Elastic net regularization in diffuse optical tomography applications

Diffuse optical tomography (DOT) uses near-infrared light to obtain quantitative information about the optical coefficients in biological tissues. Such an information can be clinically exploited for diagnostic purposes. In DOT, the surface of the investigated tissue is illuminated with a light source and the emerging light is measured at various locations on the surface itself. The minimization of the discrepancy between the observed data and the corresponding field generated by a mathematical model of light propagation is then performed, yielding an estimated distribution of the optical parameters in the tissue. This problem is characterized by severe ill-conditioning, so that appropriate regularization techniques must be applied to obtain a meaningful solution. To do this, the use of ell-2 (Tikhonov) penalization has been generally advocated in this context; more recently, ell-1 (LASSO)-norm penalization has also been proposed to detect the existence of sparsity patterns. Both approaches are classical regularization techniques and are often favored in DOT over other methods, when robustness with respect to geometry and need for almost real-time results are an issue. The goal of the present contribution is to explore the 'elastic net' regularization technique originally introduced by Zou and Hastie [1], that shares the desirable properties of both the ell-2-- and ell-1-norm penalization approaches. Whilst this technique has been largely used as a learning theory tool in different applications, at the best of our knowledge, this paper presents its first use in DOT applications. Numerical simulations are performed here on a simple 2D geometry, to assess the potentialities of this approach. The results show that this technique may be a good choice for our target application, where DOT is used as a cheap, first-level and almost real-time screening technique for breast cancer detection.