In this thesis a new type of representation for medium level vision operations is explored. We focus on representations that are sparse and monopolar. The word sparse signifies that information in the feature sets used is not necessarily present at all points. On the contrary, most features will be inactive. The word monopolar signifies that all features have the same sign, e.g. are either posi...

This discussion sparse representations of signals in R. The sparsity of a signal is quantified by the number of nonzero components in its representation. Such representations of signals are useful in signal processing, lossy source coding, image processing, etc. We first speak of an uncertainty principle regarding the sparsity of any two different orthonormal basis representations of a signal S...

Recent studies in linear inverse problems have recognized the sparse representation of unknown signal in a certain basis as an useful and effective prior information to solve those problems. In many multiscale bases (e.g. wavelets), signals of interest (e.g. piecewise-smooth signals) not only have few significant coefficients, but also those significant coefficients are well-organized in trees....

We study representations of graphs by contacts of circular arcs, CCA-representations for short, where the vertices are interiordisjoint circular arcs in the plane and each edge is realized by an endpoint of one arc touching the interior of another. A graph is (2, k)-sparse if every s-vertex subgraph has at most 2s− k edges, and (2, k)-tight if in addition it has exactly 2n− k edges, where n is ...

The capability of Convolutional Neural Networks (CNNs) for sparse representation has significant application to complex tasks like Representation Learning (RL). However, labelled datasets sufficient size learning this are not easily obtainable. unsupervised Variational Autoencoders (VAEs) and Generative Adversarial (GANs) provide a promising solution issue through their capacity learn represent...

Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and obtain the corresponding algebras of generators. In this letter, we extend technique sparse representations arbitrary Lie algebras. We show that our method reproduces canonical (sparse) generators Lorentz group, as well U(n) SU(n) families groups. This approach is completely general c...