Name
Abstract | ||
|---|---|---|
In this paper, we propose two algorithms for solving linear inverse problems when the observations are corrupted by noise. A proper data fidelity term (log-likelihood) is introduced to reflect the statistics of the noise (e.g. Gaussian, Poisson) independently of the degradation. On the other hand, the regularization is constructed by assuming several a priori knowledge on the images. Piecing together the data fidelity and the prior terms, the solution to the inverse problem is cast as the minimization of a non-smooth convex functional. We establish the well-posedness of the optimization problem, characterize the corresponding minimizers for different kind of noises. Then we solve it by means of primal and primal-dual proximal splitting algorithms originating from the field of non-smooth convex optimization theory. Experimental results on deconvolution, inpainting and denoising with some comparison to prior methods are also reported. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.5555/2151688.2151763 | VALUETOOLS |
Keywords | Field | DocType |
corresponding minimizer,prior method,fidelity term,linear inverse problem,proper data,data fidelity,prior term,mixed regularization,optimization problem,inverse problem,various noise model,non-smooth convex optimization theory | Applied mathematics,Value noise,Mathematical optimization,Computer science,Real-time computing,Inpainting,Regularization (mathematics),Inverse problem,Gaussian noise,Convex optimization,Optimization problem,Gradient noise | Conference |
ISBN | Citations | PageRank |
978-1-936968-09-1 | 3 | 0.46 |
References | Authors | |
10 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| François-Xavier Dupé | 1 | 105 | 7.85 |
| Jalal Fadili | 2 | 1184 | 80.08 |
| Jean-Luc Starck | 3 | 1183 | 122.27 |