Name
Abstract | ||
|---|---|---|
Exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems. The synthesis model, which assumes that images can be decomposed into a linear combination of very few atoms of some dictionary, is now a well established tool for the design of image reconstruction algorithms. An interesting alternative is the analysis model, where the signal is multiplied by an analysis operator and the outcome is assumed to be sparse. This approach has only recently gained increasing interest. The quality of reconstruction methods based on an analysis model severely depends on the right choice of the suitable operator. In this paper, we present an algorithm for learning an analysis operator from training images. Our method is based on l(p)-norm minimization on the set of full rank matrices with normalized columns. We carefully introduce the employed conjugate gradient method on manifolds, and explain the underlying geometry of the constraints. Moreover, we compare our approach to state-of-the-art methods for image denoising, inpainting, and single image super-resolution. Our numerical results show competitive performance of our general approach in all presented applications compared to the specialized state-of-the-art techniques. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1109/TIP.2013.2246175 | IEEE transactions on image processing : a publication of the IEEE Signal Processing Society |
Keywords | DocType | Volume |
conjugate gradient methods,geometry,image denoising,image reconstruction,image resolution,inverse problems,matrix algebra,minimisation,ℓp-norm minimization,full rank matrix,geometry,image decomposition,image denoising,image inpainting,image reconstruction method,image training,inverse problem,manifold conjugate gradient method,normalized column,operator learning analysis,signal multiplication,single image superresolution,structural information,Analysis operator learning,geometric conjugate gradient,image reconstruction,inverse problems,oblique manifold | Journal | 22 |
Issue | ISSN | Citations |
6 | 1057-7149 | 54 |
PageRank | References | Authors |
1.62 | 26 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simon Hawe | 1 | 59 | 2.37 |
| Martin Kleinsteuber | 2 | 104 | 4.69 |
| Klaus Diepold | 3 | 437 | 56.47 |