The Living Thing / Notebooks : Compressed sensing

Stand by for higgledy-piggledy notes on the theme of exploiting sparsity to recover signals from few measurements. Sparse regression in a deterministic setting (i.e. where we aren’t doing a regresssion from noisy data; Although it might stil be random if we take random measurements.)

See also matrix factorisations, random projections, optimisation, model selection, multiple testing, random linear algebra, concentration inequalities.

TBD: The Restricted Isometry Properties.

Intros

Random projections

Deterministic projection strategies

Surely this is close to quasi monte carlo?

That phase transition

How well can you recover a matrix from a certain number of measurements? In obvious metrics there is a sudden jump in how well you do with increasing measurements for a given rank.

See Igor Carron’s “phase diagram” list, and stuff like this Weng et al “Overcoming The Limitations of Phase Transition by Higher Order Analysis of Regularization Techniques” (WeMZ16)

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