Quasi-optimal filtering in inverse problems

Quasi-Invariant Optimal Control Problems

Quasi-Invariant Optimal Control Problems

We study in optimal control the important relation between invariance of the problem under a family of transformations, and the existence of preserved quantities along the Pontryagin extremals. Several extensions of Noether theorem are provided, in the direction which enlarges the scope of its application. We formulate a more general version of Noether’s theorem for optimal control problems, wh...

Optimal change-point estimation in inverse problems

We develop a method of estimating change{points of a function in the case of indirect noisy observations. As two paradigmatic problems we consider de-convolution and errors-in-variables regression. We estimate the scalar products of our indirectly observed function with appropriate test functions, which are shifted over the interval of interest. An estimator of the change point is obtained by t...

Quasi closed phase analysis for glottal inverse filtering

This study presents a new glottal inverse filtering (GIF) technique based on the closed phase analysis over multiple fundamental periods. The proposed Quasi Closed Phase Analysis (QCP) method utilizes Weighted Linear Prediction (WLP) with a specific Attenuated Main Excitation (AME) weighting function that attenuates the contribution of the glottal source in the linear prediction model optimizat...

Designing Optimal Spectral Filters for Inverse Problems

Spectral filtering suppresses the amplification of errors when computing solutions to ill-posed inverse problems; however, selecting good regularization parameters is often expensive. In many applications, data are available from calibration experiments. In this paper, we describe how to use such data to precompute optimal spectral filters. We formulate the problem in an empirical Bayes risk mi...