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 work, 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 (Lanczos T-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.

Solving inverse problems using data-driven models

“…This formulation uses a single data point g for simultaneously computing an operator update and for computing an approximation to the inverse problem. This is a heavily under-determined problem, which, however, leads to good results, at least for some applications: see Gutta et al (2019), Kluth and Maass (2017) and Hirakawa and Parks (2006). The regularized TLS approach has been analysed by Golub et al (1999), for example, who prove an equivalence result to classical Tikhonov regularization (Golub et al 1999, Theorem 2.1), which we restate here.…”

Image-guided filtering for improving photoacoustic tomographic image reconstruction

“…27 This BP image (x LBP ) is typically used as an initial guess for iterative model-based image reconstruction methods. 26,30 In this work, x LBP was used as guiding image to improve the reconstruction results obtained from model-based reconstruction methods.…”

“…The model-based image reconstruction algorithms were proposed in the literature for these limited data cases, which improve the quantitative accuracy of reconstructed images. [23][24][25][26] These algorithms especially iterative in nature also provide robustness to noise in the boundary data, 16,27 making them attractive in real-time. These model-based iterative reconstruction algorithms tend to be computationally complex compared to analytical algorithms like linear backprojection (LBP) and require utilization of regularization to constrain the solution space.…”

A New Simple, Fast and Robust Total Least Square Error Computation in E2: Experimental Comparison

“…3. The additional comparison of TLSE approximation method with other approximation methods is in [10] and the TLSE method gives the most accurate results. The more the angle of line with x axis increases, the more differs the standard approximation and the proposed approach.…”