Paper Info
Title
Statistical and Information-Theoretic Analysis of Resolution in Imaging
Abstract
In this paper, some detection-theoretic, estimation-theoretic, and information-theoretic methods are investigated to analyze the problem of determining resolution limits in imaging systems. The canonical problem of interest is formulated based on a model of the blurred image of two closely spaced point sources of unknown brightness. To quantify a measure of resolution in statistical terms, the following question is addressed: "What is the minimum detectable separation between two point sources at a given signal-to-noise ratio (SNR), and for prespecified probabilities of detection and false alarm (Pd and Pf )?". Furthermore, asymptotic performance analysis for the estimation of the unknown parameters is carried out using the Crameacuter-Rao bound. Although similar approaches to this problem (for one-dimensional (1-D) and oversampled signals) have been presented in the past, the analyzes presented in this paper are carried out for the general two-dimensional (2-D) model and general sampling scheme. In particular the case of under-Nyquist (aliased) images is studied. Furthermore, the Kullback-Liebler distance is derived to further confirm the earlier results and to establish a link between the detection-theoretic approach and Fisher information. To study the effects of variation in point spread function (PSF) and model mismatch, a perturbation analysis of the detection problem is presented as well
Year
DOI
Venue
2006
10.1109/TIT.2006.878180
IEEE Transactions on Information Theory
Keywords
Field
DocType
Nyquist criterion,image resolution,image restoration,image sampling,information theory,statistical analysis,Cramer-Rao bound,Kullback-Liebler distance,Nyquist image,PSF,asymptotic performance analysis,canonical problem,detection-theoretic method,estimation-theoretic method,image blur,imaging resolution,information-theoretic method,perturbation analysis,point spread function,sampling scheme,statistical analysis,Aliasing,Cram&#201,r&#8211,Rao bound,Fisher information,Kullback&#8211,Liebler distance,detection,estimation,imaging,information-theoretic imaging,model mismatch,perturbation analysis,resolution,variational analysis
Information theory,Cramér–Rao bound,Discrete mathematics,False alarm,Computer science,Image processing,Algorithm,Fisher information,Constant false alarm rate,Image restoration,Statistics,Point spread function
Journal
Volume
Issue
ISSN
52
8
0018-9448
Citations 
PageRank 
References 
10
0.95
10
Authors
2
Name
Order
Citations
PageRank
Shahram, M.1100.95
Peyman Milanfar270052.20