CN101583032B - Adaptive down-sampling and lapped transform-based image compression method - Google Patents

Abstract

The invention provides an adaptive down-sampling and lapped transform-based image compression method, and mainly solves the problems of low performance and high complexity existing in the prior down-sampling based compression method. The method comprises the following steps of: 1, adaptively down-sampling the prior image; 2, firstly performing lapped transform on the image after adaptive down-sampling between DCT blocks which are not subjected to the down-sampling, and then performing the DCT transformation on the whole image; 3, interweaving factors after transformation into a wavelet tree structure to obtain a low frequency subband DC and a high frequency subband AC; 4, performing the shape-adaptive DCT transformation on the low frequency subband DC, and interweaving the factors again; 5, by an object-oriented SPECK coding method, coding the factors with the wavelet tree structure to obtain a compressed bit stream; and 6, decompressing the bit stream transmitted to a decoding end to obtain a final re-constructed image. The method can obtain the performance higher than that of the prior image compression method under the condition of low bit rate, is low in complexity, and can be used for the low-bit-rate image coding which has strict requirements on complexity and real-time.

Description

Image compression method based on self-adaptive down-sampling and overlapping transformation

Technical Field

The invention belongs to the technical field of image processing, and particularly relates to an image compression method which can be used for realizing low-complexity and low-power-consumption image compression under a low code rate.

Background

Images, which are the most abundant information carriers, are one of the indispensable elements in the information age. In recent years, with the wide application of technologies such as video conferencing, video telephone, high definition television, remote monitoring and remote sensing imaging, images have become the main carrier of information communication in people's life, and high-resolution images are also required by different industries. With the development of imaging technology, many devices have been able to provide high-resolution digital images to meet people's requirements, however, the improvement of resolution makes the images contain a larger amount of information, which puts higher demands on image compression. It is therefore necessary to represent an image with as little data as possible while ensuring a certain image quality.

In recent years, Wuchang forest, Wufeng et al have tried to improve image compression at low code rate by interpolation and achieved good results in this respect. Their approach essentially follows a pattern: the whole image is downsampled at a coding end by utilizing filtering or lifting technology to obtain a pair of low-resolution images, and the low-resolution images are subjected to transform coding to obtain a compressed file; at the decoding end, the compressed file is decoded first, the low-resolution image is reconstructed, and then the resolution is improved by utilizing interpolation to obtain a decoded image. Although such methods have been able to improve coding performance at relatively low code rates, the following disadvantages remain: firstly, because the method performs down-sampling on the whole image regardless of a smooth region or an edge region, and in the edge region, the correlation between neighborhoods is difficult to estimate, it is difficult to up-sample a clear high-resolution image by using a general interpolation method, thereby affecting the quality of a decoded image; secondly, because the method uses an interpolation method with quite high complexity, the method is not suitable for being applied to some devices with strict requirements on real-time performance and complexity.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides an image compression method based on adaptive down-sampling and lapped transform so as to improve the compression performance of images at low code rate, reduce the computational complexity and meet the requirements of a plurality of devices on instantaneity, low complexity and low power consumption.

In order to achieve the above purpose, the implementation steps of the invention comprise the following steps:

(1) DCT transformation is carried out on the original image, and the transformed image is pre-coded under the current code rate by using SPECK, so as to obtain a threshold value of a cut-off bit plane, which is marked as MT;

(2) the original image is divided into 32 × 32 blocks, and the following judgment is made for each block:

2a) performing DCT on the current block, performing 5/3 wavelet transform on the current block if the number of transform coefficients larger than the threshold MT does not exceed 1.6% of the total number of coefficients in the current block, otherwise, not performing the transform, and marking the current block as 0;

2b) performing a DCT transform on 5/3 the low frequency subbands of the wavelet transformed block, if the number of transform coefficients greater than the threshold MT still does not exceed 1.6% of the total number of coefficients in the low frequency subbands, marking the 32 x 32 block as 1, otherwise, marking as 0;

2c) regarding the block marked as 1 as a smooth block, performing 5/3 wavelet transformation on the smooth block, discarding high-frequency sub-bands, and reserving low-frequency sub-bands as the down-sampling result;

(3) firstly, performing overlap transform on the down-sampled image between DCT blocks, and then performing discrete cosine transform on the image after the overlap transform to obtain a transform coefficient;

(4) coefficient interweaving is carried out on the transformed coefficients to obtain a low-frequency sub-band DC and a high-frequency sub-band AC;

(5) performing shape adaptive discrete cosine transform on the low-frequency sub-band DC, performing coefficient interleaving on the transformed coefficient again, and combining the interleaved low-frequency sub-band DC and the high-frequency sub-band AC to obtain a final transform coefficient;

(6) carrying out object-oriented SPECK coding on the final transformation coefficient, and omitting unimportant information according to the required code rate to obtain a compressed bit stream;

(7) at the decoding end, decompression is performed according to the transmitted bit stream to obtain a final decoded image.

Compared with the prior art, the invention has the following advantages:

the invention adopts the self-adaptive down-sampling method, only down-samples the smooth area of the image, and solves the problem that the reconstruction quality of the traditional down-sampling-based image compression method to the edge area is not ideal. Meanwhile, because the invention carries out the crossover transform between DCT blocks, the invention can effectively eliminate the block effect caused by the DCT transform and obtain better subjective visual effect. In addition, the invention adopts an interpolation method with small complexity, thereby overcoming the defect of poor real-time performance of the traditional image compression method based on downsampling.

Drawings

FIG. 1 is a compression flow diagram of the present invention;

FIG. 2 is a decompression flow diagram of the present invention;

FIG. 3 is a diagram of the results of the operation of the present invention prior to encoding; wherein,

FIG. 3(a) is a diagram after adaptive downsampling,

figure 3(b) is a diagram after coefficient interleaving,

figure 3(c) is an enlarged view of the low frequency subband DC of figure 3(b),

FIG. 3(d) is the DC sub-band after SA-DCT transformation;

FIG. 4 is a schematic representation of the present invention utilizing 5/3 wavelet down-sampling;

FIG. 5 is a schematic diagram of coefficient interleaving according to the present invention; wherein,

figure 5(a) is a graph of the original coefficient distribution,

FIG. 5(b) is a coefficient distribution diagram after interleaving;

fig. 6 is a comparison of the subjective visual effect of the reconstructed image of the present invention and JPEG 2000.

Detailed Description

Referring to fig. 1, the image compression process of the present invention is as follows:

step 1, performing DCT (discrete cosine transformation) on an original image, and pre-coding the transformed image at the current code rate by using SPECK (discrete cosine transformation), so as to obtain a threshold of a cut-off bit plane, which is marked as MT;

step 2, dividing the original image into blocks with the size of 32 x 32, and then judging each block as follows:

(2a) performing DCT on the current block, performing 5/3 wavelet transform on the current block if the number of coefficients larger than the threshold MT does not exceed 1.6% of the total number of coefficients in the current block, otherwise, not performing the transform, and marking the current block as 0;

(2b) the 5/3 low-frequency sub-band of the wavelet-transformed block is then DCT-transformed, if the number of coefficients greater than the threshold MT does not exceed 1.6% of the total number of coefficients in the low-frequency sub-band, the 32 x 32 block is marked as 1, otherwise, it is marked as 0;

(2c) considering the block labeled 1 as a smooth block, 5/3 wavelet transforming the smooth block, discarding the high frequency sub-bands, and reserving the low frequency sub-bands as the result of downsampling, as shown in fig. 4, wherein, fig. 4(a) is the original image block,

fig. 4(b) is an 5/3 image block after wavelet transform, and fig. 4(c) is an image block after downsampling; the downsampling result chart shown in fig. 3(a) can be obtained by the steps (2a) to (2 c).

And 3, sequentially performing overlapping transformation and DCT transformation on the down-sampled graph.

The specific process is as follows:

(3a) prior to DCT transformation, an overlap transform is chosen to be performed at DCT block boundaries that are not down-sampled to remove inter-block correlation. The lapped transform matrix P is defined as:

$P=\frac{1}{2}\left[\begin{array}{cc}I& J\\ J& -I\end{array}\right]\left[\begin{array}{cc}\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="H2009100230854E00041.png"\; state="\{\{state\}\}">I</figure-callout>}& 0\\ 0& V\end{array}\right]\left[\begin{array}{cc}I& J\\ J& -I\end{array}\right]---\left(1\right)$

wherein I is an identity matrix, J is an inverse identity matrix,

v is the free control matrix and is,

$V=J{\left(C_{M/2}^{\mathrm{II}}\right)}^T{C}_{M/2}^{\mathrm{IV}}J---\left(3\right)$

C_M/2 ^IIand C_N/2 ^IVA second type of discrete cosine transform DCT-II and a fourth type of discrete cosine transform DCT-IV of 8 points, respectively.

(3b) The overlap-transformed image is subjected to a 16-point DCT transform.

And 4, performing coefficient interleaving on the transformed image to obtain a low-frequency subband DC and a high-frequency subband AC, as shown in fig. 3 (b).

Coefficient interleaving is to interleave the transform coefficients into a wavelet tree structure, which is composed of a low frequency subband DC and a high frequency subband AC. The specific interleaving process is as follows:

(4a) initializing a cycle time variable z to be 4, and a sub-band stage number k to be 1;

(4b) taking out the DC coefficient of each block and putting the DC coefficients together to form a low-frequency sub-band DC;

(4c) taking out the sub-system number corresponding to the DC coefficient of each block and placing the sub-system number in the corresponding position to form a high-frequency sub-band AC_k；

(4d) Let z be z-1, k be k + 1; taking out the sub-coefficient corresponding to the sub-coefficient of the previous stage and placing the sub-coefficient in the corresponding position to form a high-frequency sub-band AC_k；

(4e) Judging whether z is 0, if not, returning to (4d), if so, completing coefficient interleaving, and all high-frequency sub-bandsAC_kConstituting a subband high frequency AC.

The coefficient interleaving result shown in fig. 5(b) is obtained from steps (4a) - (4e), as can be seen from fig. 5(a), the original coefficients are distributed in block before the coefficient interleaving, and the DC coefficient distribution is not concentrated, wherein 1, 2, 3, 4, 5, 6, 7, 8, 9 represent DC coefficients, gray symbols represent the number of subsystems corresponding to the DC coefficients, and other symbols represent high-frequency coefficients, as can be seen from fig. 5(b), the interleaved coefficients are distributed in tree form, the DC coefficients are concentrated at the upper left corner to form a low-frequency subband DC, and the remaining high-frequency coefficients form a high-frequency subband AC.

And step 5, performing SA-DCT on the DC sub-band shown in the figure 3(c), performing coefficient interleaving on the obtained transformation coefficient again to obtain a DC sub-band after secondary transformation, and combining the DC sub-band with the AC sub-band to obtain a final transformation image. The result of the SA-DCT transformation is shown in fig. 3(d), and the specific process is as follows:

(5a) marking the down-sampled block in the adaptive down-sampling, and determining the position of the discarded coefficient in the DC sub-band according to the marking result and the principle of coefficient interleaving;

(5b) dividing the low-frequency sub-band into 16-by-16 blocks, and performing SA-DCT on each block: the retained coefficients of each block are arranged in rows, one-dimensional DCT transformation of corresponding points is carried out on each row, the coefficients are arranged close to the left row, one-dimensional DCT transformation is carried out on each row, and the DCT of the points is carried out when the coefficients are retained in each row, so that the SA-DCT transformation is completed.

And 6, carrying out OB-SPECK coding on the final transform coefficient, and specifically comprising the following steps:

(6a) coding and initializing the transformed coefficients to obtain initial information, i.e. according to the highest bit plane

Obtaining initial bit plane, and making bit plane n equal to n_maxWherein

c_i，jis a transform coefficient; then, the whole image is taken as a block and put into an unimportant block set LIS to obtain an initial LIS; then set the significant coefficient set

(6b) Sorting the blocks in the LIS and sequentially testing the reordered sub-blocks, wherein the sub-blocks discarded due to downsampling are not tested, and if the transform coefficients satisfy 2ⁿ≤|c_i，j|＜2ⁿ⁺¹If so, the coefficient is considered as an important coefficient, or the block where the transform coefficient is located is an important block;

(6c) and thinning the important coefficient set LSP, and circularly updating the bit plane to obtain a compressed bit stream file.

Referring to fig. 2, the image decompression process of the present invention is as follows:

and step A, carrying out the reverse process of the step 6 on the bit stream transmitted by the encoding end to obtain a decoded image.

B, performing coefficient reverse interleaving on the low-frequency sub-band DC of the decoded image, namely rearranging the coefficients distributed in a wavelet tree structure into block distribution, and performing SA-DCT inverse transformation on the low-frequency sub-band DC subjected to reverse interleaving to obtain a reconstructed low-frequency sub-band DC;

and step C, combining the reconstructed low-frequency sub-band DC and the high-frequency sub-band AC of the decoded image, and sequentially performing coefficient reverse interleaving, DCT (discrete cosine transformation) inverse transformation and overlapping inverse transformation on the combined image to obtain a reconstructed image after down sampling.

And D, restoring the downsampled area by utilizing Cubic interpolation to obtain a final reconstructed image.

The effects of the present invention can be further illustrated by the following specific experimental data.

1. Conditions and contents of the experiment

The experiment of the invention is to take an image with the size of 512 multiplied by 512 and the gray scale of 8 bits: the 4 images of Barbara, Lena, Goldhill and Baboon were encoded and decoded according to the above encoding and decoding steps, respectively, and compared with the peak signal to noise ratio PSNR performance in the quality progressing mode under the conditions of compression ratios bpp of 0.125bpp, 0.25bpp and 0.5bpp, respectively. Wherein peak signal to noise ratio PSNR performance of SPECK, SPIHT method and the method of the invention are compared without arithmetic coding; the peak signal-to-noise ratio PSNR performance of SPECK-AC, SPIHT-AC, JPEG2000, SPECK-AC with lapped transform and the inventive method with arithmetic coding are compared in the presence of arithmetic coding.

2. Visual effect comparison results

As shown in FIG. 6, the subjective visual effect of the reconstructed images obtained by the method of the present invention and JPEG2000 at a code rate of 0.125bpp for two images, Lena and Barbara, respectively, is compared. Wherein fig. 6(a) is the original image of Lena, fig. 6(b) is the Lena reconfiguration image under JPEG2000, fig. 6(c) is the Lena reconfiguration image under the present invention, fig. 6(d) is the original image of Barbara, fig. 6(e) is the barbarbarbara reconfiguration image under JPEG2000, and fig. 6(f) is the barbarbara reconfiguration image under the present invention, as can be seen from fig. 6, due to the effect of the overlap transform, the method of the present invention has better retention of the texture and edge information of the image, and the visual effect is significantly better than JPEG 2000.

3. The peak signal-to-noise ratio PSNR comparison results are shown in table 1.

TABLE 1 comparison of peak SNR PSNR performance for different methods

As can be seen from Table 1, the peak signal-to-noise ratio PSNR obtained by the method of the present invention is significantly better than the existing SPECK and SPIHT methods in the absence of arithmetic coding, and in most cases the peak signal-to-noise ratio PSNR obtained by the method of the present invention is up to or even better than the SPECK-AC and SPIHT-AC methods using arithmetic coding, which is close to JPEG 2000. After arithmetic coding is added, the peak signal-to-noise ratio PSNR obtained by the method with arithmetic coding is still obviously superior to SPECK-AC, SPIHT-AC and JPEG 2000. Meanwhile, the arithmetic coding added in the method is the same arithmetic coding as the SPHIT and the SPECK, but not the high-order arithmetic coding adopted in the JPEG2000, so the method not only has higher peak signal-to-noise ratio (PSNR) performance than the SPHIT-AC, the SPIHT-AC and the JPEG2000, but also has low complexity, and is easy to realize by hardware. In addition, the method of the present invention also has significant advantages over SPECK-AC with lapped transform, which means that the adaptive down-sampling in the present invention plays a role.

Claims (3)

1. An image compression method based on adaptive down-sampling and lapped transform, comprising the steps of:

(1) DCT transformation is carried out on the original image, and the transformed image is pre-coded under the current code rate by using SPECK, so as to obtain a threshold value of a cut-off bit plane, which is marked as MT;

(2) dividing the original image into 32 × 32 blocks, and then judging each block as follows:

2a) performing DCT on the current block, performing 5/3 wavelet transform on the current block if the number of transform coefficients larger than the threshold MT does not exceed 1.6% of the total number of coefficients in the current block, otherwise, not performing 5/3 wavelet transform and marking the current block as 0;

2b) performing a DCT transform on 5/3 the low frequency subbands of the wavelet transformed block, if the number of transform coefficients greater than the threshold MT still does not exceed 1.6% of the total number of coefficients in the low frequency subbands, marking the 32 x 32 block as 1, otherwise, marking as 0;

2c) regarding the block marked as 1 as a smooth block, performing 5/3 wavelet transformation on the smooth block, discarding high-frequency sub-bands, and reserving low-frequency sub-bands as the down-sampling result;

(3) and sequentially performing the following overlapped transformation and discrete cosine transformation on the down-sampled image to obtain a transformation coefficient:

(3a) selecting, prior to the DCT transform, an lapped transform at DCT block boundaries that have not been downsampled to remove inter-block correlation;

(3b) performing 16-point DCT on the image after the overlapped transformation;

(4) coefficient interweaving is carried out on the transformed coefficients to obtain a low-frequency sub-band DC and a high-frequency sub-band AC;

(5) performing shape adaptive discrete cosine transform on the low-frequency sub-band DC, performing coefficient interleaving on the transformed coefficient again, and combining the interleaved low-frequency sub-band DC and the high-frequency sub-band AC to obtain a final transform coefficient;

(6) carrying out object-oriented SPECK coding on the final transformation coefficient, and omitting unimportant information according to the required code rate to obtain a compressed bit stream;

(7) at the decoding end, decompression is performed according to the transmitted bit stream to obtain a final decoded image.

2. The image compression method as claimed in claim 1, wherein the coefficient interleaving of step (4) is to interleave the transform coefficients into a wavelet tree structure, which is composed of a low frequency subband DC and a high frequency subband AC.

3. The image compression method as claimed in claim 1, wherein the step (6) of performing object-oriented SPECK coding on the final transform coefficients means that only the coefficients remaining after downsampling are coded.

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