Least squares QR-based decomposition provides an efficient way of computing optimal regularization parameter in photoacoustic tomography

Abstract

A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison.

Nonlinear optoacoustic readings from diffusive media at near‐infrared wavelengths

“…The nonlinearity observed was found in superficial layers at depths <2 mm for our phantoms (Figure B), but the significance of the observed nonlinearity extend to the entire image during reconstruction from collected optoacoustic data at mescoscopic scales. Since we reconstruct the entire field of view (both at the mesoscopic and macroscopic regimes), the dynamic range of the entire imaging domain will be affected due to observed nonlinearity . Therefore, it is necessary to further investigate correction for the nonlinear response to improve tomographic or spectral unmixing quantification when using pulses of higher energy.…”

Accelerated image reconstruction using extrapolated Tikhonov filtering for photoacoustic tomography

“…The forward model of PA imaging can be represented as linear system of equations, by using system matrix approachwhere A is the system matrix containing impulse responses of all pixels in the imaging region as columns, b is the measured acoustic data on the boundary, and x is the initial pressure distribution. There are many approaches to solve for initial pressure such as filtered back projection (FBP), Fourier‐domain reconstruction, and time‐reversal methods .…”

“…The standard (zeroth order) choice for L is identity matrix ( I ); thus, the solution becomesThese regularization methods involve matrix–matrix multiplications as well as solving large system of equations, which is computationally expensive. Therefore, the Tikhonov regularization was implemented in a Lanczos bidiagonalization framework, to reduce the computational complexity . The Lanczos bidiagonalization of the system matrix A can be written aswhere M q = [ m 1 , m 2 ,…, m q ] and R q = [ r 1 , r 2 ,…, r q ] are the left and right orthogonal Lanczos matrices of dimensions m × ( q + 1) and n 2 × q respectively.…”

“…The GCV and L‐curve methods do not require any prior information as discrepancy principle. Recently, a least‐squares approach was developed and was shown to be an effective alternative compared to the L‐curve and GCV methods for automatic selection of regularization parameter . Subsequent to this work, an error estimate‐based method was proposed and shown to be computationally efficient compared to the least‐squares method in determining this regularization parameter automatically .…”

High speed photoacoustic tomography system with low cost portable pulsed diode laser

“…Reconstruction techniques are used to map the initial pressure rise in the object which is in turn correlated to the absorption coefficient of the object. [8][9][10][11][12][13] The applications of PAT are varied and include blood vessel imaging, Sentinel lymph node imaging, breast cancer detection and various others. 6,[14][15][16][17][18] The functional aspect of the PAT allows for the identification of the oxygenation level in the blood, and total blood volume.…”