Robust signal recovery from incomplete observations

Recently, a series of exciting results have shown that it is possible to reconstruct a sparse signal exactly from a very limited number of linear measurements by solving a convex optimization program. If our underlying signal f can be written as a superposition of B elements from a known basis, it is possible to recover f from a projection onto a generic subspace of dimension about B log N. Moreover, the procedure is robust to measurement error; adding a perturbation of size ϵ to the measurements will not induce a recovery error of more than a small constant times ϵ. In this paper, we will briefly overview these results, and show how the recovery via convex optimization can be implemented in an efficient manner, and present some numerical results illustrating the practicality of the procedure

Cardiac Computed Tomography Methods and Systems Using Fast Exact / Quasi Exact Filtered Back Projection Algorithms

The present invention provides systems, methods, and devices for improved computed tomography. More specifically, the present invention includes methods for improved cone-beam computed tomography (CBCT) resolution using improved filtered back projection (FBP) algorithms, which can be used for cardiac tomography and across other tomographic modalities. Embodiments provide methods, systems, and devices for reconstructing an image from projection data provided by a computed tomography scanner using the algorithms disclosed herein to generate an image with improved temporal resolution