Orthonormal and biorthonormal filter banks as convolvers, and convolutional coding gain

Convolution theorems for filter bank transformers are introduced. Both uniform and nonuniform decimation ratios are considered, and orthonormal as well as biorthonormal cases are addressed. All the theorems are such that the original convolution reduces to a sum of shorter, decoupled convolutions in the subbands. That is, there is no need to have cross convolution between subbands. For the orthonormal case, expressions for optimal bit allocation and the optimized coding gain are derived. The contribution to coding gain comes partly from the nonuniformity of the signal spectrum and partly from nonuniformity of the filter spectrum. With one of the convolved sequences taken to be the unit pulse function,,e coding gain expressions reduce to those for traditional subband and transform coding. The filter-bank convolver has about the same computational complexity as a traditional convolver, if the analysis bank has small complexity compared to the convolution itself

Image Compression using Discrete Cosine Transform & Discrete Wavelet Transform

Image Compression addresses the problem of reducing the amount of data required to represent the digital image. Compression is achieved by the removal of one or more of three basic data redundancies: (1) Coding redundancy, which is present when less than optimal (i.e. the smallest length) code words are used; (2) Interpixel redundancy, which results from correlations between the pixels of an image & (3) psycho visual redundancy which is due to data that is ignored by the human visual system (i.e. visually nonessential information). Huffman codes contain the smallest possible number of code symbols (e.g., bits) per source symbol (e.g., grey level value) subject to the constraint that the source symbols are coded one at a time. So, Huffman coding when combined with technique of reducing the image redundancies using Discrete Cosine Transform (DCT) helps in compressing the image data to a very good extent. The Discrete Cosine Transform (DCT) is an example of transform coding. The current JPEG standard uses the DCT as its basis. The DC relocates the highest energies to the upper left corner of the image. The lesser energy or information is relocated into other areas. The DCT is fast. It can be quickly calculated and is best for images with smooth edges like photos with human subjects. The DCT coefficients are all real numbers unlike the Fourier Transform. The Inverse Discrete Cosine Transform (IDCT) can be used to retrieve the image from its transform representation. The Discrete wavelet transform (DWT) has gained widespread acceptance in signal processing and image compression. Because of their inherent multi-resolution nature, wavelet-coding schemes are especially suitable for applications where scalability and tolerable degradation are important. Recently the JPEG committee has released its new image coding standard, JPEG-2000, which has been based upon DWT

Block wavelet transforms for image coding

Cataloged from PDF version of article.In this paper, a new class of block transforms is presented. These transforms are constructed from subband decomposition filter banks corresponding to regular wavelets. New transforms are compared to the discrete cosine transform (DCT). Image coding schemes that employ the block wavelet transform (BWT) are developed. BWT's can be implemented by fast (O(N log N)) algorithms

Image Compression Using Subband Wavelet Decomposition and DCT-based Quantization

International audienceThe aim of this work is to evaluate the performance of an image compression system based on wavelet-based subband decomposition. The compression method used in this paper differs from the classical procedure in the direction where the scalar quantization of the coarse scale approximation sub-image is replaced by a discrete cosine transform (DCT) based quantization. The images were decomposed using wavelet filters into a set of subbands with different resolutions corresponding to different frequency bands. The resulting high frequency subbands were vector quantized according to the magnitude of their variances. The coarse scale approximation sub-image is quantized using scalar quantization and then using DCT base quantization to show the benefit of this new optional method in term of CPU computationa1 cost vs restitution quality

Image Compression by Wavelet Transform.

Digital images are widely used in computer applications. Uncompressed digital images require considerable storage capacity and transmission bandwidth. Efficient image compression solutions are becoming more critical with the recent growth of data intensive, multimedia-based web applications. This thesis studies image compression with wavelet transforms. As a necessary background, the basic concepts of graphical image storage and currently used compression algorithms are discussed. The mathematical properties of several types of wavelets, including Haar, Daubechies, and biorthogonal spline wavelets are covered and the Enbedded Zerotree Wavelet (EZW) coding algorithm is introduced. The last part of the thesis analyzes the compression results to compare the wavelet types

A comparative study of image compress schemes

Image compression is an important and active area of signal processing. All popular image compression techniques consist of three stages: Image transformation, quantization (lossy compression only), and lossless coding (of quantized transform coefficients). This thesis deals with a comparative study of several lossy image compression techniques. First, it reviews the well-known techniques of each stage. Starting with the first stage, the techniques of orthogonal block transformation and subband transform are described in detail. Then the quantization stage is described, followed by a brief review of the techniques for the third stage, lossless coding. Then these different image compression techniques are simulated and their rate-distortion performance are compared with each other. The results show that two-band multiplierless PR-QMF bank based subband image codec outperforms other filter banks considered in this thesis. It is also shown that uniform quantizers with a dead-zone perform best. Also, the multiplierless PR-QMF bank outperforms the DCT based on uniform quantization, but underperforms the DCT based on uniform quantization with a dead-zone

Wavelet Based Image Coding Schemes : A Recent Survey

A variety of new and powerful algorithms have been developed for image compression over the years. Among them the wavelet-based image compression schemes have gained much popularity due to their overlapping nature which reduces the blocking artifacts that are common phenomena in JPEG compression and multiresolution character which leads to superior energy compaction with high quality reconstructed images. This paper provides a detailed survey on some of the popular wavelet coding techniques such as the Embedded Zerotree Wavelet (EZW) coding, Set Partitioning in Hierarchical Tree (SPIHT) coding, the Set Partitioned Embedded Block (SPECK) Coder, and the Embedded Block Coding with Optimized Truncation (EBCOT) algorithm. Other wavelet-based coding techniques like the Wavelet Difference Reduction (WDR) and the Adaptive Scanned Wavelet Difference Reduction (ASWDR) algorithms, the Space Frequency Quantization (SFQ) algorithm, the Embedded Predictive Wavelet Image Coder (EPWIC), Compression with Reversible Embedded Wavelet (CREW), the Stack-Run (SR) coding and the recent Geometric Wavelet (GW) coding are also discussed. Based on the review, recommendations and discussions are presented for algorithm development and implementation.Comment: 18 pages, 7 figures, journa

Hardware Acceleration of the Embedded Zerotree Wavelet Algorithm

The goal of this project was to gain experience in designing and implementing a microelectronic system to acclerate the execution of a time-consuming software algorithm, the Embedded Zerotree Wavelet (EZW), which is used in multimedia applications. The algorithm was implemented using MATLAB to be certain it was fully understood and to serve as a validation reference. Then, the algorithm was mapped into a hardware description language, VHDL, and its resulting implementation verified with the golden reference. The hardware description was then targeted to a field-programmable gate array (FPGA). Significant acceleration was achieved since the hardware implementation in a FPGA (Xilinx Virtex-1000E using a 8.315 MHz clock) ran 10,000 times faster than the MATLAB implementation on a SUN-220 workstation. Additional speedup exploiting the parallel capabilities of the FPGA was not achieved since the EZW algorithm utilizes only sequential operations