theorem compression by formula (3)~(10) process, then using classical entropy coding (Huffman encoding or
Arithmetic coding) statistical coding is carried out to data.Since arithmetic coding is there are patent problem, Huffman is proposed in practical application
Coding is calculated.Output after statistical coding is the compressed data to original image.
When decompression, entropy decoding is carried out by known code table first, Chinese remainder theorem is then needed to decode (formula (11))
It is decoded with zero run-length, obtains original image finally by wavelet inverse transformation.
Further, it when considering Chinese remainder theorem reduction length K, needs to comprehensively consider complexity and compression ratio.Work as compression
When length K is bigger, complexity is higher, and compression ratio is also higher.General K value range is 2~12.In addition Chinese remainder theorem compression is close
Key { m1,…,mKRelatively prime positive integer is taken, the present invention is to randomly select.But the key value chosen is smaller, can make computer
Complexity reduces.
Wavelet transformation-Chinese remainder theorem compression algorithm obtains data c after wavelet transformation and zero RLE, and zero run-length is compiled
Value after code has just and has negative, is needed before entropy coding by following formula:
C'=c+ | min (c) | (1)
C indicates the value after zero RLE in formula, | min (c) | it indicates to take the absolute value of minimum value in c sequence.By this
After formula manipulation, so that c sequence only exists positive value or zero, i.e. c'.Then determine that Chinese remainder theorem is encoded according to the size of c'
Grouping number NC, it is defined as follows:
Max indicates the maximum value of taking-up c',Expression rounds up.Such as assume that the bit wide of c' maximum value has 11bits,
It then needs c' to be divided into and is cut into three tunnels, every road is 4bits, then does Chinese remainder theorem coding and entropy coding respectively.
Next with NCChinese remainder theorem coding step is stated for=2, corresponding image pixel data bit wide is 8 bits,
Pixel value range 0~255.Piecemeal is carried out to the data after zero RLE first, is divided into the data block that length is 1 × K.K
It indicates that Chinese remainder theorem encodes piecemeal size, carries out Chinese remainder theorem coding due to needing to be divided into 2 tunnels, with each of 16 removal blocks
Data, are divided into it 2 4bit data groups, this process is known as threshold values conversion [document S..Mallat.A Wavelet Tour
Of Signal Processing (the small echo guiding in signal processing) .Academic Press, NewYork, NY, 1998.]:
A'[i]=r [i] mod16, i=1,2 ..., K (4)
Mod is modulus operator in formula, and r [i] is that Chinese remainder theorem encodes i-th of data in piecemeal, half data before a [i] is indicated
Group, a ' [i] indicate later half data group,It indicates to be rounded downwards.And a group key needed for Chinese remainder theorem will meet:
mi> max (a [i], a'[i]) (5) ma x expression is maximized, miFor Chinese remainder theorem key.Formula (5) indicates
All keys have to be larger than maximum value in data group.We can acquire all key products according to Chinese remainder theorem
Value, then pass through following formula obtain Chinese remainder theorem coefficient:
Mi=m/mi(6) following formula is recycled to generate congruence expression:
Mi'Mi≡1(modmi), i=1,2 ..., K (7)
Acquire Mi', and make
Ci=Mi'Mi(8) above step is to execute before encoding.
It can see from formula (8), one group of CiIt is determined and is generated by a group key.After user selects a group key, just
One group of C can be obtained with calculated in advancei, it is then store in system.When compressing image, this, which prestores processing, can reduce entire pressure
The operand of compression process.Then we can take following coding mode, and wherein Ta and Ta ' represents the value after coding:
The encoding block of (10) one groups of 1 × K finally generates two compressed encoding values, after wherein Ta indicates the compression of first half data group
Data, Ta ' indicates later half compressed data of data group.
It encodes to obtain data (Ta and Ta ') by Chinese remainder theorem, finally by entropy coding, (arithmetic coding or Huffman are compiled
Code) obtain the output valve of entire compression algorithm.If compressed data will be transmitted, it is only necessary to the data after entropy coding
It is transmitted.When receiving end is to image decompressor, it is necessary first to which then logarithm factually row entropy decoding is given extensive by following formula
It is multiple:
Ar [i]=Ta (modmi), i=1,2 ..., K
Ar'[i]=Ta'(modmi), i=1,2 ..., ar [i] and ar ' [i] is solution Chinese remainder theorem pressure in K (11) formula
Data after reducing the staff code are decoded for zero run-length.The reconstruct of zero run-length decoded data is completed by following formula:
S [i]=ar [i] × 16+ar'[i] (12)
S [i] is the data finally restored in formula.
Chinese remainder theorem coding in the present invention can also play certain cipher round results, and reason is that Chinese remainder theorem encodes needs
One ergin array at key miTo calculate Ci, the quantity of a group key is equal to piecemeal size K value.Compression and decompression is not using
Decoded data can be impacted with key value, influence whether the display of whole picture figure.As long as therefore Chinese remainder theorem coding is close
Key be not it is disclosed, the data that the present invention compresses are exactly to maintain secrecy.
Further, it when considering Chinese remainder theorem reduction length K, needs to comprehensively consider complexity and compression ratio.Work as compression
When length K is bigger, complexity is higher, and compression ratio is also higher, and general K value range is 2~12.In addition Chinese remainder theorem compression is close
Key { m1,…,mKRelatively prime positive integer is taken, the present invention is to randomly select.But the key value chosen is smaller, can make computer
Complexity reduces.
Simulation analysis is carried out to the compression effectiveness of WT-CRT algorithm.Fig. 2 illustrates the original image " lena " for needing to compress,
Fig. 3 illustrates the original image " tire " for needing to compress, and carries out WT-CRT as entropy coding using arithmetic coding to figure " lena "
It compresses and decompresses to obtain Fig. 4, WT-CRT compression is carried out as entropy coding using Huffman encoding to figure " lena " and decompress
Obtain Fig. 5.WT-CRT algorithm compression ratio (CR) performance when Fig. 6 is provided to " lena " figure using different entropy codings.Fig. 7 is provided pair
" tire " figure uses WT-CRT algorithm compression ratio (CR) performance when different entropy codings.
Simulation analysis finally is carried out to WT-CRT algorithm for encryption performance, using Fig. 2 as original image, what original image used
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 and shows such as Fig. 9.The result shows that as long as key is without all leakages, pressure
Data after contracting cannot be decompressed correctly, and the present invention plays the role of encryption.
Fig. 2 is the image " lena " compressed, belongs to rgb format, and size is 256 × 256 × 3, memory space
For 196608 bytes
Fig. 3 is the image " tire " compressed, belongs to rgb format, and size is 256 × 256, and memory space is
65536 bytes
Fig. 4 is to carry out wavelet transformation-Chinese remainder theorem using arithmetic coding as entropy coding to " lena " figure to compress and decompress
Image, recovery effects are good.The Y-PSNR (PSNR) that can be calculated decompressed image is 26.3477 and structural similarity
It (SSIM) is 0.77626.
Fig. 5 is to carry out wavelet transformation-Chinese remainder theorem using Huffman encoding as entropy coding to " lena " figure to compress and decompress
The image of contracting, recovery effects are 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 wavelet transformation grandson of the arithmetic coding as entropy coding under " lena " figure different K values
The compression multiple that sub- theorem encodes.When using arithmetic coding, when K=2, compression multiple 26.936；When K=10, compression
Multiple is 55.870.When using Huffman encoding, when K=2, compression multiple 26.203；When K=10, compression multiple is
55.026.It can be seen that compression effectiveness is preferable.
Fig. 7 is to using Huffman encoding and wavelet transformation grandson of the arithmetic coding as entropy coding under " tire " figure different K values
The compression multiple that sub- theorem encodes.When using arithmetic coding, when K=2, compression multiple 14.658；When K=10, compression
Multiple is 30.681.When using Huffman encoding, when K=2, compression multiple 14.29；When K=10, compression multiple is
30.397.It can be seen that compression effectiveness is preferable.
Fig. 8, which illustrates " lena ", changes the decompressing image obtained after first key when compressing.Decompressed image at this time
Y-PSNR be 5.9194, and structural similarity is 0.06341, and it is poor to restore index, while basic in terms of visual effect
It can not find out original image, cipher round results are preferable.
Fig. 9 changes the decompressing image obtained after all keys when " lena " is illustrated and compressed.The peak of decompressed image at this time
Being worth signal-to-noise ratio is 5.3926, and structural similarity is 0.01492, it is poor to restore index, while finishing watching completely without method from visual effect
Find out original image, cipher round results are preferable.
Claims (1)
1. a kind of method for compressing image combined based on wavelet transformation with Chinese remainder theorem, it is characterised in that: described image compression
Method comprises the following processes:
Firstly, after to original image two-dimensional wavelet transformation, the wavelet coefficient being converted into wavelet field, next in wavelet field
Wavelet coefficient carries out quantization encoding, only retains biggish wavelet coefficient, remaining zero setting；
Zero RLE is carried out to the data after wavelet transformation, the data group after zero RLE needs plus one there are positive and negative
It is not less than zero number that constant value, which makes data group all, and constant value takes the absolute value of minimum value in data group；
The maximum bit wide of the new data set judged again selects the grouping number N for carrying out Chinese remainder theorem coding by bit wideC, into
The compression of row Chinese remainder theorem；By obtaining data c after wavelet transformation and zero RLE, the value after zero RLE have just have it is negative,
It is needed before entropy coding by following formula:
C'=c+ | min (c) | (1)
C indicates the value after zero RLE in formula, | min (c) | it indicates to take the absolute value of minimum value in c sequence, by the formula
After processing, so that c sequence only exists positive value or zero, i.e. c'；Then point of Chinese remainder theorem coding is determined according to the size of c'
Group number NC, it is defined as follows:
Max indicates the maximum value of taking-up c',Expression rounds up；
Then, statistical coding is carried out to data using classical entropy coding, the output after statistical coding is the compression to original image
Data；
The process of the Chinese remainder theorem compression is as follows:
Piecemeal is carried out to the data after zero RLE first, is divided into the data block that length is 1 × K, K indicates Chinese remainder theorem coding
Piecemeal size carries out Chinese remainder theorem coding due to needing to be divided into 2 tunnels, with each of 16 removal blocks data, it is divided into 2
4bit data group, this process are known as threshold values conversion:
A'[i]=r [i] mod16, i=1,2 ..., K (4)
Mod is modulus operator in formula, and r [i] is that Chinese remainder theorem encodes i-th of data in piecemeal, and a [i] indicates first half data group, a '
[i] indicates later half data group,It indicates to be rounded downwards, and a group key needed for Chinese remainder theorem will meet:
mi> max (a [i], a'[i]) (5) max expression is maximized, miFor Chinese remainder theorem key, formula (5) indicates all
Key have to be larger than maximum value in data group；All key products are acquired according to Chinese remainder theoremValue, then pass through
Formula (60 obtain the coefficient of Chinese remainder theorem:
Mi=m/mi(6) formula (7) are recycled to generate congruence expression:
Mi'Mi≡1(modmi), i=1,2 ..., K (7)
Acquire M 'i, and make
Ci=M 'iMi(8) see from formula (8), one group of CiDetermined and generated by a group key, user select a group key it
It afterwards, can one group of C of calculated in advance acquisitioni, it is then store in system；The coding mode of formula (9) and (10) is taken, wherein
Ta and Ta ' represents the value after coding:
(10)
The encoding block of one group of 1 × K finally generates two compressed encoding values, wherein and Ta indicates the compressed data of first half data group,
Ta ' indicates the later half compressed data of data group；
It encodes to obtain data Ta and Ta ' by Chinese remainder theorem, obtains the output valve of entire compression method finally by entropy coding.
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| 适于硬件实现的低复杂度图像压缩;徐勇，徐智勇，张启衡，赵汝进;《光学精密工程》;20090930;第17卷(第9期);全文 * |
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