33 research outputs found
Backward-optimized orthogonal matching pursuit approach
A recursive approach for shrinking coefficients of an atomic decomposition is proposed. The corresponding algorithm evolves so as to provide at each iteration 1) the orthogonal projection of a signal onto a reduced subspace and 2) the index of the coefficient to be disregarded in order to construct a coarser approximation minimizing the norm of the residual error
Constructive updating/downdating of oblique projectors: a generalization of the Gram-Schmidt process
A generalization of the Gram-Schmidt procedure is achieved by providing
equations for updating and downdating oblique projectors. The work is motivated
by the problem of adaptive signal representation outside the orthogonal basis
setting. The proposed techniques are shown to be relevant to the problem of
discriminating signals produced by different phenomena when the order of the
signal model needs to be adjusted.Comment: As it will appear in Journal of Physics A: Mathematical and
Theoretical (2007
Constructive approximations to the q=1/2 maximum entropy distribution from redundant and noisy data
An approach adopted to consider the problem of constructing the q=1/2 maximum entropy distribution from redundant and noisy data was discussed. The advantage of this generalized approach, when dealing with very noisy data was illustrated by a numerical simulation. A strategy was proposed that evolved through different steps such as independent constraints were first preselected by recourse to a data independent technique. A backward approach was also proposed for reducing the parameters of such distributions. It was found that the sub-optimal strategies could be utilized in a broad range of situations
Measurements design and phenomena discrimination
The construction of measurements suitable for discriminating signal
components produced by phenomena of different types is considered. The required
measurements should be capable of cancelling out those signal components which
are to be ignored when focusing on a phenomenon of interest. Under the
hypothesis that the subspaces hosting the signal components produced by each
phenomenon are complementary, their discrimination is accomplished by
measurements giving rise to the appropriate oblique projector operator. The
subspace onto which the operator should project is selected by nonlinear
techniques in line with adaptive pursuit strategies
Cooperative greedy pursuit strategies for sparse signal representation by partitioning
Cooperative Greedy Pursuit Strategies are considered for approximating a signal partition subjected to a global constraint on sparsity. The approach aims at producing a high quality sparse approximation of the whole signal, using highly coherent redundant dictionaries. The cooperation takes place by ranking the partition units for their sequential stepwise approximation, and is realized by means of i)forward steps for the upgrading of an approximation and/or ii) backward steps for the corresponding downgrading. The advantage of the strategy is illustrated by approximation of music signals using redundant trigonometric dictionaries. In addition to rendering stunning improvements in sparsity with respect to the concomitant trigonometric basis, these dictionaries enable a fast implementation of the approach via the Fast Fourier Transfor
From cardinal spline wavelet bases to highly coherent dictionaries
Wavelet families arise by scaling and translations of a prototype function, called the mother wavelet. The construction of wavelet bases for cardinal spline spaces is generally carried out within the multi-resolution analysis scheme. Thus, the usual way of increasing the dimension of the multi-resolution subspaces is by augmenting the scaling factor. We show here that, when working on a compact interval, the identical effect can be achieved without changing the wavelet scale but reducing the translation parameter. By such a procedure we generate a redundant frame, called a dictionary, spanning the same spaces as a wavelet basis but with wavelets of broader support. We characterize the correlation of the dictionary elements by measuring their 'coherence' and produce examples illustrating the relevance of highly coherent dictionaries to problems of sparse signal representation