Sparse deconvolution of ultrasound NDE echoes accounting for pulse variance

In this paper, we propose a new method of the material reflectivity function (MRF) recovery based on an RF measurement model in which the ultrasound signal is expressed as a sequence of parametric model echoes whose shapes are allowed to vary in accordance with the spectral characteristics of the measuring transducer. We then utilize the Model Based Estimation Pursuit (MBEP) to concurrently estimate the reflectivity and spectral parameters of the echo from the local data. We tested MBEP in comparison with a sparse deconvolution method, the ℓ1-regularized Least Squares Deconvolution (ℓ1-LSD) via a series of simulated RF data containing varying pulses. The restored MRFs are compared against the ground truths using the correlation match index (CMI) metric. MBEP not only provides more accurate recovery of MRFs but also reveals the frequency dependent attenuation as evident in the pulse spectrum. The ℓ1-LSD, however, due to its inflexibility with varying pulses, fails to recover the true scatterers. Further, compared to ℓ1-LSD, the MBEP provides about 25% improvement in CMI and is about 10 times computationally faster.