A Variational Inequality Model for the Construction of Signals from Inconsistent Nonlinear Equations

Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and recovery are reducible to the basic task finding point closed convex subset Hilbert space satisfies number nonlinear equations involving firmly nonexpansive operators. We investigate this formalism case when, due inaccurate modeling or perturbations, inconsistent. A relaxed formulation original problem is proposed form variational inequality. The properties investigated provenly convergent block-iterative algorithm, whereby only blocks underlying operators activated at given iteration, devised solve it. Numerical experiments illustrate robust recoveries several image processing applications.