250 research outputs found
Compressed Sensing with General Frames via Optimal-dual-based -analysis
Compressed sensing with sparse frame representations is seen to have much
greater range of practical applications than that with orthonormal bases. In
such settings, one approach to recover the signal is known as
-analysis. We expand in this article the performance analysis of this
approach by providing a weaker recovery condition than existing results in the
literature. Our analysis is also broadly based on general frames and
alternative dual frames (as analysis operators). As one application to such a
general-dual-based approach and performance analysis, an optimal-dual-based
technique is proposed to demonstrate the effectiveness of using alternative
dual frames as analysis operators. An iterative algorithm is outlined for
solving the optimal-dual-based -analysis problem. The effectiveness of
the proposed method and algorithm is demonstrated through several experiments.Comment: 34 pages, 8 figures. To appear in IEEE Transactions on Information
Theor
Sampling in the Analysis Transform Domain
Many signal and image processing applications have benefited remarkably from
the fact that the underlying signals reside in a low dimensional subspace. One
of the main models for such a low dimensionality is the sparsity one. Within
this framework there are two main options for the sparse modeling: the
synthesis and the analysis ones, where the first is considered the standard
paradigm for which much more research has been dedicated. In it the signals are
assumed to have a sparse representation under a given dictionary. On the other
hand, in the analysis approach the sparsity is measured in the coefficients of
the signal after applying a certain transformation, the analysis dictionary, on
it. Though several algorithms with some theory have been developed for this
framework, they are outnumbered by the ones proposed for the synthesis
methodology.
Given that the analysis dictionary is either a frame or the two dimensional
finite difference operator, we propose a new sampling scheme for signals from
the analysis model that allows to recover them from their samples using any
existing algorithm from the synthesis model. The advantage of this new sampling
strategy is that it makes the existing synthesis methods with their theory also
available for signals from the analysis framework.Comment: 13 Pages, 2 figure
- β¦