Paper Info
Title
Shape from moments - an estimation theory perspective
Abstract
This paper discusses the problem of recovering a planar polygon from its measured complex moments. These moments correspond to an indicator function defined over the polygon's support. Previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given. In this paper, we extend these results and treat the same problem in the case where a longer than necessary series of noise corrupted moments is given. Similar to methods found in array processing, system identification, and signal processing, we discuss a set of possible estimation procedures that are based on the Prony and the Pencil methods, relate them one to the other, and compare them through simulations. We then present an improvement over these methods based on the direct use of the maximum-likelihood estimator, exploiting the above methods as initialization. Finally, we show how regularization and, thus, maximum a posteriori probability estimator could be applied to reflect prior knowledge about the recovered polygon.
Year
DOI
Venue
2004
10.1109/TSP.2004.828919
Signal Processing, IEEE Transactions
Keywords
Field
DocType
array signal processing,maximum likelihood estimation,noise,Pencil method,Prony method,complex moments,estimation procedures,estimation theory,indicator function,maximum a posteriori probability estimator,maximum-likelihood estimator,necessary and sufficient conditions,noise,planar polygon,prior knowledge,recovery process,regularization
Polygon,Array processing,Mathematical optimization,Indicator function,Inverse problem,Initialization,Maximum a posteriori estimation,Estimation theory,Mathematics,Estimator
Journal
Volume
Issue
ISSN
52
7
1053-587X
Citations 
PageRank 
References 
29
2.14
16
Authors
3
Name
Order
Citations
PageRank
Michael Elad111274854.93
Peyman Milanfar270052.20
G.H. Golub3292.14