Effective contrast recovery in rapid dynamic near-infrared diffuse optical tomography using <inline-formula><math display="inline" overflow="scroll"><mrow><msub><mrow><mo mathvariant="bold-script">ℓ</mo></mrow><mrow><mn>1</mn></mrow></msub></mrow></math></inline-formula>-norm-based linear image reconstruction method

Abstract

Traditional image reconstruction methods in rapid dynamic diffuse optical tomography employ ℓ(2)-norm-based regularization, which is known to remove the high-frequency components in the reconstructed images and make them appear smooth. The contrast recovery in these type of methods is typically dependent on the iterative nature of method employed, where the nonlinear iterative technique is known to perform better in comparison to linear techniques (noniterative) with a caveat that nonlinear techniques are computationally complex. Assuming that there is a linear dependency of solution between successive frames resulted in a linear inverse problem. This new framework with the combination of ℓ(1)-norm-based regularization can provide better robustness to noise and provide better contrast recovery compared to conventional ℓ(2)-based techniques. Moreover, it is shown that the proposed ℓ(1)-based technique is computationally efficient compared to its counterpart (ℓ(2)-based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame, and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames.

An Optical Flow-Based Approach for Minimally Divergent Velocimetry Data Interpolation

“…The profiles shown in the figure show that there needs to be a balance between the divergence and the smoothing terms. The graphs in the figure are consistent with profiles of other published ℓ 2 -based regularization methods [67, 68]. Figure 10 shows the behavior of the proposed method as γ and λ increase linearly.…”

Optimizing the regularization for image reconstruction of cerebral diffuse optical tomography

“…This allowed the generation of datasets to be recorded in psycho-physiological experiments, while at the same time allowing for a direct assessment of the reconstruction quality. In contrast to other studies, 21,23 all methods were tested on a semi-infinite medium. This geometry can rely on back-reflected light only and there might be differences from the usually used circles or cylinders where light is applied from all sides.…”

“…Therefore, a variety of sparse image reconstruction methods, such as l p -norm-based algorithms with 0 ≤ p ≤ 1, have been introduced in optical imaging. [20][21][22][23][24] Other approaches to reconstruct the brain activation are provided by developments in electrophysiological dipole mapping. The inverse problem of electroencephalography (EEG) localizes the position of the active cerebral current source from the measured surface fields, and is comparable with the inverse problem of image reconstruction in DOT.…”

“…• recently proposed sparse methods (minimum l 1 -and a smooth minimum l 0 -norm estimate), 17,[21][22][23][24] • and finally, two EEG source localization algorithms adapted to DOT. More precisely, we apply the linearly constrained minimum variance (LCMV) beamformer 25 and a method for source localization using spatial flexibility (S-FLEX).…”

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

“…6,22 This method description is given as Algorithm 1 of Ref. 23. This method is briefly reviewed here.…”