L(1)-norm based nonlinear reconstruction improves quantitative accuracy of spectral diffuse optical tomography

Spectrally constrained diffuse optical tomography (SCDOT) is known to improve reconstruction in diffuse optical imaging; constraining the reconstruction by coupling the optical properties across multiple wavelengths suppresses artefacts in the resulting reconstructed images. In other work, L(1)-norm regularization has been shown to improve certain types of image reconstruction problems as its sparsity-promoting properties render it robust against noise and enable the preservation of edges in images, but because the L(1)-norm is non-differentiable, it is not always simple to implement. In this work, we show how to incorporate L(1) regularization into SCDOT. Three popular algorithms for L(1) regularization are assessed for application in SCDOT: iteratively reweighted least square algorithm (IRLS), alternating directional method of multipliers (ADMM), and fast iterative shrinkage-thresholding algorithm (FISTA). We introduce an objective procedure for determining the regularization parameter in these algorithms and compare their performance in simulated experiments, and in real data acquired from a tissue phantom. Our results show that L(1) regularization consistently outperforms Tikhonov regularization in this application, particularly in the presence of noise.