Hankel Structured Low Rank and Sparse Representation via L0-Norm Optimization for Compressed Ultrasound Plane Wave Signal Reconstruction

Ultrasound plane wave imaging is widely used in many applications thanks to its capability in reaching high frame rates. However, the amount of data acquisition and storage in a period of time can become a bottleneck in ultrasound system design for thousands frames per second. In our previous study, we proposed a low-rank and joint-sparse model to reduce the amount of sampled channel data of focused beam imaging by considering all the received data as a 2D matrix. However, for a single plane wave transmission, the number of channels is limited and the low-rank property of the received data matrix is no longer achieved. In this study, a L0-norm based Hankel structured low-rank and sparse model is proposed to reduce the channel data. An optimization algorithm, based on the alternating direction method of multipliers (ADMM), is proposed to efficiently solve the resulting optimization problem. The performance of the proposed approach was evaluated using the data published in Plane Wave Imaging Challenge in Medical Ultrasound (PICMUS) in 2016. Results on channel and plane wave data show that the proposed method is better adapted to the ultrasound channel signal and can recover the image with fewer samples than the conventional CS method.