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

A flexible hardware architecture for 2-D discrete wavelet transform: design and FPGA implementation

The Discrete Wavelet Transform (DWT) is a powerful signal processing tool that has recently gained widespread acceptance in the field of digital image processing. The multiresolution analysis provided by the DWT addresses the shortcomings of the Fourier Transform and its derivatives. The DWT has proven useful in the area of image compression where it replaces the Discrete Cosine Transform (DCT) in new JPEG2000 and MPEG4 image and video compression standards. The Cohen-Daubechies-Feauveau (CDF) 5/3 and CDF 9/7 DWTs are used for reversible lossless and irreversible lossy compression encoders in the JPEG2000 standard respectively. The design and implementation of a flexible hardware architecture for the 2-D DWT is presented in this thesis. This architecture can be configured to perform both the forward and inverse DWT for any DWTfamily, using fixed-point arithmetic and no auxiliary memory. The Lifting Scheme method is used to perform the DWT instead of the less efficient convolution-based methods. The DWT core is modeled using MATLAB and highly parameterized VHDL. The VHDL model is synthesized to a Xilinx FPGA to prove hardware functionality. The CDF 5/3 and CDF 9/7 versions of the DWT are both modeled and used as comparisons throughout this thesis. The DWT core is used in conjunction with a very simple image denoising module to demonstrate the potential of the DWT core to perform image processing techniques. The CDF 5/3 hardware produces identical results to its theoretical MATLAB model. The fixed point CDF 9/7 deviates very slightly from its floating-point MATLAB model with a ~59dB PSNR deviation for nine levels of DWT decomposition. The execution time for performing both DWTs is nearly identical at -14 clock cycles per image pixel for one level of DWT decomposition. The hardware area generated for the CDF 5/3 is -16,000 gates using only 5% of the Xilinx FPGA hardware area, 2.185 MHz maximum clock speed and 24 mW power consumption. The simple wavelet image denoising techniques resulted in cleaned images up to -27 PSNR

Implementation of fingerprint based biometric system using optimized 5/3 DWT architecture and modified CORDIC based FFT

The real-time biometric systems are used to authenticate persons for wide range of security applications. In this paper, we propose implementation of fingerprint-based biometric system using Optimized 5/3 DWT architecture and Modified CORDIC-based Fast Fourier Transform (FFT). The Optimized 2D-DWT architecture is designed using Optimized 1D-DWT architectures, Memory Units and novel Controller Unit which is used to scan rows and columns of an image. The database fingerprint image is applied to the proposed Optimized 2D-DWT architecture to obtain four sub-bands of LL, LH, HL and HH. The efficient architecture of FFT is designed by using Modified CORDIC processor which generates twiddle factor angles of range – using Pre-processing Unit and Comparator Block. Further, the LL sub-band coefficients are applied to the Modified CORDIC based FFT to generate final fingerprint

Field Programmable Gate Arrays (FPGAs) II

This Edited Volume Field Programmable Gate Arrays (FPGAs) II is a collection of reviewed and relevant research chapters, offering a comprehensive overview of recent developments in the field of Computer and Information Science. The book comprises single chapters authored by various researchers and edited by an expert active in the Computer and Information Science research area. All chapters are complete in itself but united under a common research study topic. This publication aims at providing a thorough overview of the latest research efforts by international authors on Computer and Information Science, and open new possible research paths for further novel developments

Efficient architectures for multidimensional discrete transforms in image and video processing applications

PhD ThesisThis thesis introduces new image compression algorithms, their related architectures and data transforms architectures. The proposed architectures consider the current hardware architectures concerns, such as power consumption, hardware usage, memory requirement, computation time and output accuracy. These concerns and problems are crucial in multidimensional image and video processing applications. This research is divided into three image and video processing related topics: low complexity non-transform-based image compression algorithms and their architectures, architectures for multidimensional Discrete Cosine Transform (DCT); and architectures for multidimensional Discrete Wavelet Transform (DWT). The proposed architectures are parameterised in terms of wordlength, pipelining and input data size. Taking such parameterisation into account, efficient non-transform based and low complexity image compression algorithms for better rate distortion performance are proposed. The proposed algorithms are based on the Adaptive Quantisation Coding (AQC) algorithm, and they achieve a controllable output bit rate and accuracy by considering the intensity variation of each image block. Their high speed, low hardware usage and low power consumption architectures are also introduced and implemented on Xilinx devices. Furthermore, efficient hardware architectures for multidimensional DCT based on the 1-D DCT Radix-2 and 3-D DCT Vector Radix (3-D DCT VR) fast algorithms have been proposed. These architectures attain fast and accurate 3-D DCT computation and provide high processing speed and power consumption reduction. In addition, this research also introduces two low hardware usage 3-D DCT VR architectures. Such architectures perform the computation of butterfly and post addition stages without using block memory for data transposition, which in turn reduces the hardware usage and improves the performance of the proposed architectures. Moreover, parallel and multiplierless lifting-based architectures for the 1-D, 2-D and 3-D Cohen-Daubechies-Feauveau 9/7 (CDF 9/7) DWT computation are also introduced. The presented architectures represent an efficient multiplierless and low memory requirement CDF 9/7 DWT computation scheme using the separable approach. Furthermore, the proposed architectures have been implemented and tested using Xilinx FPGA devices. The evaluation results have revealed that a speed of up to 315 MHz can be achieved in the proposed AQC-based architectures. Further, a speed of up to 330 MHz and low utilisation rate of 722 to 1235 can be achieved in the proposed 3-D DCT VR architectures. In addition, in the proposed 3-D DWT architecture, the computation time of 3-D DWT for data size of 144×176×8-pixel is less than 0.33 ms. Also, a power consumption of 102 mW at 50 MHz clock frequency using 256×256-pixel frame size is achieved. The accuracy tests for all architectures have revealed that a PSNR of infinite can be attained

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

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior

Remote Sensing Data Compression

A huge amount of data is acquired nowadays by different remote sensing systems installed on satellites, aircrafts, and UAV. The acquired data then have to be transferred to image processing centres, stored and/or delivered to customers. In restricted scenarios, data compression is strongly desired or necessary. A wide diversity of coding methods can be used, depending on the requirements and their priority. In addition, the types and properties of images differ a lot, thus, practical implementation aspects have to be taken into account. The Special Issue paper collection taken as basis of this book touches on all of the aforementioned items to some degree, giving the reader an opportunity to learn about recent developments and research directions in the field of image compression. In particular, lossless and near-lossless compression of multi- and hyperspectral images still remains current, since such images constitute data arrays that are of extremely large size with rich information that can be retrieved from them for various applications. Another important aspect is the impact of lossless compression on image classification and segmentation, where a reasonable compromise between the characteristics of compression and the final tasks of data processing has to be achieved. The problems of data transition from UAV-based acquisition platforms, as well as the use of FPGA and neural networks, have become very important. Finally, attempts to apply compressive sensing approaches in remote sensing image processing with positive outcomes are observed. We hope that readers will find our book useful and interestin