Expand this Topic clickable element to expand a topic
Skip to content
Optica Publishing Group

A shape-based reconstruction technique for DPDW data

Open Access Open Access

Abstract

We give an approach for directly localizing and characterizing the properties of a compactly supported absorption coefficient perturbation as well as coarse scale structure of the background medium from a sparsely sampled, diffuse photon density wavefield. Our technique handles the problems of localization and characterization simultaneously by working directly with the data, unlike traditional techniques that require two stages. We model the unknowns as a superposition of a slowly varying perturbation on a background of unknown structure. Our model assumes that the anomaly is delineated from the background by a smooth perimeter which is modeled as a spline curve comprised of unknown control points. The algorithm proceeds by making small perturbations to the curve which are locally optimal. The result is a global, greedy-type optimization approach designed to enforce consistency with the data while requiring the solution to adhere to prior information we have concerning the likely structure of the anomaly. At each step, the algorithm adaptively determines the optimal weighting coefficients describing the characteristics of both the anomaly and the background. The success of our approach is illustrated in two simulation examples provided for a diffuse photon density wave problem arising in a bio-imaging application.

©2000 Optical Society of America

Full Article  |  PDF Article
More Like This
Three-dimensional shape-based imaging of absorption perturbation for diffuse optical tomography

Misha E. Kilmer, Eric L. Miller, Alethea Barbaro, and David Boas
Appl. Opt. 42(16) 3129-3144 (2003)

3D shape based reconstruction of experimental data in Diffuse Optical Tomography

Athanasios Zacharopoulos, Martin Schweiger, Ville Kolehmainen, and Simon Arridge
Opt. Express 17(21) 18940-18956 (2009)

Three-dimensional tomographic reconstruction of an absorptive perturbation with diffuse photon density waves

Matthew Braunstein and Robert Y. Levine
J. Opt. Soc. Am. A 17(1) 11-20 (2000)

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1. Source/receiver configuration in the transmission geometry.
Fig. 2.
Fig. 2. Anomaly Recovery Algorithm
Fig. 3.
Fig. 3. From left to right, top to bottom: a) Contour curves for b*(r), c 0(r), b k *(r) b) True image of the perturbation in the absorption coefficient c) TSVD reconstruction of the absorption perturbation d) our reconstruction of the absorption using h=1 and λ=.005.
Fig. 4.
Fig. 4. From left to right, top to bottom: a) Contour curves for b*(r), c 0(r), b k *(r) b) True image of the perturbation in the absorption coefficient c) TSVD reconstruction of the absorption perturbation d) our reconstruction of the absorption using h=1 and λ=.05.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

y ( r k ) = υ D v G ( r k , r ) G ( r , r s ) g ( r ) d r + n ( r k )
y i = G i g + n i , i = 1 , 2 N r or N r ,
y = Gg + n
g ( r ) S ( r ) B 1 ( r ) a 1 + ( 1 S ( r ) ) B 2 ( r ) a 2 , a 1 , a 2 R p × 1 ,
c ( s ) = [ x ( s ) , y ( s ) ] = i = 0 K 1 β k i ( s ) [ x ̂ i , y ̂ i ] , s [ 0 , L ]
g = [ SB 1 ( I S ) B 2 ] [ a 1 a 2 ] Qa
J ( a 1 , a 2 ) G [ SB 1 , ( I S ) B 2 ] [ a 1 a 2 ] y 2 .
J ( a 1 , a 2 ) + λ Ω ( c ) ,
Ω ( c ) = i = 1 K 2 ( x ̂ i x ̂ i + 1 ) 2 + ( y ̂ i y ̂ i + 1 ) 2
n sr ( ω ) = σ sr ( 0 ) υ 1
σ sr ( 0 ) = γ y ˜ s ( r ) + y ˜ s inc ( r )
Select as filters


Select Topics Cancel
© Copyright 2024 | Optica Publishing Group. All Rights Reserved