Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics

04/17/2012
by   Klaus Frick, et al.
0

In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in [Frick K, Marnitz P, and Munk A. "Statistical multiresolution Dantzig estimation in imaging: Fundamental concepts and algorithmic framework". Electron. J. Stat., 6:231-268, 2012]. It constitutes a variational regularization technique that uses an supremum-type distance measure as data-fidelity combined with a convex cost functional. The resulting convex optimization problem is approached by a combination of an inexact alternating direction method of multipliers and Dykstra's projection algorithm. We describe a novel method for balancing data-fit and regularity that is fully automatic and allows for a sound statistical interpretation. The performance of our estimation approach is studied for various problems in imaging. Among others, this includes deconvolution problems that arise in Poisson nanoscale fluorescence microscopy.

READ FULL TEXT

page 9

page 16

page 17

page 18

page 20

page 21

page 22

page 23

research
01/23/2011

Statistical Multiresolution Dantzig Estimation in Imaging: Fundamental Concepts and Algorithmic Framework

In this paper we are concerned with fully automatic and locally adaptive...
research
08/08/2021

Image reconstruction in light-sheet microscopy: spatially varying deconvolution and mixed noise

We study the problem of deconvolution for light-sheet microscopy, where ...
research
09/08/2016

Adaptive Regularization in Convex Composite Optimization for Variational Imaging Problems

We propose an adaptive regularization scheme in a variational framework ...
research
05/09/2017

Adaptive Regularization of Some Inverse Problems in Image Analysis

We present an adaptive regularization scheme for optimizing composite en...
research
03/15/2013

Variational Semi-blind Sparse Deconvolution with Orthogonal Kernel Bases and its Application to MRFM

We present a variational Bayesian method of joint image reconstruction a...
research
07/21/2022

Whiteness-based parameter selection for Poisson data in variational image processing

We propose a novel automatic parameter selection strategy for variationa...
research
05/08/2015

Bilevel approaches for learning of variational imaging models

We review some recent learning approaches in variational imaging, based ...

Please sign up or login with your details

Forgot password? Click here to reset