Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio

Single-frame super-resolution in remote sensing: a practical overview

Image acquisition technology is improving very fast from a performance point of view. However, there are physical restrictions that can only be solved using software processing strategies. This is particularly true in the case of super resolution (SR) methodologies. SR techniques have found a fertile application field in airborne and space optical acquisition platforms. Single-frame SR methods may be advantageous for some remote-sensing platforms and acquisition time conditions. The contributions of this article are basically two: (1) to present an overview of single-frame SR methods, making a comparative analysis of their performance in different and challenging remote-sensing scenarios, and (2) to propose a new single-frame SR taxonomy, and a common validation strategy. Finally, we should emphasize that, on the one hand, this is the first time, to the best of our knowledge, that such a review and analysis of single SR methods is made in the framework of remote sensing, and, on the other hand, that the new single-frame SR taxonomy is aimed at shedding some light when classifying some types of single-frame SR methods.This work was supported by the Spanish Ministry of Economy under the project ESP2013 - 48458-C4-3-P, by Generalitat Valenciana through project PROMETEO-II/2014/062, and by Universitat Jaume I through project P11B2014-09

Antipodally invariant metrics for fast regression-based super-resolution

Dictionary-based super-resolution (SR) algorithms usually select dictionary atoms based on the distance or similarity metrics. Although the optimal selection of the nearest neighbors is of central importance for such methods, the impact of using proper metrics for SR has been overlooked in literature, mainly due to the vast usage of Euclidean distance. In this paper, we present a very fast regression-based algorithm, which builds on the densely populated anchored neighborhoods and sublinear search structures. We perform a study of the nature of the features commonly used for SR, observing that those features usually lie in the unitary hypersphere, where every point has a diametrically opposite one, i.e., its antipode, with same module and angle, but the opposite direction. Even though, we validate the benefits of using antipodally invariant metrics, most of the binary splits use Euclidean distance, which does not handle antipodes optimally. In order to benefit from both the worlds, we propose a simple yet effective antipodally invariant transform that can be easily included in the Euclidean distance calculation. We modify the original spherical hashing algorithm with this metric in our antipodally invariant spherical hashing scheme, obtaining the same performance as a pure antipodally invariant metric. We round up our contributions with a novel feature transform that obtains a better coarse approximation of the input image thanks to iterative backprojection. The performance of our method, which we named antipodally invariant SR, improves quality (Peak Signal to Noise Ratio) and it is faster than any other state-of-the-art method.Peer ReviewedPostprint (author's final draft

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1