The invention belongs to the field of
signal processing, and particularly relates to a two-dimensional inversion-free sparse Bayesian learning rapid sparse
reconstruction method. The method comprisesthe following steps of: S1: carrying out sparse representation modeling on a two-dimensional sparse
reconstruction problem; S2: performing statistical modeling on a vectorized sparse
signal x and vectorized
noise n; S3: solving the
posterior probability of the vectorized sparse
signal x, the vectorized inverse variance gamma and the
noise inverse variance alpha; and S4: updating the
matrix form Zof the auxiliary variables. Compared with the IFSBL method, the two-dimensional inversion-free sparse Bayesian learning rapid sparse
reconstruction method has the advantages that the two-dimensional signals are directly processed, the problem that a large matrix is generated due to vectorization of the two-dimensional signals is avoided, the operation efficiency is obviously improved, and the requirement on a calculation memory is obviously reduced; and on the other hand, sparse reconstruction is realized under a statistical
signal processing frame, and compared with a non-statistical sparse
reconstruction method, the method has the advantages of being easier to obtain a
global optimal solution, higher in
noise robustness, lower in dependence degree of
algorithm performance on parameter initialization and the like, and the
engineering practicability is high.