Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction.

PURPOSE: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. METHODS: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. RESULTS: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. CONCLUSIONS: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

Space- and intensity-constrained reconstruction for compressed ultrafast photography.

The single-shot compressed ultrafast photography (CUP) camera is the fastest receive-only camera in the world. In this Letter, we introduce an external CCD camera and a space- and intensity-constrained (SIC) reconstruction algorithm to improve the image quality of CUP. The external CCD camera takes a time-unsheared image of the dynamic scene. Unlike the previously used unconstrained algorithm, the proposed algorithm incorporates both spatial and intensity constraints based on the additional prior information provided by the external CCD camera. First, a spatial mask is extracted from the time-unsheared image to define the zone of action. Next, an intensity threshold is determined based on the similarity between the temporally projected image of the reconstructed datacube and the time-unsheared image. Both simulation and experimental studies show that the SIC reconstruction improves the spatial resolution, contrast, and general quality of the reconstructed image.

Boundary-enhancement in propagation-based x-ray phase-contrast tomosynthesis improves depth position characterization.

Propagation-based x-ray phase-contrast (PB XPC) tomosynthesis combines the concepts of tomosynthesis and XPC imaging to realize the advantages of both for biological imaging applications. Tomosynthesis permits reductions in acquisition times compared with full-view tomography, while XPC imaging provides the opportunity to resolve weakly absorbing structures. In this note, an investigation of the depth resolving properties of PB XPC tomosynthesis is conducted. The results demonstrate that in-plane structures display strong boundary-enhancement while out-of-plane structures do not. This effect can facilitate the identification of in-plane structures in PB XPC tomosynthesis that could normally not be distinguished from out-of-plane structures in absorption-based tomosynthesis.

Proximal ADMM for multi-channel image reconstruction in spectral X-ray CT.

The development of spectral X-ray computed tomography (CT) using binned photon-counting detectors has received great attention in recent years and has enabled selective imaging of contrast agents loaded with K-edge materials. A practical issue in implementing this technique is the mitigation of the high-noise levels often present in material-decomposed sinogram data. In this work, the spectral X-ray CT reconstruction problem is formulated within a multi-channel (MC) framework in which statistical correlations between the decomposed material sinograms can be exploited to improve image quality. Specifically, a MC penalized weighted least squares (PWLS) estimator is formulated in which the data fidelity term is weighted by the MC covariance matrix and sparsity-promoting penalties are employed. This allows the use of any number of basis materials and is therefore applicable to photon-counting systems and K-edge imaging. To overcome numerical challenges associated with use of the full covariance matrix as a data fidelity weight, a proximal variant of the alternating direction method of multipliers is employed to minimize the MC PWLS objective function. Computer-simulation and experimental phantom studies are conducted to quantitatively evaluate the proposed reconstruction method.

Sparsity-regularized image reconstruction of decomposed K-edge data in spectral CT.

The development of spectral computed tomography (CT) using binned photon-counting detectors has garnered great interest in recent years and has enabled selective imaging of K-edge materials. A practical challenge in CT image reconstruction of K-edge materials is the mitigation of image artifacts that arise from reduced-view and/or noisy decomposed sinogram data. In this note, we describe and investigate sparsity-regularized penalized weighted least squares-based image reconstruction algorithms for reconstructing K-edge images from few-view decomposed K-edge sinogram data. To exploit the inherent sparseness of typical K-edge images, we investigate use of a total variation (TV) penalty and a weighted sum of a TV penalty and an ℓ1-norm with a wavelet sparsifying transform. Computer-simulation and experimental phantom studies are conducted to quantitatively demonstrate the effectiveness of the proposed reconstruction algorithms.

Nondestructive volumetric imaging of tissue microstructure with benchtop x-ray phase-contrast tomography and critical point drying.

The in vitro investigation of many optically opaque biological microstructures requires 3D analysis at high resolution over a large field of view. We demonstrate a new nondestructive volumetric imaging technique that eliminates the structural and computational limitations of conventional 2D optical microscopy by combining x-ray phase-contrast tomography with critical point drying sample preparation. We experimentally demonstrate the enhancement of small features afforded by phase-contrast imaging and show the contrast improvement afforded by the drying of a hydrated specimen. We further demonstrate the biological application of this technique by imaging the microstructure of the accommodative apparatus in a primate eye using a benchtop phase-contrast tomography system.

Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography.

Differential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorption contrast. The tomographic projection data in DPCT, from which an estimate of the refractive index distribution is reconstructed, correspond to one-dimensional (1D) derivatives of the two-dimensional (2D) Radon transform of the refractive index distribution. There is an important need for the development of iterative image reconstruction methods for DPCT that can yield useful images from few-view projection data, thereby mitigating the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods. In this work, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT. We also investigate the use of one of the models with a modern image reconstruction algorithm for performing few-view image reconstruction of a tissue specimen.

Framework for computing the spatial coherence effects of polycapillary x-ray optics.

Despite the extensive use of polycapillary x-ray optics for focusing and collimating applications, there remains a significant need for characterization of the coherence properties of the output wavefield. In this work, we present the first quantitative computational method for calculation of the spatial coherence effects of polycapillary x-ray optical devices. This method employs the coherent mode decomposition of an extended x-ray source, geometric optical propagation of individual wavefield modes through a polycapillary device, output wavefield calculation by ray data resampling onto a uniform grid, and the calculation of spatial coherence properties by way of the spectral degree of coherence.

Multispectral intensity diffraction tomography: single material objects with variable densities.

A reconstruction theory for multispectral intensity diffraction tomography (I-DT) is established and investigated for use with single material objects whose dispersion characteristics are known a priori. Instead of varying the object-to-detector distance, as prescribed by the original I-DT method and other classic in-line holographic reconstruction methods, the temporal frequency of the illuminating plane wave represents the degree of freedom of the imaging system that is varied to acquire two independent intensity measurements at each tomographic view angle. Unlike previous multispectral I-DT methods, the proposed method does not require a nondispersive assumption. A computer-simulation study is presented to demonstrate and corroborate the method.