In this paper, we consider minimizing the $L_1/L_2$ term on the gradient for a limited-angle scanning problem in computed tomography (CT) reconstruction. We design a specific splitting framework for an unconstrained optimization model so that the alternating direction method of multipliers (ADMM) has guaranteed convergence under certain conditions. In addition, we incorporate a box constraint that is reasonable for imaging applications, and the convergence for the additional box constraint can also be established. Numerical results on both synthetic and experimental datasets demonstrate the effectiveness and efficiency of our proposed approach, showing significant improvements over the state-of-the-art methods in the limited-angle CT reconstruction.

MOTIVATION: Spectral unmixing methods attempt to determine the concentrations of different fluorophores present at each pixel location in an image by analyzing a set of measured emission spectra. Unmixing algorithms have shown great promise for applications where samples contain many fluorescent labels; however, existing methods perform poorly when confronted with autofluorescence-contaminated images. RESULTS: We propose an unmixing algorithm designed to separate fluorophores with overlapping emission spectra from contamination by autofluorescence and background fluorescence. First, we formally define a generalization of the linear mixing model, called the affine mixture model (AMM), that specifically accounts for background fluorescence. Second, we use the AMM to derive an affine nonnegative matrix factorization method for estimating fluorophore endmember spectra from reference images. Lastly, we propose a semi-blind sparse affine spectral unmixing (SSASU) algorithm that uses knowledge of the estimated endmembers to learn the autofluorescence and background fluorescence spectra on a per-image basis. When unmixing real-world spectral images contaminated by autofluorescence, SSASU greatly improved proportion indeterminacy as compared to existing methods for a given relative reconstruction error. AVAILABILITY AND IMPLEMENTATION: The source code used for this paper was written in Julia and is available with the test data at https://github.com/brossetti/ssasu.

Digital tomosynthesis imaging is becoming increasingly significant in a variety of medical imaging applications. Tomosynthesis imaging involves the acquisition of a series of projection images over a limited angular range, which, after reconstruction, results in a pseudo–three-dimensional (3D) representation of the imaged object. The partial separation of features in the third dimension improves the visibility of lesions of interest by reducing the effect of the superimposition of tissues. In breast cancer imaging, tomosynthesis is a viable alternative to standard mammography; however, current algorithms for image reconstruction do not take into account the polyenergetic nature of the x-ray source beam entering the object. This results in inaccuracies in the reconstruction, making quantitative analysis challenging and allowing for beam hardening artifacts. In this paper, we develop a mathematical framework based on a polyenergetic model and develop statistically based iterative methods for digital tomosynthesis reconstruction for breast imaging. By applying our algorithms to simulated data, we illustrate the success of our methods in suppressing beam hardening artifacts and improving the overall quality of the reconstruction.

Major breakthroughs in chip and software design have been observed for the last nine years. In October 2001, IBM released the world’s first multicore processor: POWER4. Six years later, in February 2007, NVIDIA made a public release of CUDA SDK, a set of development tools to write algorithms for execution on Graphic Processing Units (GPUs). Although software vendors have started working on parallelizing their products, the vast majority of existing code is still sequential and does not effectively utilize modern multicore CPUs and manycore GPUs. This article describes Parallel Colt, a multithreaded Java library for scientific computing and image processing. In addition to describing the design and functionality of Parallel Colt, a comparison to MATLAB is presented. Two ImageJ plugins for iterative image deblurring and motion correction of PET brain images are described as typical applications of this library. Performance comparisons with MATLAB, including GPU computations via AccelerEyes’ Jacket toolbox are also given.

We derive Kronecker product approximations, with the help of tensor decompositions, to construct approximations of severely ill-conditioned matrices that arise in three-dimensional (3-D) image processing applications. We use the Kronecker product approximations to derive preconditioners for iterative regularization techniques; the resulting preconditioned algorithms allow us to restore 3-D images in a computationally efficient manner. Through examples in microscopy and medical imaging, we show that the Kronecker approximation preconditioners provide a powerful tool that can be used to improve efficiency of iterative image restoration algorithms.

Removing a linear shift-invariant blur from a signal or image can be accomplished by inverse or Wiener filtering, or by an iterative least-squares deblurring procedure. Because of the ill-posed characteristics of the deconvolution problem, in the presence of noise, filtering methods often yield poor results. On the other hand, iterative methods often suffer from slow convergence at high spatial frequencies. This paper concerns solving deconvolution problems for atmospherically blurred images by the preconditioned conjugate gradient algorithm, where a new approximate inverse preconditioner is used to increase the rate of convergence. Theoretical results are established to show that fast convergence can be expected, and test results are reported for a ground-based astronomical imaging problem.