Modeling Errors Compensation With Total Least Squares for Limited Data Photoacoustic Tomography

Abstract

The limited data photoacoustic image reconstruction problem is typically solved using either weighted or ordinary least squares (LS), with regularization term being added for stability, which account only for data imperfections (noise). Numerical modeling of acoustic wave propagation requires discretization of imaging region and is typically developed based on many assumptions, such as speed of sound being constant in the tissue, making it imperfect. In this paper, two variants of total least squares (TLS), namely ordinary TLS and Sparse TLS were developed, which account for model imperfections. The ordinary TLS is implemented in the Lanczos bidiagonalization framework to make it computationally efficient. The sparse TLS utilizes the total variation penalty to promote recovery of high frequency components in the reconstructed image. The Lanczos truncated TLS and Sparse TLS methods were compared with the recently established state-of-the-art methods, such as Lanczos Tikhonov and Exponential Filtering. The TLS methods exhibited better performance for experimental data as well as in cases where modeling errors were present, such as few acoustic detectors malfunctioning and speed of sound variations. Also, the TLS methods does not require any prior information about the errors present in the model or data, making it attractive for real-time scenarios.