In this paper we consider the construction of multiresolution Gabor dictionaries appropriate for audio signal analysis. Motivated by a desire for parsimony and efficiency, we propose and formalise the idea of reduced multi-Gabor systems, showing that they constitute a frame for L2(R) and other Hilbert spaces of interest. In order to demonstrate the practicality of such a scheme, we apply it to ...

In this paper we present a method for representing complex façades. For this purpose we developed a hierarchical decomposition for the façade. The steps of the decomposition are represented as nodes in a typed graph where the leaves are the atomic façade elements. Every node includes necessary attributes for its façade structure. The edges in the graph depict adjacent façade elements providing ...

In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined sparse component analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Cont...

In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined Sparse Component Analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real £eld codes. Contr...

Dictionary-based methods (DBMs) provide rich possibilities for new sound transformations; as the analysis dual to granular synthesis, audio signals are decomposed into ‘atoms’, allowing interesting manipulations. We present various approaches to audio signal cross-synthesis and crossanalysis via atomic decomposition using scale-time-frequency dictionaries. DBMs naturally provide high-level desc...

Our aim is to give a characterization of the BMO norm via Banach function spaces based on the Rubio de Francia algorithm. Our proof is different from the one by Ho [Atomic decomposition of Hardy spaces and characterization of BMO via Banach function spaces, Anal. Math. 38 (2012), 173–185].

In this paper, we apply Basis Pursuit, an atomic decomposition technique, for spectrum estimation. Compared with several modern time series methods, our approach can greatly reduce the problem of power leakage; it is able to superresolve; moreover, it works well with noisy and unevenly sampled signals. We present experiments on bizarrely spaced radial velocity data from one of the newly-discove...

We present the atomic decomposition technique as a general method for reducing reasoning about cardinalities of sets, in the DL case the cardinalities of role llers, to equation solving problems. Then we apply the technique to a particular description logic with complex role terms and role hierarchies and a strong arithmetic component.

A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have selected classes of solvable states. The method is illustrated in the SO(6) limit of the interacting boson model of atomic nuclei and applied to the nucleus 196Pt.

This paper reviews the following problems, sampling, decomposition procedures and most important analytical methods used for selenium determination, e.g., neutron activation analysis, atomic absorption spectrometry, gas-liquid chromatography, spectrophotometry, fluorimetry, and x-ray fluorescence. This review covers the literature mainly from 1975 to 1977.