Primal-dual interior-point methods
Primal-dual interior-point methods
A Fast MAP Algorithm for High-Resolution Image Reconstruction with Multisensors
Multidimensional Systems and Signal Processing
SIAM Journal on Numerical Analysis
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Factorized Banded Inverse Preconditioners for Matrices with Toeplitz Structure
SIAM Journal on Scientific Computing
A property of the minimum vectors of a regularizing functionaldefined by means of the absolute norm
IEEE Transactions on Signal Processing
Analysis of performance of palmprint matching with enforced sparsity
Digital Signal Processing
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Image restoration problems are often solved by finding the minimizer of a suitable objective function. Usually this function consists of a data-fitting term and a regularization term. For the least squares solution, both the data-fitting and the regularization terms are in the ℓ2 norm. In this paper, we consider the least absolute deviation (LAD) solution and the least mixed norm (LMN) solution. For the LAD solution, both the data-fitting and the regularization terms are in the ℓ1 norm. For the LMN solution, the regularization term is in the ℓ1 norm but the data-fitting term is in the ℓ2 norm. The LAD and the LMN solutions are formulated as the solutions of a linear and a quadratic programming problems respectively, and solved by interior point methods. At each iteration of the interior point method, a structured linear system must be solved. The preconditioned conjugate gradient method with factorized sparse inverse preconditioners is employed to such structured inner systems. Experimental results are used to demonstrate the effectiveness of our approach. We also show the quality of the restored images using the minimization of ℓ1 norm/mixed ℓ1 and ℓ2 norms is better than that using ℓ2 norm approach.