Ultrasonic signal decomposition through gradient descent assisted successive parameter estimation

Accurate decomposition of ultrasonic signals into simple pulses is valuable both for data compression purposes, as well as various medical and engineering applications. This work proposes a matching pursuit (MP) based algorithm that deploys a traditional successive parameter estimation approach, to express ultrasonic signals as sums of Gaussian pulses or chirplets. However, here the MP algorithm is aided by mathematical optimisation (gradient descent), which allows for significantly more precise parameter estimation. Our method is validated on simple input signals, and following its validation, its performance is assessed against cases of increasing complexity. The results not only suggest the accuracy and robustness of our approach, but also show how the proposed method performs well with signals containing strongly overlapping pulses, a challenge for existing methods. Results are also obtained from realistic signals generated through finite element modelling or experimental measurements. Finally, beyond the reconstruction results, we discuss and demonstrate how even complicated signals are well described through only a few parameters, eliminating the need for storing full time traces, allowing for effective ultrasonic data compression. • Accurate decomposition of signals into sums of Gaussian pulses or chirplets. • Achieved via gradient descent assisted matching pursuit algorithm. • Process initialised via established grid search approach, avoiding local minima. • Achieved good results for challenging cases, without manual input. • Adaptable to decomposition into pulses other than Gaussian or chirplets.