Blind deconvolution using TV regularization and Bregman iteration

In this paper we formulate a new time dependent model for blind deconvolution based on a constrained variational model that uses the sum of the total variation norms of the signal and the kernel as a regularizing functional. We incorporate mass conservation and the nonnegativity of the kernel and the signal as additional constraints. We apply the idea of Bregman iterative regularization, first used for image restoration by Osher and colleagues [S.J. Osher, M. Burger, D. Goldfarb, J.J. Xu, and W. Yin, An iterated regularization method for total variation based on image restoration, UCLA CAM Report, 04-13, (2004)]. to recover finer scales. We also present an analytical study of the model discussing uniqueness of the solution, convergence to steady state and a priori parameter estimation. We present a simple algorithmic implementation of the model and we perform a series of numerical experiments to show evidence of the good behavior of the numerical scheme and quality of the results, improving on results obtained by Chan and Wang [T.F. Chan and C.K. Wong, Total variation blind deconvolution, IEEE Trans Image Process 7 (1998), 370-375]. (c) 2005 Wiley Periodicals, Inc.