Iterative model-based image reconstruction using a constrained least-squares technique

Michael C. Roggemann; David W. Tyler

doi:10.1117/12.255080

25 October 1996 Iterative model-based image reconstruction using a constrained least-squares technique

Proceedings Volume 2827, Digital Image Recovery and Synthesis III; (1996) https://doi.org/10.1117/12.255080
Event: SPIE's 1996 International Symposium on Optical Science, Engineering, and Instrumentation, 1996, Denver, CO, United States

Abstract

In this paper the problem of optimally using object model information in image reconstruction is addressed. A closed form solution for the estimated object spectrum is derived using the Lagrange multiplier technique which assumes a measured image, knowledge of the optical transfer function, statistical information about the measurement noise, and a model of the object. This reconstruction algorithm is iterative in nature for two reasons: (1) because the optimal Lagrange multiplier is not generally known at the start of the problem; and (2) we can use the object estimate obtained from one step of the algorithm as the model input for the next step. In this paper we derive the estimator, describe one technique for determining the optimal Lagrange multiplier, demonstrate a stopping criterion based on the mean squared error between a noise free image and the photon-limited version of the image, and show representative results for a sparse aperture imaging application.

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Michael C. Roggemann and David W. Tyler "Iterative model-based image reconstruction using a constrained least-squares technique", Proc. SPIE 2827, Digital Image Recovery and Synthesis III, (25 October 1996); https://doi.org/10.1117/12.255080

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KEYWORDS

Optical transfer functions

Image filtering

Image restoration

Model-based design

Data modeling

Reconstruction algorithms

Imaging systems

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