Inverse problem of ultrasound plane wave imaging with a low-rank and sparse model

Medical images can be accurately reconstructed by solving the inverse problem, which was first applied to computed tomography (CT) imaging and magnetic resonance imaging (MRI). In recent years, it has been applied to ultrasound plane wave imaging. Current sparse regularization methods usually choose Laplace(ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm) or Gaussian(ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>-norm) regular terms to improve the image contrast and resolution, but it performs poorly in the preservation of speckle texture. To solve this problem, this paper propose to use a low-rank and sparse method to modeling the ultrasound plane wave imaging process as an inverse problem, in which the low rank property can better explore the correlations between image signals, making the recovered image closer to the actual situation. An optimization algorithm, based on 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 simulation and experimental datasets show that the proposed approach is better adapted to the ultrasound plane wave imaging process and can recover the image with higher quality than the current sparse regularization method.