Total Variation Minimization with Separable Sensing Operator

Compressed Imaging is the theory that studies the problem of image recovery from an under-determined system of linear measurements. One of the most popular methods in this field is Total Variation (TV) Minimization, known for accuracy and computational efficiency. This paper applies a recently developed Separable Sensing Operator approach to TV Minimization, using the Split Bregman framework as the optimization approach. The internal cycle of the algorithm is performed by efficiently solving coupled Sylvester equations rather than by an iterative optimization procedure as it is done conventionally. Such an approach requires less computer memory and computational time than any other algorithm published to date. Numerical simulations show the improved — by an order of magnitude or more — time vs. image quality compared to two conventional algorithms.