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We propose a new method to learn overcomplete dictionaries for sparse coding structured as unions of orthonormal bases. The interest of such a structure is manifold. Indeed, it seems that many signals or images can be modeled as the superimposition of several layers with sparse decompositions in as many bases. Moreover , in such dictionaries, the efficient… (More)

Shift-invariant dictionaries are generated by taking all the possible shifts of a few short patterns. They are helpful to represent long signals where the same pattern can appear several times at different positions. We present an algorithm that learns shift invariant dictionaries from long training signals. This algorithm is an extension of K-SVD. It… (More)

This paper focuses on under-determined source separation when the mixing parameters are known. The approach is based on a sparse decomposition of the mixture. In the proposed method, the mixture is decomposed with Matching Pursuit by introducing a new class of multi-channel dictionaries, where the atoms are given by a spatial direction and a waveform. The… (More)

The performance of approximation using redundant expansions rely on having dictionaries adapted to the signals. In natural high-dimensional data, the statistical dependencies are, most of the time, not obvious. Learning fundamental patterns is an alternative to analytical design of bases and is nowadays a popular problem in the field of approximation… (More)

Real-world phenomena involve complex interactions between multiple signal modalities. As a consequence, humans are used to integrate at each instant perceptions from all their senses in order to enrich their understanding of the surrounding world. This paradigm can be also extremely useful in many signal processing and computer vision problems involving… (More)

— Sparse approximation using redundant dictionaries is an efficient tool for many applications in the field of signal processing. The performances largely depend on the adaptation of the dictionary to the signal to decompose. As the statistical dependencies are most of the time not obvious in natural high-dimensional data, learning fundamental patterns is… (More)

This paper presents a methodology for extracting meaningful synchronous structures from multi-modal signals. Simultaneous processing of multi-modal data can reveal information that is unavailable when handling the sources separately. However, in natural high-dimensional data, the statistical dependencies between modalities are, most of the time, not… (More)

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