Abstract |
The theory of sparse recovery from compressive measurements relies
predominantly on the so-called restricted isometry property. In this
talk, I shall summarize recent results based on an appropriate
modification of this property. Firstly, I will show how exact recovery
of sparse vectors can still be achieved from standard linear
measurements. Secondly, I will give a simple explanation for the
possibility of approximate recovery when these measurements are
quantized to the extreme. Thirdly, I will discuss an intermediate
situation where large measurements saturate. I will finally mention
analogous results dealing with the recovery of low-rank matrices
rather than sparse vectors.
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