Authors: W Stefan A Viswanathan A Gelb R Renaut
Publish Date: 2011/09/22
Volume: 50, Issue: 3, Pages: 536-556
Abstract
We present a new method for estimating the edges in a piecewise smooth function from blurred and noisy Fourier data The proposed method is constructed by combining the so called concentration factor edge detection method which uses a finite number of Fourier coefficients to approximate the jump function of a piecewise smooth function with compressed sensing ideas Due to the global nature of the concentration factor method Gibbs oscillations feature prominently near the jump discontinuities This can cause the misidentification of edges when simple thresholding techniques are used In fact the true jump function is sparse ie zero almost everywhere with nonzero values only at the edge locations Hence we adopt an idea from compressed sensing and propose a method that uses a regularized deconvolution to remove the artifacts Our new method is fast in the sense that it only needs the solution of a single l 1 minimization Numerical examples demonstrate the accuracy and robustness of the method in the presence of noise and blur
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