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Lossy Compression Using Stationary Wavelet Transform and Vector Quantization

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Lossy Compression Using Stationary Wavelet Transform and Vector Quantization

Produced byOmar Ghazi Abbood Khukre

Master Student in Department of Information Technology, Institute of Graduate Studies and Research, Alexandria University, Egypt.

Contents IntroductionImage Compression DefinitionImage Compression TypesWavelet Transforms Problem StatementObjectiveMethodologyExperiments and Results AnalysisConclusionFuture work

INTRODUCTIONImage Compression: It is the Art & Science of reducing the amount of data required to represent an image.It is the most useful and commercially successful technologies in the field of Digital Image Processing.The number of images compressed and decompressed daily is innumerable.Web page images & High-resolution digital camera photos also are also compressed to save storage space & reduce transmission time.The researchers have faced in the field of Image compression some difficulties especially in get the best accuracy of the image with a high compression ratio. This research aims an improving the image compression process to the maximum extent.

Image Compression DefinitionImage compression is minimizing the size in bytes of a graphics file without degrading the quality of the image to an unacceptable level . The reduction in file size allows more images to be stored in a given amount of disk or memory space. It also reduces the time required for images to be sent over the Internet or downloaded from Web pages.

Lossy Compression Techniques In information technology, lossy compression or irreversible compression is the class of data encoding methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storage, handling, and transmitting content. The amount of data reduction possible using lossy compression is often much higher than through lossless techniques.Lossless Compression Techniques Lossless compression is a class of data compression algorithms that allows the original data to be perfectly reconstructed from the compressed data. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though this usually improves compression rates (and therefore reduces file sizes)

Image Compression Types

Lossy Compression TechniquesLossy Compression Vector quantization by Linde-Buzo-GrayLossy compression technique provides higher compression ratio than lossless compression.A lossy compression scheme, shown in Figure, may examine the color data for a range of pixels, and identify subtle variations in pixel color values that are so minute that the human eye/brain is unable to distinguish the difference between them.

Vector quantization (VQ) is a classical quantization technique from signal processing that allows the modeling of probability density functions by the distribution of prototype vectors. It was originally used for data compression. It works by dividing a large set of points (vectors) into groups having approximately the same number of points closest to them.

Linde, Buzo, and Gray (LBG) proposed a VQ design algorithm based on a training sequence. The use of a training sequence bypasses the need for multi-dimensional integration. The LBG algorithm Algorithm They used a mapping function to partition training vectors into clusters and be is of iterative type and in each iteration a large set of vectors, generally referred to as training set, is needed to be processed.

Lossy Compression Techniques (cont.)

Wavelet Transforms

Represent an image as a sum of wavelet functions (wavelets) with different locations and scales. Any decomposition of an image into wavelets involves a pair of waveforms: one to represent the high frequencies corresponding to the detailed parts of an image and one for the low frequencies or smooth parts of an image.

Discrete Wavelet TransformThe Discrete Wavelet Transform (DWT) of image signals produces a nonredundant image representation, which provides better spatial and spectral localization of image formation, compared with other multi scale representations such as Gaussian and Laplacian pyramid. Recently, Discrete Wavelet Transform has attracted more and more interest in image fusion .An image can be decomposed into a sequence of different spatial resolution images using DWT.In case of a 2D image, an N level decomposition can be performed resulting in 3N+1 different frequency bands and it is shown in figure.Wavelet Transforms (cont.)

Wavelet Transforms (cont.)

2D - Discrete wavelet transform

Lifting Wavelet Transform The lifting scheme is a technique for both designing wavelets and performing the discrete wavelet transform. Actually it is worthwhile to merge these steps and design the wavelet filters while performing the wavelet transform. This is then called the second generation wavelet transform. Wavelet Transforms (cont.)

Diagram lifting wavelet scheme transform

Stationary Wavelet TransformThe stationary wavelet transform (SWT) is a wavelet transform algorithm designed to overcome the lack of translation invariance of the Discrete Wavelet Transform (DWT). Translation invariance is achieved by removing the down samplers and up samplers in the Discrete Wavelet Transform (DWT) and up sampling the filter coefficients by a factor of in the level of the algorithm. The SWT is an inherently redundant scheme as the output of each level of SWT contains the same number of samples as the input.

Wavelet Transforms (cont.)

The Stationary Wavelet Transform (SWT) is similar to the DWT except the signal is never sub-sampled and instead the filters are up sampled at each level of decomposition. The following block diagram depicts the digital implementation of SWT as shown in figure.

Wavelet Transforms (cont.)

Problem Statement The large increase in the data lead to delays in access to the information required and this leads to a delay in the time. Large data lead to data units and storage is full this leads to the need to buy a bigger space for storage and losing money. Large data lead to give inaccurate results for the similarity of data and this leads to getting inaccurate information.Also to show the difference between the types of transforms Stationary Wavelet Transform, Discrete Wavelet Transform, and Lifting Wavelet Transform because they are very similar at one level so we used three levels.

Research Objective In lossy compression, the compression ratio is unaccepted. The proposed system suggests an image compression method of lossy image compression through the three types of transformations such as stationary wavelet transform, discrete wavelet transform , and lifting wavelet transform and the comparison between the three types and the use of vector quantization (VQ) to improve the image compression process.

MethodologyThe proposed lossy compression approach applied SWT and VQ techniques in order to compressed input images in four phases; namely preprocessing, image transformation, zigzag scan, and lossy/lossless compression. In figure shows the main steps of the system that follows the schema independent and image compression techniques. We discuss how a matrix arrangement gives us the best compression ratio and lessloss of the characteristics of the image through a wavelet transform with lossy compression techniques.

Methodology (cont.)In Block Diagram in the following shows the work in sequence.

Methodology (cont.)Step 1Pre Processing First step of the proposed system When enter five images to the system, pre-processing will be applied on images which are resize of the image in accordance with the measured rate of different sizes to (8 8) And then converted from (RGB) to (gray scale).

Methodology(cont.)

Step 2Wavelet transformsImage transformation phase received the resizable gray scale images and produced transformed images. This phase used the three types of wavelet transforms such as DWT, LWT, and SWT.

Methodology(cont.)

Step 3Zigzag Scan In this step we convert the matrix from 2-D to 1-D by zigzag scan.Zigzag scans ordering converting a 2-D matrix into a 1-D array, so that the frequency (horizontal + vertical) increase in this order and the coefficient variance decreases in this order as figure.

Step 4 Lossy compression In this step we do more than try to get the highest possible compression ratio. We enter the matrix to lossy compression using (VQ). And again we enter the matrix to lossless compression(Huffman Coding and Arithmetic Coding) and make a comparison of the results Between the two experiments. And again we enter the matrix to lossy compression using (VQ), output of this process, introduce it to lossless compression(Huffman Coding and Arithmetic Coding) to get the highest possible compression ratio and compare the results and find the best

Methodology(cont.)

Methodology(cont.)Compression RatioCompression Ratio: is the ratio of size of the compressed database system with the original size of the uncompressed database systems. Also known as compression power is a computer-science term used to quantify the reduction in data-representation size produced by a data compression algorithm. Compression ratio is defined as follows:

Compression TimeCompression Time = represents the elapsed time during the compression process.

Experiments and Results Analysis

Experiments

In this section of the performance of three types of wavelet transform (SWT, DWT, and LWT) and the impact of each type on the image lossy compression performance also it shows the lossy using vector quantization (LBG) and lossless compression using Arithmetic coding and Huffman coding.The First Experiment In this experiment, four operations:1-DWT-Zigzag-Arithmetic 2-DWT-Zigzag-LBGArithmetic3-DWT-Zigzag-Huffman4-DWT-Zigzag-LBGHuffmanTable 1 showing results for the process lossy and lossless image compression to the five images using the discrete wavelet transform with arithmetic coding and huffman coding without the use of the LBG, as well as with the use of the LBG and that using three decomposition levels.

Experiments (cont.)

Discrete wavelet transform, vector quantization (LBG), Arithmetic and Huffman coding

DWTDWT Zigzag ArithmeticDWT Zigzag LBG & ArithmeticDWT Zigzag HuffmanDWT Zigzag LBG & HuffmanImageLevelC.RatioRunning time(Sec)C.RatiopsnrRunning time(Sec)C.RatioRunning time(Sec)C.RatiopsnrRunning time (Sec)Lena11.19340.49191.254918.29750.01571.14030.07351.187918.29750.05721.2610.04591.302718.27450.0121.05560.07851.140318.27450.043831.29940.07211.2818.24490.01641.0260.12371.158318.24490.0465Camera man11.25180.03511.254918.25880.01581.1770.06111.254918.25880.042121.25490.04981.264118.16480.01251.15570.09041.204718.16480.045931.28960.0621.245718.07330.01111.14540.11481.201818.07330.0609Tulips11.18510.0931.242717.40910.01531.18240.14831.19917.40910.065721.19340.09651.2817.41960.01051.1770.12311.19917.41960.045831.09160.11311.286417.39190.0111.14790.25481.182417.39190.0447White flower11.06220.04311.254916.75030.01281.03850.07641.187916.75030.041321.12030.05461.254916.76390.01061.08930.0751.193416.76390.045831.09160.04571.251816.83770.01691.0260.07851.187916.83770.047Fruits11.20470.04891.2817.56930.0131.14280.08291.210417.56930.051321.21040.09221.242717.61370.01391.13020.09671.216117.61370.04431.21610.05081.264117.57180.01481.12520.08311.196217.57180.0455

Experiments (cont.)

The Second Experiment In this experiment, four operations: 1- LWT-Zigzag-Arithmetic 2- LWT-Zigzag-LBGArithmetic 3- LWT-Zigzag- Huffman 4- LWT-Zigzag-LBGHuffmanTable 2 showing results for the process lossy and lossless image compression to the five images using the lifting wavelet transform with arithmetic coding and huffman coding without the use of the LBG, as well as with the use of the LBG and that using three decomposition levels.

Experiments (cont.)Lifting wavelet transform, vector quantization (LBG), Arithmetic and Huffman coding

LWTLWT Zigzag ArithmeticLWT Zigzag LBG & ArithmeticLWT Zigzag HuffmanLWT Zigzag LBG & HuffmanImageLevelC.RatioRunning time (Sec)C.RatiopsnrRunning time (Sec)C.RatioRunning time (Sec)C.RatiopsnrRunning time (Sec)Lena11.40650.31771.684213.18760.00811.37630.06741.454513.18760.021621.37630.42311.64111.97840.00971.1130.05271.471211.97840.016231.16360.04891.684217.43940.00731.0940.07081.454517.43940.0154Camera man11.54210.06581.64113.68950.00761.26730.05111.471213.68950.01721.24270.03261.753412.70650.00931.13270.04011.422212.70650.015531.14280.03761.662316.96490.00741.12280.08361.422216.96490.0204Tulips11.02750.09471.777716.29790.01221.37630.13571.454517.00320.019621.43820.13361.64112.26710.01111.0940.10541.471212.26710.022531.25490.11741.684219.54650.00731.05780.10671.454519.54650.0162White flower11.39130.041.64115.46610.00731.37630.05371.471215.46610.018221.30610.04731.706614.37030.01181.25490.05281.454514.37030.018631.16360.08271.64116.12410.00741.25490.05991.471216.12410.0162Fruits11.23970.04531.777712.33940.00911.12280.05571.406512.33940.01621.37630.0791.64112.22890.00891.1130.09021.471212.22890.016431.19620.08741.620218.16020.00741.07560.06521.406518.16020.0164

Experiments (cont.)

The Third Experiment In this experiment, four operations:1- SWT-Zigzag-Arithmetic 2- SWTZigzag-LBGArithmetic3- SWT-Zigzag- Huffman4- SWTZigzag-LBGHuffmanIn the table 3, showing results for the process lossy and lossless image compression to five images using stationary wavelet transform with arithmetic coding and Huffman coding without the use of the LBG, as well as with the use of the LBG and that using three decomposition levels.

Experiments (cont.)

Stationary wavelet transform, vector quantization (LBG), Arithmetic and Huffman coding

SWTSWT Zigzag ArithmeticSWT Zigzag LBG & ArithmeticSWT Zigzag HuffmanSWT Zigzag LBG & HuffmanImageLevelC.RatioRunning time(Sec)C.RatiopsnrRunning time(Sec)C.RatioRunning time(Sec)C.RatiopsnrRunning time(Sec)Lena14.36670.11555.007318.01210.06852.62560.8594.818818.01210.047324.36670.04145.007318.89820.0122.62560.84394.818818.89820.045534.36670.19065.007318.89820.01372.62560.85764.818818.89820.0422Camera man14.10420.06515.007316.84830.0112.67710.91574.85316.84830.041924.10420.05375.007318.10990.0112.67710.83464.85318.10990.044734.10420.03985.007318.10990.01032.67710.94814.85318.10990.0462Tulips13.86410.09345.657418.67870.00992.75630.89654.602218.67870.046123.86410.09615.657417.17980.01162.75630.92894.602217.17980.045633.86410.09695.657417.17980.01212.75630.89194.602217.17980.0421White flower13.73720.03934.958817.30020.01172.70180.84834.675717.30020.045923.73720.03924.958817.21420.01282.70180.84384.675717.21420.045933.73720.0414.958817.21420.0122.70180.84114.675717.21420.0412Fruits13.8280.05845.107218.95030.01322.73790.84384.320618.95030.043523.8280.4585.107218.17390.01052.73790.85854.320618.17390.056733.8280.11885.107218.17390.0122.73790.84634.320618.17390.043

Experiments (cont.)

Average Compression Ratio Level 1

In level - 1, we find that SWT & LBG Zigzag arithmetic the best thing, and find that arithmetic the best of huffman with everyone.

Experiments (cont.)

Average Compression Ratio Level 2 In level - 2 , We find that SWT & LBG Zigzag Arithmetic the best thing , and find that Arithmetic the best of Huffman with everyone, and firming (SWT) as in level 1, and the high rate of (DWT) and low rate (LWT) .

Experiments (cont.)

Average Compression Ratio Level 3In level - 3, we find that SWT & LBG Zigzag Arithmetic the best thing, and find that Arithmetic the best of Huffman with everyone, and firming (SWT) as in level 1 & 2, and the low rate of (DWT) and low rate (LWT).

1- Compression ratio in LBG Bigger without LBG.2- Stationary wavelet transform best transform.3- Arithmetic coding best of Huffman coding.4- That the best path for image compression is Stationary wavelet transform - zigzag scan Vector Quantization (LBG) - Arithmetic coding where the compression ratio achieved 5.1476 in 0.02286 Running time (Sec).

Results Analysis

This thesis introduced a novel approach that is built to work on image compression. Our approach used vector quantization LBG, Arithmetic coding and Huffman coding with three types of wavelet transforms such as Discrete Wavelet Transform DWT, Lifting Wavelet Transform LWT, and Stationary Wavelet Transform SWT on three decomposition levels. As in Stationary Wavelet Transform (SWT) compression ratio is fixed at a high level, and Discrete Wavelet Transform (DWT) compression ratio variable at a high level, either Lifting Wavelet Transform (LWT) is less than the compression at high level. We conclude that arithmetic coding is better than Huffman coding in terms of compression ratio and time. We found that the best way to compression in this system is the stationary wavelet transforms (SWT), LBG vector quantization, and arithmetic coding where it gives the best compression ratio with less time possible. Also the size of compressed data by adding arithmetic coding is better than adding Huffman coding to SWT.

CONCLUSION

Lossy Compression Using Stationary Wavelet Transform and Vector Quantization

Produced byOmar Ghazi Abbood Khukre

Master Student in Department of Information Technology, Institute of Graduate Studies and Research, Alexandria University, Egypt