The Acceleration of Polynomial Methods for Blind Image Deconvolution Using Graphical Processing Units (GPUs)

Image processing has become an integral part of many areas of study. Unfortunately, the process of capturing images can often result in undesirable blurring and noise, and thus can make processing the resulting images problematic. Methods are therefore required that attempt to remove blurring. The main body of work in this field is in Bayesian methods for image deblurring, with many algorithms aimed at solving this problem relying on the Fourier transform. The Fourier transform results in the amplification of noise in the image, which can lead to many of the same problems as blurring. Winkler presented a method of blind image deconvolution (BID) without the Fourier transform, which treated the rows and columns of the blurred image as the coefficients of univariate polynomials. By treating the rows and columns of the image in this way, the problem of computing the blurring function becomes a problem of computing the greatest common divisor (GCD) of these polynomials. The computation of the GCD of two polynomials is ill posed, as any noise in the polynomials causes them to be coprime. Thus an approximate GCD (AGCD) must be computed instead. The computation of an AGCD is a computationally expensive process, resulting in the BID algorithm being expensive. The research presented in this thesis investigates the fundamental mathematical processes underpinning such an algorithm, and presents multiple methods through which this algorithm can be accelerated using a GPU. This acceleration results in an implementation that is 30 times faster than a CPU parallel approach. The process of accelerating the BID algorithm in this way required a first of its kind GPU accelerated algorithm for the computation of an AGCD, with multiple novel techniques utilised to achieve this acceleration

A GPU-Accelerated SVD Algorithm, Based on QR Factorization and Givens Rotations, for DWI Denoising

In this work, we present a parallel implementation of the Singular Value Decomposition (SVD) method on Graphics Processing Units (GPUs) using CUDA programming model. Our approach is based on an iterative parallel version of the QR factorization by means Givens plane rotations using the Sameh and Kuck scheme. The parallel algorithm is driven by an outer loop executed on the CPU. Therefore, threads and blocks configuration is organized in order to use the shared memory and avoid multiple accesses to global memory. However, the main kernel provides coalesced accesses to global memory using contiguous indices. As case study, we consider the application of the SVD in the Overcomplete Local Principal Component Analysis (OLPCA) algorithm for the Diffusion Weighted Imaging (DWI) denoising process. Our results show significant improvements in terms of performances with respect to the CPU version that encourage its usability for this expensive application