I've been a long time visitor to Nuit Blanche, and have enjoyed your updates on the advances in the compressive sensing community. Given your discussion the last few days, we have recently submitted a paper which we believe may be of interest to yourself and the CS community: "Re-weighted l1 dynamic filtering for time-varying sparse signal estimation" (the pre-print is available here: http://arxiv.org/pdf/1208.0325v1.pdf). In this work we approach the problem of causally estimating dynamically changing sparse vectors by taking inspiration from both Kalman filtering and hierarchical sparsity models (used to induce correlations between coefficients). Our approach is meant to be robust to non-Gaussian statistics even in the model errors (e.g., shot noise), and is based on re-weighted L1 optimization (which can leverage efficient L1 solvers).Regards,
-Adam CharlesThanks Adam !
Adam tells me that they should release an implementation of this algorithm soon. stay tuned. If memory serves (my memory has been known to fail!) this is the first I see a mention of UKF / Particle Filter in a Kalman-CS paper. In the meantime, here is the paper:
Re-Weighted l_1 Dynamic Filtering for Time-Varying Sparse Signal Estimation by Adam Charles , and Christopher J. Rozell. The abstract reads:
Signal estimation from incomplete observations improves as more signal structure can be exploited in the inference process. Classic algorithms (e.g., Kalman ﬁltering) have exploited strong dynamic structure for time-varying signals while modern work has often focused on exploiting low-dimensional signal structure (e.g., sparsity in a basis) for static signals. Few algorithms attempt to merge both static and dynamic structure to improve estimation for time-varying sparse signals (e.g., video). In this work we present a re-weighted `1 dynamic ﬁltering scheme for causal signal estimation that utilizes both sparsity assumptions and dynamic structure. Our algorithm leverages work on hierarchical Laplacian scale mixture models to create a dynamic probabilistic model. The resulting algorithm incorporates both dynamic and sparsity priors in the estimation procedure in a robust and efﬁcient algorithm. We demonstrate the results in simulation using both synthetic and natural data.- Update: The attendant code is located here -
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