Quadratic functional estimation in inverse problems

Quadratic functional estimation in inverse problems

We consider in this paper a Gaussian sequence model of observations Yi, i ≥ 1 having mean (or signal) θi and variance σi which is growing polynomially like i γ , γ > 0. This model describes a large panel of inverse problems. We estimate the quadratic functional of the unknown signal ∑ i≥1 θ 2 i when the signal belongs to ellipsoids of both finite smoothness functions (polynomial weights i, α > ...

Parameter Estimation and Inverse Problems

System Parameter Estimation in Tomographic Inverse Problems

Inverse problems are typically solved under the assumption of known geometric system parameters describing the forward problem. Should such information be unavailable or inexact, the estimation of these parameters from only observed sensor data may be necessary prior to reconstruction of the desired signal. We demonstrate the feasibility of such estimation via maximum-likelihood methods for the...

Needlet algorithms for estimation in inverse problems

Abstract: We provide a new algorithm for the treatment of inverse problems which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. Our goal is to devise an inversion procedure which has the advantages of localization and multiscale analysis of wavelet representations without losing the stability and computability of the SVD decompositi...

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...