Patent ID: 8861655

Claim:
A method of performing structure-based Bayesian sparse signal reconstruction, comprising the steps of: (a) receiving a signal x; (b) establishing an observation vector y and a sensing matrix Ψ such that y=Ψx+n, where n represents complex additive white Gaussian noise; (c) correlating the observation vector y with columns of the sensing matrix Ψ; (d) generating a correlation vector comprised of correlations between the observation vector y with columns of the sensing matrix Ψ above a set threshold value; (e) determining a vector index of the correlation vector with a highest level of correlation and generating a cluster of set length L centered about the vector index with the highest level of correlation; (f) determining a vector index of the correlation vector with the next highest level of correlation and generating a cluster of set length L centered about the vector index with the next highest level of correlation with a correlation above a set correlation threshold κ; (g) repeating step (f) until all possible correlations with a correlation above the set correlation threshold κ are exhausted to form a set of semi-orthogonal clusters; (h) calculating a likelihood of support |S i | for each of the semi-orthogonal clusters in the range of |S i |=1 to |S i |=P c , wherein P c represents a maximum possible support size in the cluster, and |S i | represents the likelihood support of the i-th cluster; and (i) calculating an estimated signal vector x MMSE as: x MMSE = [ Σ Z 1 ⋐ S 1 ⁢ p ⁡ ( Z 1 | y ) ⁢ 𝔼 ⁡ [ x | y , Z 1 ] Σ Z 2 ⋐ S 2 ⁢ p ⁡ ( Z 2 | y ) ⁢ 𝔼 ⁡ [ x | y , Z 2 ] ⋮ Σ Z C ⋐ S C ⁢ p ⁡ ( Z C | y ) ⁢ 𝔼 ⁡ [ x | y , Z C ] ] , wherein Z 1 . . . Z C are a set of dummy variables (each ranging through a respective likelihood of support), [x|y, Z 1 ] . . . [x|y, Z C ] are a set of expected values of the sparse vector x, and p(Z 1 |y) . . . p(Z C |y) are a set of probable support sizes of the respective semi-orthogonal clusters.