Ultrasonic reflectivity function estimation using Cepstrum Sparse Deconvolution

The ultrasonic signals backscattered from multilayered materials using a pulse-echo method are inherently low-resolution due to the band-limited nature of the interrogating transducer. To improve resolution, the Wiener Filter (WF) based solutions have been used traditionally, although they provide limited improvement and are highly sensitive to noise. More recently, sparse deconvolution techniques (e.g., ℓ1-regularized Least Squares Deconvolution (ℓ1-LSD)) have proved to be effective in improving the resolution; however, they are highly dependent on pulse invariance. It is common for an ultrasonic wavelet to change its shape as it propagates through the materials due to frequency dependent attenuation, scattering and dispersion. Consequently, these changes in pulse shape limit the application of these algorithms which need a prior knowledge of pulse-wave of the system. In this paper we present an adaptive and highly efficient deconvolution technique, Cepstrum Sparse Deconvolution (CSD), which does not require any prior information of the system or the detected object but compensates for the pulse-wave variation by estimating the fundamental pulse-wave shape directly from the backscattered signal. This pulse-wave estimation is based on cepstrum processing of the signal prior to the deconvolution process. Applications and comparisons are made to evaluate the performance of CSD, WF and ℓ1-LSD through experimental and simulated ultrasound data which contain varying-shape wavelets with respect to amplitude, center frequency, arrival time, bandwidth, and phase parameters. The Normalized Mean Absolute Score (NMAS) index, a measure of distance between the actual reflectivity function and the estimated function is used to evaluate these algorithms' performance. The results show that CSD is the fastest algorithm and offers highest resolution among these three algorithms even though the pulse-wave may have gone through a significant change.