A property of the minimum vectors of a regularizing functional defined by means of the absolute norm
- 1 April 1997
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Signal Processing
- Vol. 45 (4) , 913-917
- https://doi.org/10.1109/78.564179
Abstract
We consider a regularizing functional defined by means of the l/sub 1/ norm, where the regularization is obtained using first differences; as is well-known, such a functional can be put in relation with recursive median filters of appropriate window length. We show that at least one of the minima is reached at a vector, whose components have values over the same discrete set of the given signal. This suggests a simple method to refine the approximate solution to the regularization problem, which can be obtained with recursive median filters of increasing order. We also report an example of application, where the refinement method is employed for a signal detection problem.Keywords
This publication has 8 references indexed in Scilit:
- Recursive median filters of increasing order: a variational approachIEEE Transactions on Signal Processing, 1996
- An algorithm for the minimization of mixed l/sub 1/ and l/sub 2/ norms with application to Bayesian estimationIEEE Transactions on Signal Processing, 1994
- Digital filters as absolute norm regularizersIEEE Transactions on Signal Processing, 1992
- Adaptive stack filtering under the mean absolute error criterionIEEE Transactions on Acoustics, Speech, and Signal Processing, 1990
- Minimum mean absolute error stack filtering with structural constraint and goalsIEEE Transactions on Acoustics, Speech, and Signal Processing, 1990
- Maximum likelihood estimation of a class of non-Gaussian densities with application to I/sub p/ deconvolutionIEEE Transactions on Acoustics, Speech, and Signal Processing, 1989
- A smoothness priors time-varying AR coefficient modeling of nonstationary covariance time seriesIEEE Transactions on Automatic Control, 1985
- Convex AnalysisPublished by Walter de Gruyter GmbH ,1970