Reconstructing low-dose X-ray computed tomography (CT) images is a noise problem. This work investigated a penalized weighted least-squares (PWLS) approach to address this problem in two dimensions, where the WLS considers first- and second-order noise moments and the penalty models signal spatial correlations. Three different implementations were studied for the PWLS minimization. One utilizes a Markov random field (MRF) Gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the PWLS cost function by iterative Gauss-Seidel algorithm. Another employs Karhunen-Loeve (KL) transform to de-correlate data signals among nearby views and minimizes the PWLS adaptively to each KL component by analytical calculation, where the spatial correlation among nearby bins is modeled by the same Gibbs functional. The third one models the spatial correlations among image pixels in image domain also by a MRF Gibbs functional and minimizes the PWLS by iterative successive over-relaxation algorithm. In these three implementations, a quadratic functional regularization was chosen for the MRF model. Phantom experiments showed a comparable performance of these three PWLS-based methods in terms of suppressing noise-induced streak artifacts and preserving resolution in the reconstructed images. Computer simulations concurred with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS implementation may have the advantage in terms of computation for high-resolution dynamic low-dose CT imaging

Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography

From the perspective of a chemist, biology confers a rich variety of roles on a number of metal ions. It is widely agreed that a large fraction of the genomic output of living things contains metal or metalloid ions, although estimates of this fraction vary widely and depend upon which metal ions are considered.1−3 Moreover, recent reports suggest that, at least in some cases, there are many uncharacterized metalloproteins.4 With inclusion of the s-block metals such as Na, K, Mg, and Ca, the proportion likely approaches 100%; recent estimates from the protein data bank indicate that the prevalence of heavier metal ions of atomic number above 20 within proteins is around 22%,5 with Zn2+ proteins alone constituting about 11%. Living organisms have an inherent and very rich physical structure, with relevant length scales ranging from the nanometer scale for subcellular structure to hundreds of micrometers and above for tissue, organ, or organism-level organization. The ability to derive the spatial distribution of elements on this diversity of length scales is a key to understanding their function.

Metals play essential and central roles in the most important and chemically challenging processes required for life, with active site structures and mechanisms that, at the time of their discovery, have usually not yet been duplicated in the chemical laboratory. Furthermore, diseases of metal dysregulation can cause disruption in the distribution of metals.6 For example, Menke’s disease and Occipital Horn Syndrome,7 and Wilson’s disease,8 involve disruption in copper uptake and excretion, respectively, through mutation in the ATP7A and ATP7B Cu transporters.9 The mechanisms of action of toxic elements such as mercury and arsenic are also of interest, as are essential nonmetal trace elements, such as selenium. Likewise, an increasing number of pharmaceuticals include metals or heavier elements; such chemotherapeutic drugs include the platinum derivatives cisplatin and carboplatin,10 some promising new ruthenium drugs,11 and arsenic trioxide, which has been used to treat promyelocytic leukemia.12 Understanding the localization, speciation, and distribution of these at various length scales is of significant interest.

A wide variety of heavier elements can be probed by X-ray spectroscopic methods; these are shown graphically in Figure ​Figure1.1. X-ray fluorescence imaging is a powerful technique that can be used to determine elemental and chemical species distributions at a range of spatial resolutions within samples of biological tissues. Most modern applications require the use of synchrotron radiation as a tunable and high spectral brightness source of X-rays. The method uses a microfocused X-ray beam to excite X-ray fluorescence from specific elements within a sample. Because the method depends upon atomic physics, it is highly specific and enables a wide range of chemical elements to be investigated. A significant advantage over more conventional methods is the ability to measure intact biological samples without significant treatment with exogenous reagents. The technique is capable of determining metal and nonmetal distributions on a variety of length scales, with information on chemical speciation also potentially available. Figure ​Figure22 shows examples of rapid-scan X-ray fluorescence imaging at two contrasting length scales: rapid-scan imaging13 of a section of a human brain taken from an individual suffering from multiple sclerosis and showing elemental profiles for Fe, Cu, and Zn;14 and a high-resolution image showing mercury and other elements in a section of retina from a zebrafish larva treated with methylmercury chloride.15 We will discuss both the state of the art in terms of experimental methods and some recent applications of the methods. This Review considers X-ray fluorescence imaging with incident X-ray energies in the hard X-ray regime, which we define as 2 keV and above. We review technologies for producing microfocused X-ray beams and for detecting X-ray fluorescence, as well as methods that confer chemical selectivity or three-dimensional visualization. We discuss applications in key areas with a view to providing examples of how the technique can provide information on biological systems. We also discuss synergy with other methods, which have overlapping or complementary capabilities. Our goal is to provide useful and pertinent information to encourage and enable further use of this powerful method in chemical and biochemical studies of living organisms.



Figure 1

Periodic table of the elements showing elements of biological interest that can be probed using X-ray fluorescence imaging. Elements are divided into three categories, those that are physiologically important, those that are pharmacologically active, ...

Elemental and Chemically Specific X-ray Fluorescence Imaging of Biological Systems

Recent advances in murine cardiac studies with three-dimensional (3D) cone beam micro-CT used a retrospective gating technique However, this sampling technique results in a limited number of projections with an irregular angular distribution due to the temporal resolution requirements and radiation dose restrictions Both angular irregularity and undersampling complicate the reconstruction process, since they cause significant streaking artifacts This work provides an iterative reconstruction solution to address this particular challenge A sparseness prior regularized weighted l2 norm optimization is proposed to mitigate streaking artifacts based on the fact that most medical images are compressible Total variation is implemented in this work as the regularizer for its simplicity Comparison studies are conducted on a 3D cardiac mouse phantom generated with experimental data After optimization, the method is applied to in vivo cardiac micro-CT data

Sparseness prior based iterative image reconstruction for retrospectively gated cardiac micro-CT

The advent of nanosciences calls for the development of local structural probes, in particular to characterize ill-ordered or heterogeneous materials. Furthermore, because materials properties are often related to their heterogeneity and the hierarchical arrangement of their structure, different structural probes covering a wide range of scales are required. X-ray diffraction is one of the prime structural methods but suffers from a relatively poor detection limit, whereas transmission electron analysis involves destructive sample preparation. Here we show the potential of coupling pencil-beam tomography with X-ray diffraction to examine unidentified phases in nanomaterials and polycrystalline materials. The demonstration is carried out on a high-pressure pellet containing several carbon phases and on a heterogeneous powder containing chalcedony and iron pigments. The present method enables a non-invasive structural refinement with a weight sensitivity of one part per thousand. It enables the extraction of the scattering patterns of amorphous and crystalline compounds with similar atomic densities and compositions. Furthermore, such a diffraction-tomography experiment can be carried out simultaneously with X-ray fluorescence, Compton and absorption tomographies, enabling a multimodal analysis of prime importance in materials science, chemistry, geology, environmental science, medical science, palaeontology and cultural heritage.

Probing the structure of heterogeneous diluted materials by diffraction tomography.

This paper shows that synchrotron-based fluorescence and absorption-edge computed microtomographies (CMT) are well-suited for determining the compartmentalization and concentration of metals in hyperaccumulating plant tissues. Fluorescence CMT of intact leaf, stem, and root samples revealed that Ni concentrated in stem and leaf dermal tissues and, together with Mn, in distinct regions associated with the Ca-rich trichomes on the leaf surface of the nickel hyperaccumulator Alyssum murale “Kotodesh”. Metal enrichment was also observed within the vascular system of the finer roots, stem, and leaves but absent from the coarser root, which had a well-correlated metal coating. Absorption-edge CMT showed the three-dimensional distribution of the highest metal concentrations and verified that epidermal localization and Ni and Mn co-localization at the trichome base are phenomena that occurred throughout the entire leaf and may contribute significantly to metal detoxification and storage. Ni was also observed in t...

Application of quantitative fluorescence and absorption-edge computed microtomography to image metal compartmentalization in Alyssum murale.

We present a statistically principled sinogram smoothing approach for X-ray computed tomography (CT) with the intent of reducing noise-induced streak artifacts. These artifacts arise in CT when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines. Attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements. While these approaches involve loose consideration of the measurement statistics to determine smoothing levels, they do not explicitly model the statistical distributions of the measurement data. We present an explicitly statistical approach to sinogram smoothing in the presence of photon-starved measurements. It is an extension of a nonparametric sinogram smoothing approach using penalized Poisson-likelihood functions that we have previously developed for emission tomography. Because the approach explicitly models the data statistics, it is naturally adaptive-it will smooth more variable measurements more heavily than it does less variable measurements. We find that it significantly reduces streak artifacts and noise levels without comprising image resolution.

Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing

X-ray fluorescence computed tomography (XFCT) allows for the reconstruction of the distribution of elements within a sample from measurements of fluorescence x rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality; thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. This is challenging because the attenuation map is, in general, known only at the stimulating beam energy and not at the various fluorescence energies of interest. We make use of empirically fitted analytic expressions for x-ray attenuation coefficients to express the unknown attenuation maps as linear combinations of known quantities and the unknown elemental concentrations of interest. We then develop an iterative image reconstruction algorithm based on penalized-likelihood methods that have been developed for medical emission tomography. Studies with numerical phantoms indicate that the approach is able to produce qualitatively and quantitatively accurate reconstructed images even in the face of severe attenuation. We also apply the method to real synchrotron-acquired data and demonstrate a marked improvement in image quality relative to filtered backprojection reconstruction.

Penalized-likelihood image reconstruction for x-ray fluorescence computed tomography

X-ray fluorescence computed tomography (XFCT) allows for the reconstruction of the distribution of nonradioactive elements within a sample from measurements of fluorescence x-rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality and thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. This is challenging because the attenuation map is, in general, known only at the stimulating beam energy and not at the various fluorescence energies of interest. We make use of empirically fit analytic expressions for x-ray attenuation coefficients to express the unknown attenuation maps as linear combinations of known quantities and the unknown elemental concentrations of interest. We develop an alternating-update iterative reconstruction algorithm based on maximizing a penalized Poisson likelihood objective function. Studies with numerical phantoms indicate that the approach is able to produce qualitatively and quantitatively accurate reconstructed images of numerical phantoms even in the face of severe attenuation.

David M. Billmire

Papers

Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing

Penalized-likelihood image reconstruction for x-ray fluorescence computed tomography

Penalized-likelihood image reconstruction for x-ray fluorescence computed tomography with unknown fluorescence attenuation maps