A Novel Multiband Fusion Method Based on a Small Multiband-Measurement Matrix and a Nonconvex Log-Sum Regularization

A multiband fusion (MF) method can estimate a full-band echo (FBE) with a bandwidth larger than the sum of bandwidths of several subbands echoes. To improve estimation speed and estimation accuracy of the FBE, a novel MF method based on a small multiband-measurement matrix and a nonconvex log-sum regularization (LSR) is proposed and experimentally verified. In the method, the multiband-measurement matrix, which is in a subbands-echoes expression, provides a beneficial tool for speeding up the estimation of the FBE due to its small size. The small size is obtained by constructing the matrix only using the parameters of existing subbands and ignoring parameters of gaps between subbands. The LSR is developed in a multiband cost function to improve the estimation accuracy of the FBE, for its corresponding geometric property is similar to a geometric property of an
$l_{0}$
-norm regularization that can guarantee an unbiased estimate of FBE. In addition, since the imaging scene is sparse and the lack of several pulses does not affect the sparsity, the proposed method is robust to missing pulses. Simulation-data and real-date experimental results proved that the bandwidth of a fused FBE is 1.67 times the sum bandwidth of two subbands, the estimation accuracy and the estimation speed corresponding to the proposed method are 5.56 times and 1.11 times those of the traditional MF methods, respectively, and the proposed MF method is still feasible even when 10% of pulses are randomly missing.