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    This study introduces a flexible method for diffuse optical tomographic image reconstruction using various penalty functions. Geman-McClure penalty optimizes reconstruction for complex targets, outperforming others like quadratic and L1 penalties.

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    Area of Science:

    • Medical Imaging
    • Computational Imaging
    • Biomedical Engineering

    Background:

    • Diffuse optical tomography (DOT) is a non-invasive imaging technique.
    • Image reconstruction in DOT often relies on regularization methods.
    • Nonquadratic penalty functions offer potential advantages over traditional quadratic penalties.

    Purpose of the Study:

    • To introduce a versatile framework for incorporating generic penalty functions into DOT image reconstruction.
    • To evaluate the performance of various nonquadratic penalty functions (L1, Cauchy, Geman-McClure) against quadratic (L2) penalties.
    • To demonstrate the utility of nonquadratic penalties for reconstructing complex targets in DOT.

    Main Methods:

    • Developed a generalized approach to integrate arbitrary penalty functions into the DOT image reconstruction algorithm.
    • Implemented and compared quadratic (L2), absolute (L1), Cauchy, and Geman-McClure penalty functions.
    • Utilized generalized cross-validation for automatic regularization parameter selection.
    • Quantitatively assessed reconstruction quality using relative error and Pearson correlation metrics.

    Main Results:

    • Nonquadratic penalties (L1, Cauchy, Geman-McClure) showed superior performance in reconstructing high-contrast and complex-shaped targets compared to the quadratic penalty.
    • The quadratic penalty provided better separation for closely spaced targets but had limited contrast recovery.
    • The Geman-McClure penalty emerged as the most optimal, demonstrating the best overall reconstruction quality for complex scenarios.

    Conclusions:

    • Nonquadratic penalty functions significantly enhance diffuse optical tomographic image reconstruction, particularly for complex targets.
    • The proposed framework allows for flexible integration of various penalty functions, enabling tailored image reconstruction.
    • The Geman-McClure penalty is a highly effective choice for improving contrast recovery and target shape fidelity in DOT.