We featured Karin Knudson's work before here in One-bit compressive sensing with norm estimation - implementation - well, Karin graduated and here is her very interesting thesis. It is interesting in part because it is part of the continuum of studies between traditional compressive sensing and neural networks.
Gigem, uh....Congratulations Karin ! here is the thesis: Recovery of Continuous Quantities from Discrete and Binary Data with Applications to Neural Data
We consider three problems, motivated by questions in computational neuroscience, related to recovering continuous quantities from binary or discrete data or measurements in the context of sparse structure. First, we show that it is possible to recover the norms of sparse vectors given one-bit compressive measurements, and provide associated guarantees. Second, we present a novel algorithm for spike-sorting in neural data, which involves recovering continuous times and amplitudes of events using discrete bases. This method, Continuous Orthogonal Matching Pursuit, builds on algorithms used in compressive sensing. It exploits the sparsity of the signal and proceeds greedily,achieving gains in speed and accuracy over previous methods. Lastly, we present a Bayesian method making use of hierarchical priors for entropy rate estimation from binary sequences.
N00235465.jpg was taken on February 16, 2015 and received on Earth February 17, 2015. The camera was pointing toward SATURN, and the image was taken using the CL1 and CL2 filters. This image has not been validated or calibrated. Image Credit: NASA/JPL/Space Science Institute
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