81 research outputs found
Oblique Matching Pursuit
A method for selecting a suitable subspace for discriminating signal
components through an oblique projection is proposed. The selection criterion
is based on the consistency principle introduced by M. Unser and A. Aldroubi
and extended by Y. Elder. An effective implementation of this principle for the
purpose of subspace selection is achieved by updating of the dual vectors
yielding the corresponding oblique projector.Comment: Last version- as it will appear in IEEE SPL. IEEE Signal Processing
Letters (in press
Sparsity and `Something Else': An Approach to Encrypted Image Folding
A property of sparse representations in relation to their capacity for
information storage is discussed. It is shown that this feature can be used for
an application that we term Encrypted Image Folding. The proposed procedure is
realizable through any suitable transformation. In particular, in this paper we
illustrate the approach by recourse to the Discrete Cosine Transform and a
combination of redundant Cosine and Dirac dictionaries. The main advantage of
the proposed technique is that both storage and encryption can be achieved
simultaneously using simple processing steps.Comment: Revised manuscript- Software for implementing the Encrypted Image
Folding proposed in this paper is available on
http://www.nonlinear-approx.info
Nonlinear non-extensive approach for identification of structured information
The problem of separating structured information representing phenomena of
differing natures is considered. A structure is assumed to be independent of
the others if can be represented in a complementary subspace. When the
concomitant subspaces are well separated the problem is readily solvable by a
linear technique. Otherwise, the linear approach fails to correctly
discriminate the required information. Hence, a non extensive approach is
proposed. The resulting nonlinear technique is shown to be suitable for dealing
with cases that cannot be tackled by the linear one.Comment: Physica A, in pres
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
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