ExCoV: Expansion-Compression Variance-component Based Sparse-signal Reconstruction from Noisy Measurements by Aleksandar Dogandžić and Kun Qiu. The abstract reads:
We present an expansion-compression variance component based method (ExCoV) for reconstructing sparse or compressible signals from noisy measurements. The measurements follow an underdetermined linear model, with noise covariance matrix known up to a constant. To impose sparse or compressible signal structure, we define high- and low-signal coefficients, where each high-signal coefficient is assigned its own variance, low-signal coefficients are assigned a common variance, and all the variance components are unknown. Our expansion-compression scheme approximately maximizes a generalized maximum likelihood (GML) criterion, providing an approximate GML estimate of the high-signal coefficient set and an empirical Bayesian estimate of the signal coefficients.We apply the proposed method to reconstruct signals from compressive samples, compare it with existing approaches, and demonstrate its performance via numerical simulations.
The authors have also made a webpage hosting the ExCoV implementation. It is listed in the reconstruction section of the Big Picture.
I recently talked about a seminar by Patrick Flandrin earlier but as Pierre Borgnat mentioned to me it was postponed until March 5th, 2009 at 11 am at the SCAM (Séminaire Cristolien d'Analyse Multifractale, Université de Paris 12--Val-de-Marne, salle : P3-036) . The title of the talk is: Une approche "compressed sensing" pour la localisation temps-fréquence ( or Time-frequency localization from sparsity constraints) The summary in English is:
In the case of multicomponent AM-FM signals, the idealized representation which consists of weighted trajectories on the time-frequency (TF) plane, is intrinsically sparse. Recent advances in optimal recovery from sparsity constraints thus suggest to revisit the issue of TF localization by exploiting sparsity, as adapted to the specific context of (quadratic) TF distributions. Based on classical results in TF analysis, it is argued that the relevant information is mostly concentrated in a restricted subset of Fourier coefficients of the Wigner-Ville distribution neighbouring the origin of the ambiguity plane. Using this incomplete information as the primary constraint, the desired distribution follows as the minimum $\ell_1$-norm solution in the transformed TF domain. Possibilities and limitations of the approach are demonstrated via controlled numerical experiments, its performance is assessed in various configurations and the results are compared with standard techniques. It is shown that improved representations can be obtained, though at a computational cost which is significantly increased.
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