Compressive Sensing with structured random matrices

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A compressed sensing approach for partial differential equations with random input data (2012, background): “In recent work, Rauhut (2010), Rauhut and Ward (2010) investigate the recovery properties of a strategy based on an approximation basis generated by a system of polynomials {ψα} orthonormal with respect to a measure μξ(ξ) satisfying (in 1-D)”
A Probabilistic and RIPless Theory of Compressed Sensing (2010, background): “Similarly to the theory in this paper, near optimal theoretical guarantees on sparse-signal recovery are non-uniform [40, 41], whereas uniform recovery through RIP machinery has been quite suboptimal.”
Towards Efficient Data Valuation Based on the Shapley Value (2019, background): “It has been shown in [25] that every k-sparse vector s can be recovered by solving a convex optimization problem”
New and Improved Johnson-Lindenstrauss Embeddings via the Restricted Isometry Property (2010, methodology): “zero. This observation has several consequences in the area of compressed sensing, and also allows us to obtain improved JL embedding results for several matrix constructions with existing RIP bounds [13, 35, 31, 38, 33]. Of particular interest is the random partial Fourier or the random partial Had”