Compressed sensing in diffuse optical tomography.

Diffuse optical tomography (DOT) allows tomographic (3D), non-invasive reconstructions of tissue optical properties for biomedical applications. Severe under-sampling is a common problem in DOT which leads to image artifacts. A large number of measurements is needed in order to minimize these artifacts. In this work, we introduce a compressed sensing (CS) framework for DOT which enables improved reconstructions with under-sampled data. The CS framework uses a sparsifying basis, ℓ1-regularization and random sampling to reduce the number of measurements that are needed to achieve a certain accuracy. We demonstrate the utility of the CS framework using numerical simulations. The CS results show improved DOT results in comparison to "traditional" linear reconstruction methods based on singular-value decomposition (SVD) with ℓ2-regularization and with regular and random sampling. Furthermore, CS is shown to be more robust against the reduction of measurements in comparison to the other methods. Potential benefits and shortcomings of the CS approach in the context of DOT are discussed.