Obtaining a 35x Speedup in 2D Phase Unwrapping Using Commodity Graphics Processors

Abstract

Graphics processing units (GPUs) are a powerful tool The programmability of the most recent generation of for numerical computation. The GPU architecture and GPUs creates the opportunity to develop very powerful, low computational model are uniquely designed for high-resolution cost accelerators for key radar signal processing algorithms. In high-speed grid-based calculations. This capability can be this paper, we describe an experiment in the application of utilized to accelerate certain classes of compute-intensive radar GPUs to the two-dimensional phase unwrapping problem at signal processing algorithms. Characteristics of a problem wellsuited for computation on a GPU include high levels of data the heart of interferometric synthetic aperture radar (IFSAR) parallelism, low control logic, uniform boundary conditions, and processing. While phase unwrapping is relatively simple in well-defined input and output. one dimension, it becomes quite complex in multiple dimensions. One approach to the problem of recovering the We describe the implementation of two-dimensional multigrid * -least-squares weighted phase unwrapping on a GPU and original phase from a measurement of wrapped phase in the demonstrate a large speedup over C and MATLAB presence of noise or other distortions casts it into the implementations. Details of the GPU computation are provided. mathematical framework of a solution to the discretized Background information on the GPU architecture and its Poisson's equation [2]. The resulting least squares solution for applicability to general-purpose computation is discussed. the weighted phase unwrapping problem involves the use of an iterative solution technique requiring only scalar add, subtract, multiply, and divide operations at each step, and is

Unwrapping magnetic resonance phase maps with Chebyshev polynomials

“…The proposed phase-unwrapping algorithm computes each expansion coefficient in a single step unlike the iterative WLS method described in [26]. At least 4M 2 L operations are needed for the WLS method [24], where M is the number of pixels along one edge of the phase map and L is the number of iterations required to unwrap the phase map.…”

“…Both methods require the same number of operations when L=3N 2 . For example, the phase map in [26] required 11,712 iterations; the algorithm described in this note will require fewer operations as long as the expansion order is below 62. The proposed method has another advantage over the WLS method; the proposed method does not require a mask or threshold to be placed over the phase map as shown in Fig.…”

“…However, background noise and residues make this process a nontrivial task. To date, many phase-unwrapping algorithms have been proposed for or can be applied to MR applications, including path-following schemes [12,13], region growing techniques [6,[14][15][16], a cost function minimization technique [17], Markov random field methods [18,19], minimum spanning tree methods [20,21], unwrapped phase maps as the solution to Poisson's equation [22,23], a Fourier space method [24] and least squares methods [25][26][27]. It is still very difficult to obtain satisfactory results when noisy and/or dense fringes occur in the wrapped phase.…”

Implementing phase unwrapping using Field Programmable Gate Arrays or Graphics Processing Units: A comparison

“…Karasev et al [14] implement 2D phase unwrapping on NVIDIA GPUs using CG [15] and achieve a 35x speedup. They implement a weighted least squares algorithm and apply it to Interferometric Synthetic Aperture Radar (IFSAR) data.…”

Accelerating phase unwrapping and affine transformations for optical quadrature microscopy using CUDA

“…Previous work done on applying GPUs for 2D unwraps includes Karasev et al [8] who used GPUs to implement 2D phase unwrapping on NVIDIA GPUs using CG (C for Graphics), achieving a 35x speedup. They implemented a weighted least squares algorithm, similar to the PCG algorithm shown in Section 3.3.1, and applied it to Interferometric Synthetic Aperture Radar (IFSAR) data.…”