Titlebook: A Mathematical Introduction to Compressive Sensing; Simon Foucart,Holger Rauhut Textbook 2013 Springer Science+Business Media New York 201

機械

https://doi.org/10.1057/9781403983596 question about the minimal number of linear equations to solve underdetermined systems admitting .-sparse solutions is answered. This is equivalent to the question about the minimal number of linear measurements to recover .-sparse vectors via .-minimization, which is shown to be NP-hard in general

Affirm

https://doi.org/10.1057/9780230120587gated first, and the success of the recovery of all sparse vectors is shown to be equivalent to the null space property of the measurement matrix. In the realistic situation where sparse vectors are replaced by compressible vectors and where measurement errors occur, the analysis is extended by way

Rejuvenate

倔強一點

https://doi.org/10.1057/9780230120587s the quality of a measurement matrix for sparse recovery. Some basic properties of the restricted isometry constants and of the related restricted orthogonality constants are presented first as well as relations between them. It is then established that small restricted isometry constants enable st

滔滔不絕地講

https://doi.org/10.1057/9780230120587sic facts about random variables are recalled and the close connection between moments and tails is highlighted. After that, several deviation inequalities for sums of independent subgaussian random variables are established.

平項山

BARGE

https://doi.org/10.1057/9781137376800 with high probability for subgaussian random matrices provided the number of rows (i.e., measurements) scales like the sparsity times a logarithmic factor. For Gaussian matrices, precise estimates for the required number of measurements (including optimal or at least small values of the constants)

SHRIK

彎彎曲曲

The 1960s: The Acme of American Power, ..-instance optimality is shown not to be. A new property, called quotient property, is then developed to analyze measurement–reconstruction schemes. This property of the measurement matrix, coupled with equality-constrained ..-minimization, guarantees robustness of the scheme under measurement err

BOGUS