February Fourier Talks 2011

Rosemary Renaut


Sparsity enforcing edge detection method for blurred and noisy Fourier data


I will discuss a method for estimating the edges in a piecewise smooth function from blurred and noisy Fourier data. The proposed method is constructed by combining the Concentration Factor (CF) 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. While the CF method can cause misidentifi cation of edges when simple thresholding techniques are used, due to the Gibbs phenomenon, adopting an idea from compressed sensing and using a regularized deconvolution removes the artifacts.

This is joint work with

W. Stefan, A. Viswanathan, A. Gelb