Robust adaptive Wiener filtering

Abstract

A recent paper by Anderes and Paul [1] analyze a regression characterization of a new estimator of lensing from cosmic microwave observations, developed by Hu and Okamoto [2, 3, 4]. A key tool used in that paper is the application of the robust generalized shrinkage priors developed 30 years ago in [5, 6, 7] to the problem of adaptive Wiener filtering. The technique requires the user to propose a fiducial model for the spectral density of the unknown signal but the resulting estimator is developed to be robust to misspecification of this model. The role of the fiducial spectral density is to give the estimator superior statistical performance in a “neighborhood of the fiducial model” while controlling the statistical errors when the fiducial spectral density is drastically wrong. One of the main advantages of this adaptive Wiener filter is that one can easily obtain posterior samples of the true signal given the unknown data. These posterior samples are particularly advantageous when studying non-linear functions of the signal, cross correlating with other independent measurements of the same signal and can be used to propagate uncertainty when the filtering is done in a scientific pipeline. In this paper we explore these advantages with simulations and examine the possibility of widespread application in more general image and signal processing problems.