Nonlinear compressed sensing for multi-emitter X-ray imaging

Compressed sensing is a powerful mathematical modelling tool to recover sparse signals from undersampled measurements in many applications, including medical imaging. A large body of work investi- gates the case with linear measurements, while compressed sensing with nonlinear measurements has been considered more recently. We continue this line of investigation by considering a novel type of nonlinearity with special structure that occurs in data acquired by multi-emitter X-ray tomosynthesis systems with spatio-temporal overlap. In [16] we proposed a nonlinear optimization model to deconvolve the overlapping measure- ments. In this paper we propose a model that exploits the structure of the nonlinearity and a nonlinear tomosynthesis algorithm that has a practical running time of solving only two linear subproblems at the equivalent resolution. We underpin and justify the algorithm by deriving RIP bounds for the linear subproblems and conclude with numerical experiments that validate the approach.