The LASSO with Non-linear Measurements is Equivalent to One With Linear Measurements

Chrtistos Thrampoulidis, Ehsan Abbasi, Babak Hassibi

Consider estimating an unknown, but structured, signal $x_0\in R^n$ from $m$ measurement $y_i=g_i(a_i^T{x}_0)$, where the $a_i$'s are the rows of a known measurement matrix $A$, and,…