Pixel Recovery via l1 Minimization in the Wavelet Domain (TP-L2)

Author(s) : Ivan Selesnick (Polytechnic University, USA) Richard Van Slyke (Polytechnic University, USA) Onur Guleryuz (DoCoMo USA Laboratories, Inc., USA)

Abstract : This paper uses probability models on expansive wavelet transform coefficients with interpolation constraints to estimate missing blocks in images. We use simple probability models on wavelet coefficients to formulate the estimation process as a linear programming problem and solve it to recover the missing pixels. Our formulation is general and can be augmented with more sophisticated probability models to obtain even better estimates on a variety of image regions. The presented approach has many parallels to recently introduced dictionary based signal representations with which it shares certain optimality properties. We provide simulation examples over edge regions and compare results to an earlier nonconvex technique which utilizes similar ideas on overcomplete dictionaries.

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