Earlier this month, you might remember that we featured version 2 of this paper: Analysis Based Blind Compressive Sensing by Julian Wörmann, Simon Hawe, Martin Kleinsteuber
In this work we address the problem of blindly reconstructing compressively sensed signals by exploiting the co-sparse analysis model. In the analysis model it is assumed that a signal multiplied by an analysis operator results in a sparse vector. We propose an algorithm that learns the operator adaptively during the reconstruction process. The arising optimization problem is tackled via a geometric conjugate gradient approach. Different types of sampling noise are handled by simply exchanging the data fidelity term. Numerical experiments are performed for measurements corrupted with Gaussian as well as impulsive noise to show the effectiveness of our method.
Well Julian let me know that the attendant implementation of this algorithm is available here on this page. Thanks Julian !
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