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A fast regularized least-squares method for retinal vascular oxygen tension estimation using a phosphorescence lifetime imaging model.

Gunay G, Yildirim I - Biomed Eng Online (2013)

Bottom Line: In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates.This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

View Article: PubMed Central - HTML - PubMed

Affiliation: Electrical and Electronics Engineering Department, Istanbul Technical University, 34469 Istanbul, Turkey. iyildirim@itu.edu.tr.

ABSTRACT

Background: Monitoring retinal oxygenation is of primary importance in detecting the presence of some common eye diseases. To improve the estimation of oxygen tension in retinal vessels, regularized least-squares (RLS) method was shown to be very effective compared with the conventional least-squares (LS) estimation. In this study, we propose an accelerated RLS estimation method for the problem of assessing the oxygenation of retinal vessels from phosphorescence lifetime images.

Methods: In the previous work, gradient descent algorithms were used to find the minimum of the RLS cost function. This approach is computationally expensive, especially when the oxygen tension map is large. In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates. This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.

Results: Performance analyses are conducted using both real and simulated data sets. In terms of computational complexity, the proposed RLS estimation method is significantly better than RLS methods that use gradient descent algorithms to find the minimum of the cost function. Additionally, there is no significant difference between the estimates acquired by the proposed and conventional RLS estimation methods.

Conclusion: The proposed RLS estimation method for computing the retinal oxygen tension is computationally efficient, and produces estimates with negligible difference from those obtained by iterative RLS methods. Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

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Flowchart of the proposed method.
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Figure 1: Flowchart of the proposed method.

Mentions: The proposed method is visualized in Figure 1 as a flow chart: (A) Using the phosphorescence lifetime images, (B-C) the LS estimates of the model parameters a1 and b1 of the original pO2 map are found in matrix form. (D), whose dimension is Rs2× Rs2, is found for a small Rs× RspO2 map, and (E) its middle row is chosen. Rs is chosen as an odd number to ensure symmetry with respect to the middle unit in the chosen row. Because is in Toeplitz form except for the first and last two rows, all other rows can be recovered exactly using this row with appropriate shifts. Additionally, elements in the middle row that determine the weights to obtain approximate RLS estimates of the model parameters (F) can be reshaped to give an Rs× Rs weighted averaging window. (G) Finally, this weighted averaging window is applied to the LS estimates of the a1 and b1 parameter maps to find approximate RLS estimates of the model parameters.


A fast regularized least-squares method for retinal vascular oxygen tension estimation using a phosphorescence lifetime imaging model.

Gunay G, Yildirim I - Biomed Eng Online (2013)

Flowchart of the proposed method.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3818002&req=5

Figure 1: Flowchart of the proposed method.
Mentions: The proposed method is visualized in Figure 1 as a flow chart: (A) Using the phosphorescence lifetime images, (B-C) the LS estimates of the model parameters a1 and b1 of the original pO2 map are found in matrix form. (D), whose dimension is Rs2× Rs2, is found for a small Rs× RspO2 map, and (E) its middle row is chosen. Rs is chosen as an odd number to ensure symmetry with respect to the middle unit in the chosen row. Because is in Toeplitz form except for the first and last two rows, all other rows can be recovered exactly using this row with appropriate shifts. Additionally, elements in the middle row that determine the weights to obtain approximate RLS estimates of the model parameters (F) can be reshaped to give an Rs× Rs weighted averaging window. (G) Finally, this weighted averaging window is applied to the LS estimates of the a1 and b1 parameter maps to find approximate RLS estimates of the model parameters.

Bottom Line: In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates.This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

View Article: PubMed Central - HTML - PubMed

Affiliation: Electrical and Electronics Engineering Department, Istanbul Technical University, 34469 Istanbul, Turkey. iyildirim@itu.edu.tr.

ABSTRACT

Background: Monitoring retinal oxygenation is of primary importance in detecting the presence of some common eye diseases. To improve the estimation of oxygen tension in retinal vessels, regularized least-squares (RLS) method was shown to be very effective compared with the conventional least-squares (LS) estimation. In this study, we propose an accelerated RLS estimation method for the problem of assessing the oxygenation of retinal vessels from phosphorescence lifetime images.

Methods: In the previous work, gradient descent algorithms were used to find the minimum of the RLS cost function. This approach is computationally expensive, especially when the oxygen tension map is large. In this study, using a closed-form solution of the RLS estimation and some inherent properties of the problem at hand, the RLS process is reduced to the weighted averaging of the LS estimates. This decreases the computational complexity of the RLS estimation considerably without sacrificing its performance.

Results: Performance analyses are conducted using both real and simulated data sets. In terms of computational complexity, the proposed RLS estimation method is significantly better than RLS methods that use gradient descent algorithms to find the minimum of the cost function. Additionally, there is no significant difference between the estimates acquired by the proposed and conventional RLS estimation methods.

Conclusion: The proposed RLS estimation method for computing the retinal oxygen tension is computationally efficient, and produces estimates with negligible difference from those obtained by iterative RLS methods. Further, the results of this study can be applied to other lifetime imaging problems that have similar properties.

Show MeSH
Related in: MedlinePlus