Denoising RF Data via Robust Principal Component Analysis: Results in Ultrasound Elastography.

Ultrasound data often suffers from an excessive amount of noise especially from deep tissue or in synthetic aperture imaging where the acoustic wave is weak. Such noisy data renders Time Delay Estimation (TDE) inaccurate in the context of ultrasound elastography. Herein, a novel two-step elastography technique is presented to ensure accurate TDE while dealing with noisy ultrasound data. In the first step, instead of one, we acquire several Radio-Frequency (RF) frames from both pre- and post-deformed positions of the tissue. We stack the frames collected from pre- and post-deformed planes in separate data matrices. Since each set is collected from the same level of tissue compression, we assume that the Casorati data matrices exhibit underlying low-rank structures, which are sought by taking the low-rank and sparse decomposition framework into account. This Robust Principal Component Analysis (RPCA) approach removes the random noise from the datasets as sparse error components. In the second step, we select one frame from each denoised ensemble and employ GLobal Ultrasound Elastography (GLUE) to perform the strain elastography. We call the proposed technique RPCA-GLUE. Our preliminary validation of RPCA-GLUE against simulation phantoms containing hard and soft inclusions proves its robustness to large noise. Substantial improvement in Signal-to-Noise Ratio (SNR) and Contrast-to-Noise Ratio (CNR) has also been observed. Simulation results show that in the presence of large noise, the proposed method substantially improves CNR from 5.0 to 22.6 in a soft inclusion and from 2.2 to 21.7 in a hard inclusion phantom.