Jixing Yao

Graduation Semester and Year

2013

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Electrical Engineering

Department

Electrical Engineering

First Advisor

Soontorn Oraintara

Abstract

Conventional reconstruction algorithms for diffuse optical tomography (DOT) is based on Tikhonov regularization method and the simple white Gaussian noise (WGN) assumption. These approaches usually lead to the following problems: 1. The reconstructed images are blurry; 2. In 3D reconstruction problems, the reconstructed objects are usually in the wrong depths; 3. The shape of a reconstructed object might be different from its original one due to the noise.In this work, after study the nature of DOT images as well as the data acquisition process, several sparsity regularization related reconstruction methods were developed to improve the spatial resolution as well as the fidelity of the reconstructed image. First, this thesis presents a simple reconstruction formula that adjusts the sensing matrix to improve the depth reconstruction in the 3D space. With the sparsity constraint, the spatial resolutions of a reconstructed image can also be improved even with WGN added to the measurements.Next, to make the reconstruction formula more practical, the physical sensing model and its relationship with the measurement noise are further studied. Consequently, an effective noise quantification method is derived. By incorporating this noise level information to the reconstruction process, objects with more complex shapes can be recovered almost correctly.Finally, the relative noise (RN) model is derived by considering the transformation from the light intensity measurements to relative light density changes. Thereafter, a maximum a posteriori (MAP) estimator, together with both $\ell_1$ norm and $\ell_2$ norm regularization terms, is developed. The resulting optimization problem is solved by the ellipsoid algorithm. The improvement of using this more accurate noise model is demonstrated by both computer simulation and phantom experiments.

Disciplines

Electrical and Computer Engineering | Engineering

Comments

Degree granted by The University of Texas at Arlington

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