Browsing by Subject "Filtered variation"

Now showing 1 - 2 of 2

Open Access
Filtered Variation method for denoising and sparse signal processing
(IEEE, 2012) Köse, Kıvanç; Cevher V.; Çetin, A. Enis
We 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.
Open Access
Projections onto the epigraph set of the filtered variation function based deconvolution algorithm
(IEEE, 2017) Tofighi, M.; Çetin, A. Enis
A new deconvolution algorithm based on orthogonal projections onto the hyperplanes and the epigraph set of a convex cost function is presented. In this algorithm, the convex sets corresponding to the cost function are defined by increasing the dimension of the minimization problem by one. The Filtered Variation (FV) function is used as the convex cost function in this algorithm. Since the FV cost function is a convex function in RN, then the corresponding epigraph set is also a convex set in the lifted set in RN+1. At each step of the iterative deconvolution algorithm, starting with an arbitrary initial estimate in RN+1, first the projections onto the hyperplanes are performed to obtain the first deconvolution estimate. Then an orthogonal projection is performed onto the epigraph set of the FV cost function, in order to regularize and denoise the deconvolution estimate, in a sequential manner. The algorithm converges to the deblurred image.