Critical point theory for sparse recovery

We study the problem of sparse recovery in context compressed sensing. This is to minimize sensing error linear measurements by vectors with at most s non-zero entries. develop so-called critical point theory for recovery. done introducing nondegenerate M-stationary points which adequately describe global structure this non-convex optimization problem. show that all are generically nondegenerate. In particular, sparsity constraint active local minimizers a generic Additionally, equivalence strong stability and nondegeneracy shown. claim appearance saddle – these exactly s−1 entries cannot be neglected. For purpose, we derive Morse relation, gives lower bound on number terms minimizers. The relatively involved can seen as source well-known difficulty solving optimality.