Ultrasonic range resolution enhancement using L1 norm deconvolution

Deconvolution techniques have been widely used to improve resolution and quality of ultrasonic images One of the optimality criteria is minimizing the Lp norm of the estimation error. It has been shown that the L1 norm deconvolution is more robust than the L2 norm. Linear programming and iterative reweighted least squares (IRLS) algorithms have been implemented in L1 deconvolution. Because the linear programming algorithm does not always guarantee selection of a reasonable prediction error filter from the many which may solve the problem, the IRLS L1 norm deconvolution starts from the well-known p=2 case (Wiener filter) and iterates toward a solution from there. In this paper, the split spectrum processing (SSP) spectral histogram is utilized to estimate the Wiener filter transfer function. The spectral histogram technique is based on the statistics of narrowband and signals selected by the absolute-minimization operation. Theoretical analysis indicates that the spectral histogram is similar in nature to the Wiener filter transfer function and can therefore be used to estimate the optimal frequency region for L1 deconvolution. The theoretical and experimental results indicate resolution enhancement in identifying and extracting multiple targets