On the Relation Between Sparse Reconstruction and Parameter Estimation With Model Order Selection

Homotopy Based Algorithms for $\ell _{\scriptscriptstyle 0}$-Regularized Least-Squares

“…The second are cross-validation criteria [48], [49]. The sparse approximation framework allows one to derive simplified expressions of the latter up to the storage of intermediate solutions of greedy algorithms for consecutive cardinalities [8], [47], [50].…”

Theoretical results for sparse signal recovery with noises using generalized OMP algorithm

“…it is nontrivial to prove that the righthand side (RHS) of (18) is larger than that of (17). Therefore, the tighter bound between them is given by (18).…”

“…In real applications, with the sparse signal unavailable, it is impossible to know its sparsity beforehand. Although there exist methods to estimate K [17], the value of K is nontrivial to be estimated exactly and efficiently. In the noiseless case, the gOMP algorithm can iterate until the residual signal is equal to a zero vector.…”

Comparison of sparse recovery algorithms for channel estimation in underwater acoustic OFDM with data-driven sparsity learning

“…For the L 1 problem, Ref. [21] adopts the BIC criterion to choose λ, Ref. [22] proposes to use the minimal description length (MDL) to select λ based on a maximum a posteriori probability (MAP) estimator aiming to find the minimal data error, while the minimum noiseless description length (MNDL) criterion extends the selection of λ to minimize the reconstruction error [23].…”