Multiscale Higher Order TV for l1 Regularization and Applications to Particular Inverse Problems

Toby Sanders

Arizona State University

L1 regularization techniques have generated a great deal of attention with many variants to solve a wide variety of inverse problems. A key component for their success is that under certain assumptions, the solution of minimum L1 norm (a reasonably solvable problem) is a good approximation to the solution of minimum L0 norm (an NP hard problem). In this talk, we demonstrate for L1 regularization approaches, known as higher order total variation (HOTV), this approximation may yield suboptimal results in some instances. To overcome this drawback, we have developed a multiscale higher order total variation (MHOTV) approach, which we argue is closely related to the use of multiscale Daubechies wavelets. In the talk we will outline all of the necessary ingredients for efficient and effective implementation of the design, and show a number of promising numerical examples with both real and simulated data.

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