Lossless and low-cost integer-based lifting wavelet transform

Discrete wavelet transform (DWT) is a powerful tool for analyzing real-time signals, including aperiodic, irregular, noisy, and transient data, because of its capability to explore signals in both the frequency- and time-domain in different resolutions. For this reason, they are used extensively in a wide number of applications in image and signal processing. Despite the wide usage, the implementation of the wavelet transform is usually lossy or computationally complex, and it requires expensive hardware. However, in many applications, such as medical diagnosis, reversible data-hiding, and critical satellite data, lossless implementation of the wavelet transform is desirable. It is also important to have more hardware-friendly implementations due to its recent inclusion in signal processing modules in system-on-chips (SoCs). To address the need, this research work provides a generalized implementation of a wavelet transform using an integer-based lifting method to produce lossless and low-cost architecture while maintaining the performance close to the original wavelets. In order to achieve a general implementation method for all orthogonal and biorthogonal wavelets, the Daubechies wavelet family has been utilized at first since it is one of the most widely used wavelets and based on a systematic method of construction of compact support orthogonal wavelets. Though the first two phases of this work are for Daubechies wavelets, they can be generalized in order to apply to other wavelets as well. Subsequently, some techniques used in the primary works have been adopted and the critical issues for achieving general lossless implementation have solved to propose a general lossless method. The research work presented here can be divided into several phases. In the first phase, low-cost architectures of the Daubechies-4 (D4) and Daubechies-6 (D6) wavelets have been derived by applying the integer-polynomial mapping. A lifting architecture has been used which reduces the cost by a half compared to the conventional convolution-based approach. The application of integer-polynomial mapping (IPM) of the polynomial filter coefficient with a floating-point value further decreases the complexity and reduces the loss in signal reconstruction. Also, the “resource sharing” between lifting steps results in a further reduction in implementation costs and near-lossless data reconstruction. In the second phase, a completely lossless or error-free architecture has been proposed for the Daubechies-8 (D8) wavelet. Several lifting variants have been derived for the same wavelet, the integer mapping has been applied, and the best variant is determined in terms of performance, using entropy and transform coding gain. Then a theory has been derived regarding the impact of scaling steps on the transform coding gain (GT). The approach results in the lowest cost lossless architecture of the D8 in the literature, to the best of our knowledge. The proposed approach may be applied to other orthogonal wavelets, including biorthogonal ones to achieve higher performance. In the final phase, a general algorithm has been proposed to implement the original filter coefficients expressed by a polyphase matrix into a more efficient lifting structure. This is done by using modified factorization, so that the factorized polyphase matrix does not include the lossy scaling step like the conventional lifting method. This general technique has been applied on some widely used orthogonal and biorthogonal wavelets and its advantages have been discussed. Since the discrete wavelet transform is used in a vast number of applications, the proposed algorithms can be utilized in those cases to achieve lossless, low-cost, and hardware-friendly architectures

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

DESIGN AND IMPLEMENTATION OF LIFTING BASED DAUBECHIES WAVELET TRANSFORMS USING ALGEBRAIC INTEGERS

Over the past few decades, the demand for digital information has increased drastically. This enormous demand poses serious difficulties on the storage and transmission bandwidth of the current technologies. One possible solution to overcome this approach is to compress the amount of information by discarding all the redundancies. In multimedia technology, various lossy compression techniques are used to compress the raw image data to facilitate storage and to fit the transmission bandwidth. In this thesis, we propose a new approach using algebraic integers to reduce the complexity of the Daubechies-4 (D4) and Daubechies-6 (D6) Lifting based Discrete Wavelet Transforms. The resulting architecture is completely integer based, which is free from the round-off error that is caused in floating point calculations. The filter coefficients of the two transforms of Daubechies family are individually converted to integers by multiplying it with value of 2x, where, x is a random value selected at a point where the quantity of losses is negligible. The wavelet coefficients are then quantized using the proposed iterative individual-subband coding algorithm. The proposed coding algorithm is adopted from the well-known Embedded Zerotree Wavelet (EZW) coding. The results obtained from simulation shows that the proposed coding algorithm proves to be much faster than its predecessor, and at the same time, produces good Peak Signal to Noise Ratio (PSNR) at very low bit rates. Finally, the two proposed transform architectures are implemented on Virtex-E Field Programmable Gate Array (FPGA) to test the hardware cost (in terms of multipliers, adders and registers) and throughput rate. From the synthesis results, we see that the proposed algorithm has low hardware cost and a high throughput rate

A Novel Methodology for Memory Reduction in Distributed Arithmetic Based Discrete Wavelet Transform

AbstractDiscrete Wavelet Transform (DWT) is widely used in image compression standards such as JPEG 2000. DWT can be implemented on FPGA using parallel Distributed Arithmetic (DA) architecture, which is suitable for low power implementation. However, the size of the memory in DA increases with the number of wavelet coefficients. In this paper, we propose a novel methodology to reduce the size of the Look-Up Tables (LUTs) used in DA for DWT. The table entries are sorted using Burrows-Wheeler Transform (BWT) and then compressed. The compressed table is stored in memory. During DWT/IDWT computation, without reconstructing the entire table we can recover only the required table entry. A comparative study of this methodology among different wavelets is performed. We demonstrate that the method is very effective for reducing the memory of DA architectures. A compression ratio of around 2.3:1 is achieved for the look-up table which stores the inner product of high-pass filter coefficients of Daubechies-4 (Db4) wavelet which is used in JPEG2000

Speech Compression Using Discrete Wavelet Transform

Speech compression is an area of digital processing that is focusing on reducing bit rate of the speech signal for transmission or storage without significant loss of quality. Wavelet transform has been recently proposed for signal analysis. Speech signal compression using wavelet transform is given a considerable attention in this thesis. Speech coding is a lossy scheme and is implemented here to compress onedimensional speech signal. Basically, this scheme consists of four operations which are the transform, threshold techniques (by level and global threshold), quantization, and entropy encoding operations. The reconstruction of the compressed signal as well as the detailed steps needed are discussed.The performance of wavelet compression is compared against linear Productive Coding and Global System for Mobile Communication (GSM) algorithms using SNR, PSNR, NRMSE and compression ratio. Software simulating the lossy compression scheme is developed using Matlab 6. This software provides the basic speech analysis as well as the compression and decompression operations. The results obtained show reasonably high compression ratio and good signal quality

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

Design of wireless swallowable capsule with minimum power consumption and high resolution images

Medical technology has undergone major breakthroughs in recent years, especially in the area of the examination tools for diagnostic purposes. The traditional examination method for the diagnosis of gastrointestinal diseases is gastroscopy with the use of an endoscope. Wireless camera pill has created a new perspective for engineers and physicians. After years of great innovation, commercial swallowable pills have been produced and applied in clinical practice. These pills can cover the examination of the gastrointestinal system and provide to the physicians not only a lot more useful data that is not available from the traditional methods, but also elimination of the use of the painful endoscopy procedure. In this paper, a new design of the wireless swallowable pills has been proposed. It takes advantage of the benefits of every sub-system, like camera lenses, image compressor and RF sub-system. In this way our system can provide enough and accurate data to the physicians

Image Compression Techniques by using Wavelet Transform

This paper is concerned with a certain type of compression techniques by using wavelet transforms. Wavelets are used to characterize a complex pattern as a series of simple patterns and coefficients that, when multiplied and summed, reproduce the original pattern.  The data compression schemes can be divided into lossless and lossy compression. Lossy compression generally provides much higher compression than lossless compression. Wavelets are a class of functions used to localize a given signal in both space and scaling domains. A MinImage was originally created to test one type of wavelet and the additional functionality was added to Image to support other wavelet types, and the EZW coding algorithm was implemented to achieve better compression. Keywords: Wavelet Transforms, Image Compression, Lossless Compression, Lossy Compressio