In case of fuzzy reasoning in sparse fuzzy rule bases, the question of selecting the suitable fuzzy similarity measure is essential. The rule antecedents of the sparse fuzzy rule bases are not fully covering the input universe therefore fuzzy reasoning methods applied for sparse fuzzy rule bases requires similarity measures able to distinguish the similarity of non-overlapping fuzzy sets, too. ...

Building on a recent breakthrough by Ogihara, we resolve a conjecture made by Hartmanis in 1978 regarding the (non-) existence of sparse sets complete for P under logspace many-one reductions. We show that if there exists a sparse hard set for P under logspace many-one reductions, then P = LOGSPACE. We further prove that if P has a sparse hard set under many-one reductions computable in NC1, th...

This paper presents a new approach to obtain a high resolution image from a single image low resolution by a technique of sparse representation. Sparse representation is a way of representing a signal sparsely i.e. with fewer non zero elements. In this method we find the sparse representation of the input low resolution image patches and then use the coefficient of this representation to genera...

In many deep learning/sparse coding papers involving images, it is a common trend that patterns resembling Gabor filters/edge filters are usually present in the learnt bases. In this project, we investigate whether various sparse learning models are able to learn edge filter bases for sparse representation of both natural and non-natural images. Experiments are also conducted for each of the th...

This paper presents new univariate linear non-uniform interpolatory subdivision constructions that yield high smoothness, C and C, and are based on least-degree spline interpolants. This approach is motivated by evidence, partly presented here, that constructions based on high-degree local interpolants fail to yield satisfactory shape, especially for sparse, non-uniform samples. While this impr...

Active appearance models (AAMs) have been widely used in many face modeling and facial feature extraction methods. One of the problems of AAMs is that it is difficult to model a sufficiently wide range of human facial appearances, the pattern of intensities across a face image patch. Previous researches have used principal component analysis (PCA) for facial appearance modeling, but there has b...

Automatic relevance determination (ARD) and the closely-related sparse Bayesian learning (SBL) framework are effective tools for pruning large numbers of irrelevant features leading to a sparse explanatory subset. However, popular update rules used for ARD are either difficult to extend to more general problems of interest or are characterized by non-ideal convergence properties. Moreover, it r...

Recently, sparse coding has been widely used in many applications ranging from image recovery to pattern recognition. The low mutual coherence of a dictionary is an important property that ensures the optimality of the sparse code generated from this dictionary. Indeed, most existing dictionary learning methods for sparse coding either implicitly or explicitly tried to learn an incoherent dicti...

In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples involving extremely sparse signals. We s...