Continuous-Domain Formulation of Inverse Problems for Composite Sparse-Plus-Smooth Signals

We present a novel framework for the reconstruction of 1D composite signals assumed to be mixture two additive components, one sparse and other smooth, given finite number linear measurements. formulate problem as continuous-domain regularized inverse with multiple penalties. prove that these penalties induce reconstructed indeed take desired form sum smooth component. then discretize this using Riesz bases, which yields discrete can solved by standard algorithms. Our discretization is exact in sense we are solving over search space specified our bases without any error. propose complete algorithmic pipeline demonstrate its feasibility on simulated data.