CN111340900A - Image compression method based on double complex wavelets - Google Patents
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Abstract
The invention provides an image compression method based on a double-number complex wavelet, which is used for compressing an original image so as to transmit the original image, and comprises the following steps: reading an original image; decomposing the original image by adopting an even-number complex wavelet algorithm to obtain four-level even-number complex wavelet decomposition subgraphs of the original image; calculating the four-level double-number complex wavelet decomposition subgraph by adopting a self-adaptive threshold value binarization algorithm to obtain a threshold value, so as to obtain a binarization image; carrying out scanning coding processing on the binary image by adopting an embedded zerotree wavelet algorithm, and then outputting scanning coding information; compressing the binary image by adopting a recursion form continuous coding arithmetic coding method according to the scanning coding information to obtain an arithmetic coding image; carrying out double complex wavelet inverse transformation on the arithmetic coding image to obtain a compressed image; and outputting the compressed image. The method has the advantages of low hardware requirement, low cost, simple operation process, ideal compression result and high practicability.
Description
Technical Field
The invention relates to an image compression method, in particular to an image compression method based on a dual complex wavelet.
Background
At present, under the background that multimedia technology is more deeply integrated into daily life of people, the requirements of human beings on image definition and fluency are increasing day by day, and the image compression technology is an important link for solving the problem. In modern communications, image transmission is a very important component, and the use of coding compression technology is a very important technical means for reducing the amount of transmitted data.
Currently, various compression algorithms are applied to image compression methods. For example, a design method for implementing a high definition photo compression algorithm in an FPGA provides great flexibility for image coding, and can be utilized by different numbers of target application programs, but is not suitable for most images, and the coding process is cumbersome. A hyperspectral compression algorithm based on hybrid coding combines band optimization grouping and wavelet transformation, has good performance in the aspects of reconstructed image quality and calculation complexity, and under the same compression ratio, the average peak signal-to-noise ratio is improved by 0.21-0.81 db compared with other algorithms, but the same image characteristic is stronger. In 2016, a new lossless compression method is proposed, which can further reduce the size of a jpeg encoding related image set under the condition of not losing any information, but has higher complexity and higher calculation cost in the calculation process. Subsequently, a new compression method has been proposed, which replaces the jpeg-dct standard in the transform chain with quasi-orthogonal transformation based on the use of a new large-size quasi-orthogonal matrix. The method changes the type of the quantization matrix and the position of the low-frequency component after conversion, optimizes the image compression algorithm, but cannot completely meet the modern parameters of resolution images such as 4k and 8 k.
Although the algorithm realizes the compression of the image and optimizes the image compression algorithm to a certain extent, the problems of large calculation amount or low compression efficiency still exist.
Disclosure of Invention
The present invention has been made in view of the above problems, and it is an object of the present invention to provide an image compression method based on a dual complex wavelet, which is used for compressing an original image and transmitting the compressed image.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention provides an image compression method based on a double-number complex wavelet, which is characterized by comprising the following steps of: reading an image, namely reading an original image to be compressed; decomposing the image, namely decomposing the original image by adopting a dual complex wavelet algorithm to obtain four-level dual complex wavelet decomposition subgraphs of the original image; performing image binarization, namely calculating a four-level dual complex wavelet decomposition subgraph by adopting a self-adaptive threshold value binarization algorithm to obtain a threshold value Ti to obtain a binarized image; scanning and coding, namely scanning and coding the binary image by adopting an embedded zerotree wavelet algorithm, and then outputting scanning and coding information; compressing the binary image by adopting a successive-pushing type continuous coding arithmetic coding method according to the scanning coding information so as to obtain an arithmetic coding image; performing inverse image transformation, namely performing double-number complex wavelet inverse transformation on the arithmetic coding image to obtain a compressed image; and outputting the image and outputting the compressed image.
The image compression method based on the double complex wavelet provided by the invention can also have the characteristics that the image decomposition comprises the following specific steps: according to the dual-tree complex wavelet algorithm, two paths of parallel discrete wavelet transform of a binary tree structure are adopted to decompose an original image, one path generates a real part, the other path generates an imaginary part, edges of the two-dimensional dual-number complex wavelet transform are detected at six angles of +/-15 degrees, +/-45 degrees and +/-75 degrees, and a two-dimensional dual-tree complex wavelet function is as follows:
ψ(x,y)＝ψ(x)ψ(y)＝[ψh(x)+jψg(x)][ψh(y)+jψg(y)]
＝[ψh(x)ψh(y)-ψg(x)ψg(y)]+j[ψh(y)ψg(x)+ψh(x)ψg(y)]
in the formula, #hAnd psigRespectively orthogonal or biorthogonal real wavelets,
complex wavelet function according to real part:
{ψc(x,y)}＝ψh(x)ψh(y)-ψg(x)ψg(y)
for real part
And (3) normalizing to obtain six two-dimensional real wavelets:
wherein k is 1, 2, 3,
complex wavelet function according to imaginary part:
{ψc(x,y)}＝ψg(x)ψh(y)+ψh(x)ψg(y)
for imaginary part
And (3) normalizing to obtain six two-dimensional virtual wavelets:
wherein k is 1, 2, 3,
according to the six obtained two-dimensional real wavelets and six two-dimensional virtual wavelets, six complex wavelets are obtained by calculation:
the image compression method based on the double-number complex wavelet provided by the invention can also have the characteristics that the image binarization method comprises the specific steps of calculating four-level double-number complex wavelet decomposition subgraphs by adopting an adaptive threshold value binarization algorithm, setting the pixel gray level as f (i, j), dividing a rectangular region with the size of s × s by taking the pixel as the center, and calculating the sum of the pixels of the rectangular region and PnThe calculation formula is as follows:
in the formula, tn(n is 1, 2, 3, 4) is the result of image binarization, and then P is the sum of pixels in rectangular areanCalculating the area of the rectangular region to obtain the average value of the pixels in the rectangular region as the threshold value TiAnd comparing the pixel gray level f (i, j) with the calculated average value, setting the pixel to be white once the pixel gray level f (i, j) is greater than the threshold value, and setting the pixel to be black once the pixel gray level f (i, j) is less than or equal to the threshold value.
The image compression method based on the double complex wavelet provided by the invention can also have the characteristics that the scanning coding processing comprises the following specific steps: selecting series threshold T by adopting embedded zerotree wavelet algorithm1,T2......Tw-1Determining the importance of wavelet coefficient, and setting initial threshold
Where X is the wavelet coefficient of a w-level wavelet. The threshold value T is aligned according to the scanning sequence of wavelet coefficientsiScanning and comparing in sequence, once the wavelet coefficient is greater than the corresponding threshold, judging the wavelet coefficient as an important coefficient XiThen, the positive significance P or the negative significance N is expressed according to the sign of the wavelet coefficient and recorded in the main scanning table. Then find out X through the main scanning tablei＞T1Is important coefficient XiAnd recorded in the secondary scan table. For significant coefficient X recorded in the auxiliary scan tableiWhen X is presenti＞1.5T1When X is 1, the numberi≤1.5T1When it is, it is programmed to 0. And outputting the main scanning table, the auxiliary scanning table and the threshold as scanning coding information, and using the threshold and the important coefficient for the next scanning.
The image compression method based on the double complex wavelet provided by the invention can also have the characteristics that the specific steps of arithmetic coding compression are as follows: the arithmetic coding obtains the probability of each sequence through the positive important symbol and the symbol sequence of the load important symbol output by the scanning image binarization step and the scanning coding processing step, and ensures that the sum of the occurrence probabilities of the sequences is 1. And allocating an interval with corresponding size to the sequence numbers according to the probability of the occurrence of the sequence numbers. And examining each symbol, sequentially extending the corresponding subinterval to the whole symbol sequence, and then dividing the subinterval into n subintervals, wherein n is the symbol from n information source symbol sequences, so as to obtain the interval sequence corresponding to each symbol. Coding the symbol is to select the value of any point in the interval corresponding to the symbol.
Action and Effect of the invention
According to the image compression method based on the even-number complex wavelet, the original image is decomposed by adopting the even-number complex wavelet algorithm, and the even-number complex wavelet algorithm has the characteristic of stability, can reflect the signal change situation along a plurality of directions under different resolutions, better describes the signal direction, improves the definition of the final output image and reduces the distortion part. The threshold value is obtained by adopting a self-adaptive threshold value binarization algorithm, the calculation method is simple, and the efficiency of image compression is improved. The image is compressed by arithmetic coding, and is continuously coded in a recursion form from the whole sequence, the idea of replacing input symbols by specific codes is bypassed, and the symbol sequence in an input file is replaced by a single floating point number. The compression method has the advantages of low hardware requirement, low cost, simple operation process, ideal compression result and high practicability.
Drawings
FIG. 1 is a flowchart of an algorithm of an image compression method based on a dual complex wavelet according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of an analysis filter bank for a dual complex wavelet transform in accordance with an embodiment of the present invention;
fig. 3 is a compression effect diagram of only using the embedded zerotree wavelet algorithm and entropy coding combination for the original image in the embodiment of the present invention, where fig. 3(a) is the original image, fig. 3(b) is the effect diagram after the first compression, and fig. 3(c) is the effect diagram after the second compression;
FIG. 4 is a diagram illustrating the effect of compressing an original image by the method of the present invention in an embodiment of the present invention, wherein FIG. 4(a) is the original image, FIG. 4(b) is the effect of scanning 5 times by the method of the present invention, FIG. 4(c) is the effect of scanning 6 times by the method of the present invention, and FIG. 4(d) is the effect of scanning 7 times by the method of the present invention;
fig. 5 is an effect diagram obtained after images are compressed by different decomposition levels in the embodiment of the present invention, where fig. 5(a) is an effect diagram after two-level decompression, fig. 5(b) is an effect diagram after three-level decomposition compression, and fig. 5(c) is an effect diagram after four-level decompression.
Detailed Description
The following description of the embodiments of the present invention will be made in conjunction with the accompanying drawings.
< example >
The embodiment provides an image compression method based on a double-number complex wavelet, which is used for carrying out compression processing on an original image so as to carry out transmission.
In this embodiment, a personal computer with an operating system of windows10 is used for operation, the computer processor is intel (r) core (tm) i7-7500U CPU @2.70GHz 2.90GHz, the memory is 8GB, and the codes are implemented by Matlab.
Fig. 1 is a flowchart of an algorithm of an image compression method based on a dual complex wavelet according to an embodiment of the present invention.
As shown in fig. 1, an image compression method based on a dual complex wavelet comprises the following steps:
in step S1, image reading is performed to read the original image to be compressed.
Step S2, image decomposition, decomposing the original image by using the double complex wavelet algorithm to obtain four-level double complex wavelet decomposition subgraph of the original image, specifically comprising the following steps:
fig. 2 is a schematic diagram of an analysis filter bank for the double complex wavelet transform in accordance with an embodiment of the present invention.
As shown in fig. 2, according to the dual-tree complex wavelet algorithm, two paths of parallel discrete wavelet transforms of a binary tree structure are used to decompose an original image, one path generates a real part h0 and a real part h1, and the other path generates an imaginary part g0 and a g1, and edges of a two-dimensional dual-number complex wavelet transform are detected at six angles of ± 15 °, ± 45 °, ± 75 °, and a two-dimensional dual-tree complex wavelet function is:
ψ(x,y)＝ψ(x)ψ(y)＝[ψh(x)+jψg(x)][ψh(y)+jψg(y)]
＝[ψh(x)ψh(y)-ψg(x)ψg(y)]+j[ψh(y)ψg(x)+ψh(x)ψg(y)]
in the formula, #hAnd psigRespectively orthogonal or biorthogonal real wavelets,
complex wavelet function according to real part:
{ψc(x,y)}＝ψh(x)ψh(y)-ψg(x)ψg(y)
for real part
And (3) normalizing to obtain six two-dimensional real wavelets:
wherein k is 1, 2, 3,
complex wavelet function according to imaginary part:
{ψc(x,y)}＝ψg(x)ψh(y)+ψh(x)ψg(y)
for imaginary part
And (3) normalizing to obtain six two-dimensional virtual wavelets:
wherein k is 1, 2, 3,
according to the six obtained two-dimensional real wavelets and six two-dimensional virtual wavelets, six complex wavelets are obtained by calculation:
step S3, image binarization, calculating the four-level double-number complex wavelet decomposition subgraph by adopting an adaptive threshold value binarization algorithm to obtain a threshold value Ti, and obtaining a binarization image, which specifically comprises the following steps:
calculating four-level double-number complex wavelet decomposition subgraph by adopting an adaptive threshold value binarization algorithm, setting the gray level of a pixel as f (i, j), dividing a rectangular region with the size of s × s by taking the pixel as the center, and calculating the sum P of pixels in the rectangular regionnThe calculation formula is as follows:
in the formula, tn(n is 1, 2, 3, 4) is the result of image binarization, and then P is the sum of pixels in rectangular areanCalculating the area of the rectangular region to obtain the average value of the pixels in the rectangular region as the threshold value Ti。
The pixel gradation f (i, j) is compared with the calculated average value.
Once the pixel grayscale is f (i, j) greater than the threshold, the pixel is set to white.
Once the pixel grayscale is f (i, j) equal to or less than the threshold, the pixel is set to black.
Step S4, scanning and coding, which is to adopt the embedded zerotree wavelet algorithm to scan and code the binary image and then output the scanning and coding information, and the method specifically comprises the following steps:
selecting series threshold T by adopting embedded zerotree wavelet algorithm1,T2......Tw-1Determining the importance of wavelet coefficient, and setting initial threshold
Where X is the wavelet coefficient of a w-level wavelet.
Threshold value T is paired according to scanning sequence of wavelet coefficientsiScanning and comparing in sequence, judging the wavelet coefficient as important coefficient X once the wavelet coefficient is greater than the corresponding threshold valueiThen, positive important symbol P or negative important symbol N is used to represent and record in the main scanning table according to the positive and negative of wavelet coefficient, and then X is found out through the main scanning tablei＞T1Is important coefficient XiAnd recorded in the secondary scan table.
For significant coefficient X recorded in the auxiliary scan tableiWhen X is presenti＞1.5T1When X is 1, the numberi≤1.5T1When it is, it is programmed to 0.
And outputting the main scanning table, the auxiliary scanning table and the threshold as scanning coding information, and using the threshold and the important coefficient for the next scanning.
Step S5, compressing the binary image by using a recursive continuous encoding method according to the scanning encoding information, so as to obtain an arithmetic encoded image, which specifically includes the following steps:
the arithmetic coding obtains the probability of each sequence through the positive important symbol and the symbol sequence of the load important symbol output by the scanning image binarization step and the scanning coding processing step, and ensures that the sum of the occurrence probabilities of the sequences is 1.
And allocating an interval with corresponding size to the sequence numbers according to the probability of the occurrence of the sequence numbers.
And examining each symbol, sequentially extending the corresponding subinterval to the whole symbol sequence, and then dividing the subinterval into n subintervals, wherein n is the interval sequence corresponding to each symbol and the symbol comes from n information source symbol sequences.
Coding the symbol is to select the value of any point in the interval corresponding to the symbol.
In step S6, the image is inverse-transformed, and the arithmetic coded image is subjected to an inverse double complex wavelet transform, thereby obtaining a compressed image.
In step S7, the image is output and the compressed image is output.
Fig. 3 is a graph of the effect of compression using only the combination of the embedded zerotree wavelet algorithm and entropy coding on the original image according to the embodiment of the present invention, where fig. 3(a) is the original image, fig. 3(b) is the effect graph after the first compression, and fig. 3(c) is the effect graph after the second compression.
As shown in fig. 3, the effect graph after the first compression in fig. 3(b) and the effect graph after the second compression in fig. 3(c) are compared with the original image in fig. 3(a), it can be seen that the image obtained by only using the embedded zerotree wavelet algorithm and entropy coding in combination is poor in effect and serious in image distortion.
Fig. 4 is an effect diagram of compressing an original image by the method of the present invention in the embodiment of the present invention, where fig. 4(a) is the original image, fig. 4(b) is the effect diagram of scanning 5 times by the method of the present invention, fig. 4(c) is the effect diagram of scanning 6 times by the method of the present invention, and fig. 4(d) is the effect diagram of scanning 7 times by the method of the present invention.
As shown in fig. 4, comparing fig. 4 with fig. 3, it can be seen that the picture compressed by the image compression method based on the dual complex wavelet provided by this embodiment has higher compression quality compared to the picture obtained by only using the embedded zerotree wavelet algorithm and entropy coding in combination with compression, and the compressed image obtained by more than 7 times of scanning has higher image compression effect and clearer human outline. Therefore, it can be seen that, in the case where the aforementioned conditions are the same, the image is less likely to be distorted as the number of scans is larger.
Fig. 5 is an effect diagram obtained after images are compressed by different decomposition levels in the embodiment of the present invention, where fig. 5(a) is an effect diagram after two-level decompression, fig. 5(b) is an effect diagram after three-level decomposition compression, and fig. 5(c) is an effect diagram after four-level decompression.
TABLE 1
As shown in fig. 5 and table 1, with the image compression rate as the main reference value and the image distortion rate and the compression efficiency as the auxiliary reference standard, when the number of scanning times is 7, the compressed image obtained by four-level decomposition is 3.02KB which is much smaller than the original image size and smaller than the image sizes obtained by other decomposition levels. Because the common standard of the peak signal-to-noise ratio is 30dB, the image degradation below 30dB is obvious, and the peak signal-to-noise ratio of the compressed image is 31.09dB to more than 30dB, four-level wavelet decomposition is selected as the optimal choice. Similarly, under the condition of the same decomposition series, the compression ratio of the images obtained by 6 and less than 6 scans is relatively large, namely the compression efficiency of the images is high, but the peak signal-to-noise ratio is far less than 30dB, the image degradation is obvious, and in addition, the operation time is increased by increasing the scanning times, so that 7 scans with the peak signal-to-noise ratio which is closest to the 6 scans and is greater than 30dB are selected as the optimal scanning times.
Examples effects and effects
According to the image compression method based on the even-number complex wavelet of the embodiment, the original image is decomposed by adopting the even-number complex wavelet algorithm, and the even-number complex wavelet algorithm has a stable characteristic, can reflect the signal change situation along a plurality of directions under different resolutions, better describes the signal direction, improves the definition of the final output image and reduces the distortion part. The compression method has the advantages of low hardware requirement, low cost, simple operation process, ideal compression result and high practicability.
According to the image compression method based on the dual complex wavelet, the threshold value is obtained by adopting the self-adaptive threshold value binarization algorithm, the calculation method is simple, and the efficiency of image compression is improved.
According to the image compression method based on the double-number complex wavelet, the image is compressed by adopting arithmetic coding, the whole sequence is continuously coded in a recursion mode, the idea of replacing input symbols by specific codes is bypassed, and the symbol sequence in an input file is replaced by a single floating point number.
The above-mentioned embodiments are merely illustrative of specific embodiments of the present invention, and the present invention is not limited to the description of the above-mentioned embodiments.
Claims (5)
1. An image compression method based on a double-number complex wavelet, which is used for compressing an original image so as to transmit the original image, and is characterized by comprising the following steps:
reading an image, namely reading the original image to be compressed;
decomposing the image, namely decomposing the original image by adopting a dual complex wavelet algorithm to obtain four-level dual complex wavelet decomposition subgraphs of the original image;
performing image binarization, and calculating the four-level double-number complex wavelet decomposition subgraph by adopting a self-adaptive threshold value binarization algorithm to obtain a threshold value TiObtaining a binary image;
scanning and coding, namely scanning and coding the binary image by adopting an embedded zerotree wavelet algorithm and then outputting scanning and coding information;
compressing the binary image by adopting a recursion form continuous coding arithmetic coding method according to the scanning coding information to obtain an arithmetic coding image;
an image inverse transform, which performs a double complex wavelet inverse transform on the arithmetic coded image, thereby obtaining a compressed image;
and outputting the compressed image.
2. The image compression method based on the even-number complex wavelet of claim 1, wherein the image decomposition comprises the following specific steps:
according to the dual-tree complex wavelet algorithm, two paths of parallel discrete wavelet transform of a binary tree structure are adopted to decompose the original image, one path generates a real part and the other path generates an imaginary part, the edges of the two-dimensional dual-tree complex wavelet transform are detected at six angles of +/-15 degrees, +/-45 degrees and +/-75 degrees, and the two-dimensional dual-tree complex wavelet function is as follows:
ψ(x,y)＝ψ(x)ψ(y)＝[ψh(x)+jψg(x)][ψh(y)+jψg(y)]
＝[ψh(x)ψh(y)-ψg(x)ψg(y)]+j[ψh(y)ψg(x)+ψh(x)ψg(y)]
in the formula, #hAnd psigRespectively orthogonal or biorthogonal real wavelets,
according to the complex wavelet function of the real part:
{ψc(x,y)}＝ψh(x)ψh(y)-ψg(x)ψg(y)
for the real part
And (3) normalizing to obtain six two-dimensional real wavelets:
wherein k is 1, 2, 3,
according to the complex wavelet function of the imaginary part:
{ψc(x,y)}＝ψg(x)ψh(y)+ψh(x)ψg(y)
for the imaginary part
And (3) normalizing to obtain six two-dimensional virtual wavelets:
wherein k is 1, 2, 3,
calculating to obtain six complex wavelets according to the six obtained two-dimensional real wavelets and the six two-dimensional virtual wavelets:
3. the image compression method based on the dual complex wavelet as claimed in claim 1, wherein the specific steps of the image binarization are as follows:
calculating the four-level double-number complex wavelet decomposition subgraph by adopting the self-adaptive threshold value binarization algorithm, setting the gray level of a pixel as f (i, j), dividing a rectangular region with the size of s × s by taking the pixel as the center, and calculating the sum P of pixels in the rectangular regionnThe calculation formula is as follows:
in the formula, tn(n-1, 2, 3, 4) is the result of the image binarization, and then P is the sum of the pixels of the rectangular areanCalculating the area of the rectangular region to obtain the average value of the pixels in the rectangular region as the threshold value Ti，
Comparing the pixel gradation f (i, j) with the average value obtained by calculation,
once the pixel gray scale is f (i, j) greater than the threshold, the pixel is set to white,
once the pixel grayscale is f (i, j) equal to or less than the threshold, the pixel is set to black.
4. The image compression method based on the even-number complex wavelet of claim 1, wherein the specific steps of the scan coding process are as follows:
selecting a series of threshold values T by adopting the embedded zerotree wavelet algorithm1,T2......Tw-1Determining the importance of wavelet coefficient, and setting initial threshold
Where X is the wavelet coefficient of a w-level wavelet,
the threshold value T is processed according to the scanning sequence of the wavelet coefficientsiScanning and comparing in sequence, judging the wavelet coefficient as important coefficient X once the wavelet coefficient is greater than the corresponding threshold valueiThen, positive important symbols P or negative important symbols N are used for representing and recording the wavelet coefficients in a main scanning table according to the signs of the positive and negative of the wavelet coefficients, and then X is found out through the main scanning tablei＞T1Is important coefficient XiAnd is recorded in the auxiliary scanning table,
for the significant coefficient X recorded in the secondary scan tableiWhen X is presenti＞1.5T1When X is 1, the numberi≤1.5T1When the number of the fibers is more than 0,
and outputting the main scanning table, the auxiliary scanning table and the threshold as scanning coding information, and using the threshold and the important coefficient for next scanning.
5. The image compression method based on the even-number complex wavelet of claim 1, wherein the specific steps of the arithmetic coding compression are as follows:
arithmetic coding obtains the probability of occurrence of each sequence by scanning the symbol sequences of the positive significant symbol and the negative significant symbol output by the image binarization step and the scan coding processing step, and ensures that the sum of the occurrence probabilities of the sequences is 1,
allocating a section with corresponding size to the sequence numbers according to the probability of the occurrence of the sequence numbers,
examining each symbol, sequentially extending the corresponding subinterval to the whole symbol sequence, then dividing into n subintervals, wherein n is the symbol from n source symbol sequences to obtain the interval sequence corresponding to each symbol,
and coding the symbol, namely selecting the value of any point on the interval corresponding to the symbol.
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