Low-rank tensor recovery from memory-efficient measurements
Abstract: Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. For the now ubiquitous tensor data, direct application of the known recovery algorithms to the vectorized or matricized tensors is awkward and memory-heavy because of the huge measurement matrices to be constructed and stored. A way to better compression and reconstruction is to create structure-aware measurement schemes that work directly with tensors, not with their unfoldings, and then exploit tensor low-rankness to provide the reconstruction guarantees. In this talk, I will discuss recent progress on low-rank tensor recovery from various structure-aware (and so, memory-efficient) linear measurements.
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