Towards improved image reconstruction in breast diffuse optical tomography using compressed sensing: a comparative study among L_p (0≤p≤2) sparsity regularizations

摘要

The underdeterminedness of the inverse problems encountered in diffuse optical tomography (DOT) becomes especially severe when detecting breast cancers, because much more variables are needed to be reconstructed due to the big-size. With the addition of ill-condition caused by the diffusive nature of light propagation, the ill-posedness makes it very difficult to improve the image reconstruction. Fortunately, from the anatomy viewpoint, we have known that the cancer is distributed locally and only amounts to a small percentage of the whole breast. This makes it possible to employ the compressive sensing theory to mitigate the ill-posedness, based on the prior knowledge about the sparsity of the signal to be reconstructed. Specifically speaking, sparsity regularizations can be used in DOT to improve the image reconstruction under the premise that un-increase the number of measurements required in the reconstruction. In this paper, we primarily focus on comparing the performances of different kinds of Lp-norm-based regularizations in terms of theory and real effects, respectively. The numerical and phantom experiments have proven that the sparsity regularizations can dramatically improve the image reconstruction. Furthermore, as the p in the L_p-norm decreasing to zero, the solutions become sparser and the corresponding image quality gets higher, with smooth L_0-norm-based regularization providing the highest image quality.