TCI Volume 5 Issue 1

Signal reconstruction is a challenging aspect of computational imaging as it often involves solving ill-posed inverse problems. Recently, deep feed-forward neural networks have led to state-of-the-art results in solving various inverse imaging problems. However, being task specific, these networks have to be learned for each inverse problem. On the other hand, a more flexible approach would be to learn a deep generative model once and then use it as a signal prior for solving various inverse problems.

It is well-established in the compressive sensing (CS) literature that sensing matrices whose elements are drawn from independent random distributions exhibit enhanced reconstruction capabilities. In many CS applications, such as electromagnetic imaging, practical limitations on the measurement system prevent one from generating sensing matrices in this fashion.

The low-rank plus sparse (L+S) decomposition model enables the reconstruction of undersampled dynamic parallel magnetic resonance imaging data. Solving for the low rank and the sparse components involves nonsmooth composite convex optimization, and algorithms for this problem can be categorized into proximal gradient methods and variable splitting methods. This paper investigates new efficient algorithms for both schemes.

Ghost imaging has recently been successfully achieved in the X-ray regime. Due to the penetrating power of X-rays this immediately opens up the possibility of ghost-tomography. No research into this topic currently exists in the literature. Here, we present adaptations of conventional X-ray tomography techniques to this new ghost-imaging scheme. Several numerical implementations for tomography through X-ray ghost-imaging are considered.