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Image Coding Using Zero Tree Wavelet

Published on Apr 02, 2024


Image compression is very important for efficient transmission and storage of images. Embedded Zerotree Wavelet (EZW) algorithm is a simple yet powerful algorithm having the property that the bits in the stream are generated in the order of their importance.

Image compression can improve the performance of the digital systems by reducing time and cost in image storage and transmission without significant reduction of the image quality. For image compression it is desirable that the selection of transform should reduce the size of resultant data set as compared to source data set. EZW is computationally very fast and among the best image compression algorithm known today.

This paper proposes a technique for image compression which uses the Wavelet-based Image Coding. A large number of experimental results are shown that this method saves a lot of bits in transmission, further enhances the compression performance. This paper aims to determine the best threshold to compress the still image at a particular decomposition level by using Embedded Zero-tree Wavelet encoder. Compression Ratio (CR) and Peak-Signal-to-Noise (PSNR) is determined for different threshold values ranging from 6 to 60 for decomposition level 8.

Introduction of Image Coding Using Zero Tree Wavelet

Most natural images have smooth colour variations, with the fine details being represented as sharp edges in between the smooth variations. Technically, the smooth variations in colour can be termed as low frequency variations and the sharp variations as high frequency variations. The low frequency components (smooth variations) constitute the base of an image, and the highfrequency components (the edges which give the detail)add upon them to refine the image, thereby giving a detailed image. Hence, the smooth variations are demanding more importance than the details. Separating the smooth variations and details of the image can be done in many ways. One such way is the decomposition of the image using a Discrete Wavelet Transform (DWT).

Wavelets are being used in a number of different applications. The practical implementation of wavelet compression schemes is very similar to that of subband coding schemes. As in the case of subband coding, the signal is decomposed using filter banks. In a discrete wavelet transform, an image can be analyzed by passing it through an analysis filter bank followed by a decimation operation. This analysis filter bank, which consists of a low pass and a high pass filter at each decomposition stage, is commonly used in image compression.

When a signal passes through these filters, it is split into two bands. The low pass filter, which corresponds to an averaging operation, extracts the coarse information of the signal. The high pass filter, which corresponds to a differencing operation, extracts the detail information of the signal. The output of the filtering operations is then decimated by two. A two-dimensional transform can be accomplished by performing two separate one-dimensional transforms. First, the image is filtered along the x-dimension using low pass and high pass analysis filters and decimated by two.

Low pass filtered coefficients are stored on the leftpart of the matrix and high pass filtered on the right.Because of decimation, the total size of the transformed image is same as the original image. Then, it is followed by filtering the sub-image along the y-dimension and decimated by two. Finally, the image has been split into four bands denoted by LL, HL, LH, and HH, after one level of decomposition. The LL band is again subject to the same procedure.

Quantization :

Quantization refers to the process of approximating the continuous set of values in the image data with a finite, preferably small, set of values. The input to a quantizer is the original data and the output is always one among a finite number of levels. The quantizer is a function whose set of output values are discrete and usually finite. Obviously, this is a process of approximation and a good quantizer is one which represents the original signal with minimum loss or distortion.

here are two types of quantization: scalar quantization and vector quantization. In scalar quantization, each input symbol is treated in producing the output while in vector quantization the input symbols are clubbed together in groups called vectors, and processed to give the output. This clubbing of data and treating them as a single unit,increases the optimality of the vector quantizer, but at thecost of increased computational complexity

Image coding utilizing scalar quantization on hierarchical structures of transformed images has been a very effective and computationally simple technique. Shapiro was the first to introduce such a technique with his EZW [13] algorithm. Different variants of this technique have appeared in the literatures which providean improvement over the initial work. Said & Pearlman[1] successively improved the EZW algorithm byextending this coding scheme, and succeeded in presenting a different implementation based on a setpartitioning sorting algorithm. This new coding scheme, called the SPIHT [1], provided an even better performance than the improved version of EZW.

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