We design a dictionary in which speech signals have a sparse representation. We utilize the property that speech is comprised of a fixed number of phonemes. The dictionary is a concatenation of the principal components of all these phonemes, and hence information about each phoneme is present in a block. Since any speech signal is a concatenation of phonemes, it can be represented as a linear c...

We present some results obtained recently in signal processing in the so-called “sparse representations” domain and indicate how they can be applied to a very specific and limited problem in realization theory. This is mainly to bring these type of results to the knowledge of this community. Other applications in order estimation for instance are potentially feasible. The basic problem is the f...

Recently, sparsity has become a key concept in various areas of applied mathematics, computer science, and electrical engineering. One application of this novel methodology is the separation of data, which is composed of two (or more) morphologically distinct constituents. The key idea is to carefully select representation systems each providing sparse approximations of one of the components. T...

The problem of removing white zero-mean Gaussian noise from an image is an interesting inverse problem to be investigated in this paper through sparse and redundant representations. However, finding the sparsest possible solution in the noise scenario was of great debate among the researchers. In this paper we make use of new approach to solve this problem and show that it is comparable with th...

We describe a method for learning sparse multiscale image representations using a sparse prior distribution over the basis function coefficients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coefficients to have exact zero values. Coefficients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. Th...

A supervised topic model can use side information such as ratings or labels associated with documents or images to discover more predictive low dimensional topical representations of the data. However, existing supervised topic models predominantly employ likelihood-driven objective functions for learning and inference, leaving the popular and potentially powerful max-margin principle unexploit...

Finding image representations with a dimensionality reduction while maintaining relevant information for classification, remains a major issue. Effective approaches have recently been developed based on locally orderless representations as proposed by Koendering and Van Doom [1]. They observed that high frequency structures are important for recognition but do not need to be precisely located. ...

In the last two decades, sparse representations have gained increasing attention in a variety of engineering applications. A sparse representation of a signal requires a dictionary of basic elements that describe salient and discriminant features of that signal. When the dictionary is created from a mathematical model, its expressiveness depends on the quality of this model. In this dissertatio...

Dictionary Learning and sparse coding methods have been widely used in computer vision with applications to face and object recognition. A common challenge when performing expression recognition is that face similarities may confound the expression recognition process. An approach to deal with this problem is to learn expression specific dictionaries, so that each atom corresponds to one expres...