Mark Plumbley just reminded me that on top of Zhilin's selection of papers related to CS at ICASSP 2012, there was also a session he is co-organizing on Analysis Sparsity. It turns out that at MIA2012, Miki Elad's presentation was also on an analysis based method featured in The Analysis Sparse Model - Definition, Pursuit, Dictionary Learning, and Beyond and I was bugged because of this slide:
or this slide:
I was bugged, because clearly this analysis approach seems to provide the equivalent of the discretization of an operator, an operator that is at play in this scene. It turns out, it really is not a coincidence as witnessed in this paper featured at ICASSP: Physics -Driven Structured CoSparse Modeling for Source Localization by Sangnam Nam and Remi Gribonval. The abstract reads:
Cosparse modeling is a recent alternative to sparse modeling, where the notion of dictionary is replaced by that of an analysis operator. When a known analysis operator is well adapted to describe the signals of interest, the model and associated algorithms can be used to solve inverse problems. Here we show how to derive an operator to model certain classes of signals that satisfy physical laws, such as the heat equation or the wave equation. We illustrate the approach on an acoustic inverse problem with a toy model of wave propagation and discuss its potential extensions and the challenges it raises.
also from this presentation by Remi Gribonval.
In other words, maybe structured sparsity does not need to be adhoc after all, maybe using an analysis approach we could really figure out how Life works and wow biologists instead of just trying to please them.
Thanks Mark for the reminder.
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