Köse, KıvançCevher V.Çetin, A. Enis2016-02-082016-02-0820121520-6149http://hdl.handle.net/11693/28155Date of Conference: 25-30 March 2012We propose a new framework, called Filtered Variation (FV), for denoising and sparse signal processing applications. These problems are inherently ill-posed. Hence, we provide regularization to overcome this challenge by using discrete time filters that are widely used in signal processing. We mathematically define the FV problem, and solve it using alternating projections in space and transform domains. We provide a globally convergent algorithm based on the projections onto convex sets approach. We apply to our algorithm to real denoising problems and compare it with the total variation recovery. © 2012 IEEE.EnglishFiltered variationAlternating projectionsDe-noisingDenoising problemsDiscrete-time filtersFiltered variationGlobally convergentIll posedProjection onto convex setsProjections onto convex setsSparse signalsTotal variationTransform domainVariation methodAlgorithmsSet theorySignal processingProblem solvingConference Paper10.1109/ICASSP.2012.6288628