Sparse signal reconstruction via concave continuous piecewise linear programming

Piecewise linear neural networks and deep learning

“…Note that with d = 1, the PWL function f (x x x) is reduced to be linear, thus, we regard linear functions as a special case of PWL functions throughout the Primer. Compared to other nonlinear models, PWL functions possess explicit geometric interpretation, and many practical systems can be easily transformed into PWL nonlinear functions 37 , such as PWL memristors [G] 38,39 , specialized cost functions [40][41][42][43][44] , and part mathematical programmings [45][46][47][48][49][50] . As powerful nonlinear models, PWL functions are proven universal approximators 51 : let Ω ⊂ R n be a compact domain, and p(x x x) : Ω → R be a continuous function.…”

Simplicity-based recovery of finite-alphabet signals for large-scale MIMO systems

“…It is a signal processing technique to efficiently acquire and reconstruct signals, by finding solutions to underdetermined linear systems. It exploits the sparsity of the signal to recover it and thus, it uses far fewer samples than required by the sampling theorem [7,8]. A source is sparse in a given representation domain if most of its elements are close to zero.…”