Ultrasonic echo spike detection using ℓ1-regularized sparse deconvolution

Ultrasonic backscattered echoes measured from materials or tissues are inherently complex due to the band-limited nature of the interrogating transducer and high degree of speckle noise. In the ultrasonic detection, the first and most important goal is to determine spikes which represent the position and amplitude of reflection echoes from objects. To identify those spikes, in our previous work, we adopted Wiener Filter (WF), ℓ1-regularized Least Squares Deconvolution (ℓ1-LSD), Model Based Estimation Pursuit (MBEP) and Cepstrum Sparse Deconvolution (CSD) for deconvolution. WF has low resolution and is sensitive to noise. ℓ1-LSD is good to eliminate white noise but it fails to extract the right spike. CSD has an advantage in terms of separating two heavily interfered echoes, however it may fail when the signal is embedded in heavy noise. Since it has the best performance to deal with a noisy signal, this paper further explores ℓ1-LSD. A new solver based on AR model of ℓ1-LSD is studied. To differentiate this solver from previous solver (ℓ1-LSD), we named it ℓ1-regularizd Sparse Deconvolution (ℓ1-RSD). This paper analyzes ℓ1-RSD and Gaussian model theoretically. Performance evaluation of ℓ1-RSD for LTI system signal and ultrasonic signal is illustrated. As usual, simulations show that this ℓ1-regularized algorithm fail to determine true spikes for ultrasonic signal although it has excellent performance for LTI system signal. ℓ1-LSD or ℓ1-RSD is based on linear time invariant (LTI) systems theory, their performance deteriorates dramatically when the system becomes non-linear and time variant. Gaussian echo model which is widely verified and used in ultrasonic signal is nonlinear. This essential difference between ℓ1-RSD and Gaussian model leads to a poor performance of ℓ1-regularized algorithms when processing ultrasonic signal. This encourages us to investigate more new algorithms as an adapter to solve the incompatibility in the future.