Iterative Ultrasonic Signal and Image Deconvolution for Estimation of the Complex Medium Response

摘要

The ill-conditioned inverse problem of estimating ultrasonic medium responses by deconvolution of RF signals is investigated. The primary difference between the proposed method and others is that the medium response function is assumed to be complex-valued rather than restricted to being real-valued. Derived from the complex medium model, complex Wiener filtering is presented, and a Hilbert transform related limitation to inverse filtering type methods is discussed. We introduce a nonparametric iterative algorithm, the least squares method with point count regularization (LSPC). The algorithm is successfully applied to simulated and experimental data and demonstrates the capability of recovering both the real and imaginary parts of the medium response. The simulation results indicate that the LSPC method can outperform Wiener filters and improve the resolution of the ultrasound system by factors as high as 3.7. Experimental results using a single element transducer and a conventional medical ultrasound system with a linear array transducer show that despite the errors in pulse estimation and the noise in the RF signals, excellent results can be obtained, demonstrating the stability and robustness of the algorithm.