Optimizing the regularization for image reconstruction of cerebral diffuse optical tomography

Abstract

Functional near-infrared spectroscopy (fNIRS) is an optical method for noninvasively determining brain activation by estimating changes in the absorption of near-infrared light. Diffuse optical tomography (DOT) extends fNIRS by applying overlapping “high density” measurements, and thus providing a three-dimensional imaging with an improved spatial resolution. Reconstructing brain activation images with DOT requires solving an underdetermined inverse problem with far more unknowns in the volume than in the surface measurements. All methods of solving this type of inverse problem rely on regularization and the choice of corresponding regularization or convergence criteria. While several regularization methods are available, it is unclear how well suited they are for cerebral functional DOT in a semi-infinite geometry. Furthermore, the regularization parameter is often chosen without an independent evaluation, and it may be tempting to choose the solution that matches a hypothesis and rejects the other. In this simulation study, we start out by demonstrating how the quality of cerebral DOT reconstructions is altered with the choice of the regularization parameter for different methods. To independently select the regularization parameter, we propose a cross-validation procedure which achieves a reconstruction quality close to the optimum. Additionally, we compare the outcome of seven different image reconstruction methods for cerebral functional DOT. The methods selected include reconstruction procedures that are already widely used for cerebral DOT [minimum l2-norm estimate (l2MNE) and truncated singular value decomposition], recently proposed sparse reconstruction algorithms [minimum l1- and a smooth minimum l0-norm estimate (l1MNE, l0MNE, respectively)] and a depth- and noise-weighted minimum norm (wMNE). Furthermore, we expand the range of algorithms for DOT by adapting two EEG-source localization algorithms [sparse basis field expansions and linearly constrained minimum variance (LCMV) beamforming]. Independent of the applied noise level, we find that the LCMV beamformer is best for single spot activations with perfect location and focality of the results, whereas the minimum l1-norm estimate succeeds with multiple targets.

An optical flow-based approach for the interpolation of minimally divergent velocimetry data

“…The profiles shown in the figure show that there needs to be a balance between the divergence and smoothing terms. The graphs in the figure are consistent with profiles of other published 2 -based regularization methods [69,70]. Figure 10 shows the behavior of the proposed method as γ and λ increase linearly.…”

Overview of diffuse optical tomography and its clinical applications

“…Finding an appropriate regularization parameter is crucial to the reconstruction of high-quality images. 109,110 A recent cerebral DOT study has reported that the appropriate regularization parameter varies with the number of activation spots; the linearly constrained minimum variance beamforming is the best for single spot activation, while the minimum l 1 -norm estimate resolves two activation spots best. 110 Unlike magnetic resonance imaging (MRI) and x-ray CT, DOT itself does not provide anatomical (structural) information, which makes it difficult to solve the forward model correctly.…”

Estimating Functional Connectivity Symmetry between Oxy- and Deoxy-Haemoglobin: Implications for fNIRS Connectivity Analysis

“…However, not accounting for them might lead to a misleading interpretation due to the appearance of spurious associations. This risk can be reduced by simultaneously measuring physiological data alongside fNIRS, performing digital filtering as a preprocessing step, or including systemic confounders when modelling the fNIRS signal reconstruction, processing and analysis to compute relative changes in Hb species [19,[61][62][63]. However, to date, only few researchers have considered the inclusion of physiological measurements when dealing with fNIRS FC analysis [10,60,64].…”