Gradient-based quantitative photoacoustic image reconstruction for molecular imaging

Image reconstruction in fluorescence molecular tomography involves seeking stable and meaningful solutions via the inversion of a highly under-determined and severely ill-posed linear mapping. An attractive scheme consists of minimizing a convex objective function that includes a quadratic error term added to a convex and nonsmooth sparsity-promoting regularizer. Choosing [Formula: see text]-norm as a particular case of a vast class of nonsmooth convex regularizers, our paper proposes a low per-iteration complexity gradient-based first-order optimization algorithm for the [Formula: see text]-regularized least squares inverse problem of image reconstruction. Our algorithm relies on a combination of two ideas applied to the nonsmooth convex objective function: Moreau–Yosida regularization and inertial dynamics-based acceleration. We also incorporate into our algorithm a gradient-based adaptive restart strategy to further enhance the practical performance. Extensive numerical experiments illustrate that in several representative test cases (covering different depths of small fluorescent inclusions, different noise levels and different separation distances between small fluorescent inclusions), our algorithm can significantly outperform three state-of-the-art algorithms in terms of CPU time taken by reconstruction, despite almost the same reconstructed images produced by each of the four algorithms.

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Inverse Surfacelet Transform for Image Reconstruction With Constrained-Conjugate Gradient Methods

Journal of Computing and Information Science in Engineering ◽

10.1115/1.4026376 ◽

2014 ◽

Vol 14 (2) ◽

Cited By ~ 3

Author(s):

Wei Huang ◽

Yan Wang ◽

David W. Rosen

Keyword(s):

Image Reconstruction ◽

Conjugate Gradient ◽

Gradient Methods ◽

Optimization Methods ◽

Transformation Process ◽

Geometric Constraints ◽

Least Square ◽

Reconstruction Methods ◽

Gradient Based ◽

Surfacelet Transform

Image reconstruction is the transformation process from a reduced-order representation to the original image pixel form. In materials characterization, it can be utilized as a method to retrieve material composition information. In our previous work, a surfacelet transform was developed to efficiently represent boundary information in material images with surfacelet coefficients. In this paper, new constrained-conjugate-gradient based image reconstruction methods are proposed as the inverse surfacelet transform. With geometric constraints on boundaries and internal distributions of materials, the proposed methods are able to reconstruct material images from surfacelet coefficients as either lossy or lossless compressions. The results between the proposed and other optimization methods for solving the least-square error inverse problems are compared.

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