Greedy subspace pursuit for joint sparse recovery

Tree search network for sparse estimation

“…Then every node in TSN generates a support estimate of size k by utilizing its parital support estimate ∆ and the trained DNN-SR. To do this, each node generates an extended support estimate Ψ of size m − 1 via the DNN-based index selection at the first stage, and estimate the support by selecting k indices out of the set at the second stage. This two-stage process is a variant of the two-stage process shown in [36]; the existing process selects an extended support estimate Ψ of m − 1 indices based on OMP, whereas the proposed process is based on DNN. April 2, 2019 DRAFT It is guaranteed theoretically and experimentally in [36] that exploiting the extended support estimate Ψ of size m−1, generated by the OMP-based rule, improves the performance for the support recovery in comparison to the case without considering it, i.e., the case when the size of Ψ is equal to k. 4 We accepted this principle, i.e., selecting the m − 1 incides instead of k incides, for estimating the support at each node, but used a different index selection technique, i.e., the DNN-based index selection.…”

“…This two-stage process is a variant of the two-stage process shown in [36]; the existing process selects an extended support estimate Ψ of m − 1 indices based on OMP, whereas the proposed process is based on DNN. April 2, 2019 DRAFT It is guaranteed theoretically and experimentally in [36] that exploiting the extended support estimate Ψ of size m−1, generated by the OMP-based rule, improves the performance for the support recovery in comparison to the case without considering it, i.e., the case when the size of Ψ is equal to k. 4 We accepted this principle, i.e., selecting the m − 1 incides instead of k incides, for estimating the support at each node, but used a different index selection technique, i.e., the DNN-based index selection. As shown in Figure 1 and experimental results in [30], the DNN-based index selection has shown better performance for the loose accuracy and lower complexity than OMP-based approaches.…”

“…[36] shows that this re-estimation method using an extended support estimate of size m − 1 is guaranteed to further mitigate the sufficient conditions for SR algorithms based on the OMP-based index selection to restore the sparse signal.April 2, 2019 DRAFT…”

Weak RIC Analysis of Finite Gaussian Matrices for Joint Sparse Recovery

“…For instance, considering A S as the submatrix of A with columns indexed by the matrix support S, the WRIC tells how close is the column space of A S to that spanned by another disjoint set of columns with cardinality r [6]. 2 In fact, sufficient recovery conditions for various reconstruction methods are based on the WRIC, e.g., ℓ 2,1 -minimization [17], SA-Music [18], and OSMP [19]. The WRIC for Gaussian matrices has been bounded using concentration of measure inequalities and the union bound [17]- [19].…”

“…2 In fact, sufficient recovery conditions for various reconstruction methods are based on the WRIC, e.g., ℓ 2,1 -minimization [17], SA-Music [18], and OSMP [19]. The WRIC for Gaussian matrices has been bounded using concentration of measure inequalities and the union bound [17]- [19]. However, this approach results in a large overestimation of the WRIC leading to an underestimation of the maximum achievable s.…”