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

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