Augmented Lagrangian method for total variation restoration with non-quadratic fidelity
Chunlin Wu, Juyong Zhang, Xue‐Cheng Tai · Inverse Problems and Imaging · 2011
Recently augmented Lagrangian method has been successfully appliedto image restoration. We extend the method to total variation (TV)restoration models with non-quadratic fidelities. We will firstintroduce the method and present an iterative algorithm for TVrestoration with a quite general fidelity. In each iteration, threesub-problems need to be solved, two of which can be very efficientlysolved via Fast Fourier Transform (FFT) implementation or closedform solution. In general the third sub-problem need iterativesolvers. We then apply our method to TV restoration with $L^1$ andKullback-Leibler (KL) fidelities, two common and important dataterms for deblurring images corrupted by impulsive noise and Poissonnoise, respectively. For these typical fidelities, we show that thethird sub-problem also has closed form solution and thus can beefficiently solved. In addition, convergence analysis of thesealgorithms are given. Numerical experiments demonstrate theefficiency of our method.