L1-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, L1-norm regularization has been shown to improve certain types of image reconstruction problem as its sparsity-promoting properties render it robust against noise and enable preservation of edges in images, but because the L1-norm is non-differentiable, it is not always simple to implement. In this work, we show how to incorporate L1 regularization into SCDOT. Three popular algorithms for L1 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 L1 regularization consistently outperforms Tikhonov regularization in this application, particularly in the presence of noise.