## “Plug-and-Play” Edge-Preserving Regularization

Donghui Chen, Misha E. Kilmer, and Per Christian Hansen

### Abstract

In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated algorithms are complex and require a good knowledge of large-scale optimization algorithms, and they involve certain tolerances that the user must choose. We present a simpler approach that relies only on standard computational building blocks in matrix computations, such as orthogonal transformations, preconditioned iterative solvers, Kronecker products, and the discrete cosine transform – hence the term “plug-and-play.” We do not attempt to improve on TV reconstructions, but rather provide an easy-to-use approach to computing reconstructions with similar properties.

Full Text (PDF) [969 KB]

### Key words

image deblurring, inverse problems, $p$-norm regularization, projection algorithm

65F22, 65F30

### Links to the cited ETNA articles

 [4] Vol. 28 (2007-2008), pp. 149-167 Julianne Chung, James G. Nagy, and Dianne P. O'Leary: A weighted-GCV method for Lanczos-hybrid regularization [9] Vol. 31 (2008), pp. 204-220 Per Christian Hansen and Toke Koldborg Jensen: Noise propagation in regularizing iterations for image deblurring

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