A LSQR‐type method provides a computationally efficient automated optimal choice of regularization parameter in diffuse optical tomography

Abstract

The LSQR-type method was able to overcome the inherent limitation of computationally expensive nature of MRM-based automated way finding the optimal regularization parameter in diffuse optical tomographic imaging, making this method more suitable to be deployed in real-time.

Image-guided filtering for improving photoacoustic tomographic image reconstruction

“…49. The left and right Lanczos matrices and the bidiagonal matrix are related to the system matrix A as follows: 29,46 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 6 ; 6 3 ; 2 9 6 M kþ1 ðβ 0 e 1 Þ ¼ b;…”

“…(9) in Eq. (4) and using the property M T Kþ1 M Kþ1 ¼ I, the cost function can be rewritten as follows: 29,46 E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 1 0 ; 3 2 6 ; 7 2 9Ω…”

“…There exists an optimal k, which reduces the error between x est and x Tikh within the precision limits. 46,49 Since dimensionality reduction is obtained using the Lanczos algorithm, this method offers computationally efficient solutions as compared to the other methods, including the solution given in Eq. (5).…”

Basis pursuit deconvolution for improving model-based reconstructed images in photoacoustic tomography

“…[37]. The left and right Lanczos matrices and the bidiagonal matrix is related to system matrix (A) as [22,23] U k+1 (β 0 e 1 ) = b (6)…”

“…Previous works have used least-square QR (LSQR) based decomposition methods in obtaining accurate reconstruction with less number of detectors [19][20][21][22]. Moreover, optimal selection of regularization parameter using LSQR based method provides quantitatively more accurate reconstruction compared to L-curve and GCV based methods [22,23]. Hence in this work, LSQR based method was deployed to estimate optimal regularization parameter [22].…”