Fast and Scalable Architectures and Algorithms for the Computation of the Forward and Inverse Discrete Periodic Radon Transform with Applications to 2D Convolutions and Cross-Correlations

作     者：Cesar Carranza 

作者单位：University of New Mexico 

学位级别：博士

导师姓名：Marios Pattichis

授予年度：2016年

摘      要：The Discrete Radon Transform (DRT) is an essential component of a wide range of applications in image processing, e.g. image denoising, image restoration, texture analysis, line detection, encryption, compressive sensing and reconstructing objects from projections in computed tomography and magnetic resonance imaging. A popular method to obtain the DRT, or its inverse, involves the use of the Fast Fourier Transform, with the inherent approximation/rounding errors and increased hardware complexity due the need for floating point arithmetic implementations. An alternative implementation of the DRT is through the use of the Discrete Periodic Radon Transform (DPRT). The DPRT also exhibits discrete properties of the continuous-space Radon Transform, including the Fourier Slice Theorem and the convolution property. Unfortunately, the use of the DPRT has been limited by the need to compute a large number of additions O(N^3) and the need for a large number of memory accesses. This PhD dissertation introduces a fast and scalable approach for computing the forward and inverse DPRT that is based on the use of: (i) a parallel array of fixed-point adder trees, (ii) circular shift registers to remove the need for accessing external memory components when selecting the input data for the adder trees, and (iii) an image block-based approach to DPRT computation that can fit the proposed architecture to available resources, and as a result, for an NxN image (N prime), the proposed approach can compute up to N^2 additions per clock cycle. Compared to previous approaches, the scalable approach provides the fastest known implementations for different amounts of computational resources. For the fastest case, I introduce optimized architectures that can compute the DPRT and its inverse in just 2N +ceil(log2 N)+1 and 2N +3(log2 N)+B+2 clock cycles respectively, where B is the number of bits used to represent each input pixel. In comparison, the prior state of the art method required N^2 +N