Pouyan Mohajerani, Ali A. Eftekhar, and Ali Adibi, "Object localization in the presence of a strong heterogeneous background in fluorescent tomography," J. Opt. Soc. Am. A 25, 1467-1479 (2008)
We propose a method for object localization in fluorescent tomography (FT) in the presence of a highly heterogeneous background. Existing approaches typically assume a homogeneous background distribution; thus, they are incapable of accurately accounting for the more general case of an unconstrained, possibly heterogeneous, background. The proposed method iteratively solves the inverse problem over a solution space partitioned into a background subspace and an object subspace to simultaneously estimate the background and localize the target fluorescent objects. Simulation results of this algorithm applied to continuous-wave FT demonstrate effective localization of target objects in the presence of highly heterogeneous background distributions.
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(e) If the estimation is not stable,cthen and go to (b).
(f) If in the OMP mode, then switch to the BP mode and go to (b), else finished.
The estimated background and object signals at iteration i are given as and , respectively.
The value of the constant λ is adjusted based on the system matrix and the noise power. For a discussion, see [26].
Stability of the estimation error is assessed based on the amount of variations in the last three values of .
Table 2
Orthogonal Matching Pursuit
(a) Initialization; set and .
(b) Choose the next best index .
(c) Form the set of indices .
(d) Estimate the optimal coefficients given the indices
(e) Calculate the residual signal
(f) If ,then and go to (b).
Table 3
Iterative Method for Joint Estimation over Two Arbitrary Subspaces
(a) Initialization; set , , and .
(b) Find the best vector in given ;
.
(c) Find the best vector in given ;
.
(d) Calculate the estimation error .
(e) If the estimation error has converged,a then and go to (b).
(f) Set and .
Since the estimation error is positive and decreasing, it is converging (see Appendix C).
Tables (3)
Table 1
Proposed Method for Estimation of Object and Background Distributions
(a) Initialization; , , and . Start in the OMP mode.
(b) Estimate the background distribution given the current estimation of the object distribution;
(e) If the estimation is not stable,cthen and go to (b).
(f) If in the OMP mode, then switch to the BP mode and go to (b), else finished.
The estimated background and object signals at iteration i are given as and , respectively.
The value of the constant λ is adjusted based on the system matrix and the noise power. For a discussion, see [26].
Stability of the estimation error is assessed based on the amount of variations in the last three values of .
Table 2
Orthogonal Matching Pursuit
(a) Initialization; set and .
(b) Choose the next best index .
(c) Form the set of indices .
(d) Estimate the optimal coefficients given the indices
(e) Calculate the residual signal
(f) If ,then and go to (b).
Table 3
Iterative Method for Joint Estimation over Two Arbitrary Subspaces
(a) Initialization; set , , and .
(b) Find the best vector in given ;
.
(c) Find the best vector in given ;
.
(d) Calculate the estimation error .
(e) If the estimation error has converged,a then and go to (b).
(f) Set and .
Since the estimation error is positive and decreasing, it is converging (see Appendix C).