Analysis Operator Learning and Its Application to Image Reconstruction

Details Analysis Operator Learning and Its Application to Image Reconstruction Analysis Operator Learning and Its Application to Image Reconstruction

2012-04-24

arxiv.org/abs/1204.5309v1

Computer Science

Learning

18 pages, 43 figures

Scientific paper

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 the 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 work, we present an algorithm for learning an analysis operator from training images. Our method is based on an $\ell_p$-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.

Affiliated with

Also associated with

No associations

Rating

Analysis Operator Learning and Its Application to Image Reconstruction does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Analysis Operator Learning and Its Application to Image Reconstruction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analysis Operator Learning and Its Application to Image Reconstruction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-519445