Applied Math-Multichannel deconvolution with Fourier and wavelet regularization

Speaker: Dr. Debdeep Bhattacharya

Date and Time: October 1st, 3:15p-4:15p DC time

Place: Rome Hall 771

Title: Multichannel deconvolution with Fourier and wavelet regularization

Abstract: The deconvolution problem naturally occurs in the fields of signal and image processing where the goal is to estimate an unknown signal function that is blurred in the presence of an additive noise, mostly due to sensor limitations or external interference. In this talk, we focus on multichannel deconvolution, where multiple observations of the same signal are available. Each observation corresponds to a sensor (or channel) with its own impulse response and noise level. This type of problem arises in electron microscopy, phased array antennas, and in computational photography.

In this talk, we propose a hybrid approach to perform a multichannel deconvolution both in Fourier and the wavelet domains to exploit the independence of the noise data present in various channels. We extend the framework of Fourier-Wavelet Regularized Deconvolution (ForWaRD) introduced by Neelamani, Baranuik, and Choi (2004) to the multichannel setup by first deconvolving the observations partially using a regularized Schiske deconvolution. Next, we trim the effective leaked noise in a wavelet domain to obtain the estimate. We determine the ideal regularization parameter for oracle thresholding by minimizing a cost function that approximates the mean-squared error. The advantage of our approach over a single-channel deconvolution and over Fourier-based multichannel techniques is demonstrated numerically for various signals. As an application, we use our algorithm to deconvolve electro-magnetic signals recorded by the Antarctic Impulsive Transient Antenna (ANITA) project.