Multi-step material decomposition for spectral computed tomography

Fredette, Nathaniel R.; Kavuri, Amar; Das, Mini

doi:10.1088/1361-6560/ab2b0e

Cited by 22 publications

(24 citation statements)

References 45 publications

(84 reference statements)

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“…Exploiting spectral information allows quantitative material identification and characterization. Examples of these techniques include K-edge imaging [3,4,5], material decomposition [6,7,8] and phase-contrast imaging [9,10,11]. Their other advantages include zero dark noise, and the ability for flexible energy weighting [12,13,14].…”

Section: Introductionmentioning

confidence: 99%

Spectral Signatures of X-ray Scatter Using Energy-Resolving Photon-Counting Detectors

Lewis

Das

2019

Sensors

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Energy-resolving photon-counting detectors (PCDs) separate photons from a polychromatic X-ray source into a number of separate energy bins. This spectral information from PCDs would allow advancements in X-ray imaging, such as improving image contrast, quantitative imaging, and material identification and characterization. However, aspects like detector spectral distortions and scattered photons from the object can impede these advantages if left unaccounted for. Scattered X-ray photons act as noise in an image and reduce image contrast, thereby significantly hindering PCD utility. In this paper, we explore and outline several important characteristics of spectral X-ray scatter with examples of soft-material imaging (such as cancer imaging in mammography or explosives detection in airport security). Our results showed critical spectral signatures of scattered photons that depend on a few adjustable experimental factors. Additionally, energy bins over a large portion of the spectrum exhibit lower scatter-to-primary ratio in comparison to what would be expected when using a conventional energy-integrating detector. These important findings allow flexible choice of scatter-correction methods and energy-bin utilization when using PCDs. Our findings also propel the development of efficient spectral X-ray scatter correction methods for a wide range of PCD-based applications.

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Section: Introductionmentioning

confidence: 99%

Spectral Signatures of X-ray Scatter Using Energy-Resolving Photon-Counting Detectors

Lewis

Das

2019

Sensors

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“…For spectral CT, sequential approaches (also known as two-step methods) are mainly (i) reconstruction followed by unmixing [13,14,15,16,17,18], and (ii) unmixing followed by reconstruction [19,20,21]. In the former category, material decomposition is carried out in the image domain, while in the latter category, it is carried out in the projection domain (see Figure 2).…”

Section: Related Workmentioning

confidence: 99%

“…In both approaches, independent methods for material decomposition in the projection domain [22], (multi-channel) spectral reconstruction [23] with various forms of structural or spectral regularization [24,25,26], and material decomposition in the image domain [15] can be plugged in. Although these sequential two-step methods are computationally inexpensive, separating the reconstruction and unmixing steps causes information loss [27,28].…”

Section: Related Workmentioning

confidence: 99%

“…All current one-step methods are iterative in nature and allow for the incorporation of prior knowledge through regularization. For example, (i) structure on material maps is imposed through various penalties [19,27], (ii) material maps are constrained using simplex constraints [15,16,17], and (iii) structure on spectral signatures is enforced using a spectral dictionary [17,30]. In particular, when the materials present in the object of interest are precisely known, various techniques improve the quality of the reconstructions.…”

Section: Related Workmentioning

confidence: 99%

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ADJUST: A Dictionary-Based Joint Reconstruction and Unmixing Method for Spectral Tomography

Zeegers¹,

Kadu²,

Leeuwen³

et al. 2021

Preprint

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Advances in multi-spectral detectors are causing a paradigm shift in X-ray Computed Tomography (CT). Spectral information acquired from these detectors can be used to extract volumetric material composition maps of the object of interest. If the materials and their spectral responses are known a priori, the image reconstruction step is rather straightforward. If they are not known, however, the maps as well as the responses need to be estimated jointly. A conventional workflow in spectral CT involves performing volume reconstruction followed by material decomposition, or vice versa. However, these methods inherently suffer from the ill-posedness of the joint reconstruction problem. To resolve this issue, we propose 'A Dictionary-based Joint reconstruction and Unmixing method for Spectral Tomography' (ADJUST). Our formulation relies on forming a dictionary of spectral signatures of materials common in CT and prior knowledge of the number of materials present in an object. In particular, we decompose the spectral volume linearly in terms of spatial material maps, a spectral dictionary, and the indicator of materials for the dictionary elements.We propose a memory-efficient accelerated alternating proximal gradient method to find an approximate solution to the resulting bi-convex problem. From numerical demonstrations on several synthetic phantoms, we observe that ADJUST performs exceedingly well when compared to other state-of-the-art methods. Additionally, we address the robustness of ADJUST against limited measurement patterns.

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“…ME measurements can be acquired with varying source settings 14,15 or with detectors with varying energy responses, such as sandwich detectors, 16 counting and integrating X‐ray (CIX) detectors, 17 and multibin photon‐counting (PC) detectors 18 . More specifically, the recent advancement in PC detectors with pulse‐height analysis, which output signals in multiple energy levels, provides a paradigm shift in X‐ray detector technology and is enabling many new applications 19,20 …”

Section: Introductionmentioning

confidence: 99%

Invertibility of multi‐energy X‐ray transform

2021

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The goal is to provide a sufficient condition for the invertibility of a multi-energy (ME) X-ray transform. The energy-dependent X-ray attenuation profiles can be represented by a set of coefficients using the Alvarez-Macovski (AM) method. An ME X-ray transform is a mapping from N AM coefficients to N noise-free energy-weighted measurements, where N ≥ 2. Methods: We apply a general invertibility theorem to prove the equivalence of global and local invertibility for an ME X-ray transform. We explore the global invertibility through testing whether the Jacobian of the mapping J(A) has zero values over the support of the mapping. The Jacobian of an arbitrary ME X-ray transform is an integration over all spectral measurements. A sufficient condition for J(A) ≠ 0 for all A is that the integrand of J(A) is ≥ 0 (or ≤ 0) everywhere. Note that the trivial case of the integrand equals 0 everywhere is ignored. Using symmetry, we simplified the integrand of the Jacobian to three factors that are determined by the total attenuation, the basis functions, and the energy-weighting functions, respectively. The factor related to the total attenuation is always positive; hence, the invertibility of the X-ray transform can be determined by testing the signs of the other two factors. Furthermore, we use the Cramér-Rao lower bound (CRLB) to characterize the noise-induced estimation uncertainty and provide a maximum-likelihood (ML) estimator. Results:The factor related to the basis functions is always negative when the photoelectric/Compton/Rayleigh basis functions are used and K-edge materials are not considered. The sign of the energy-weighting factor depends on the system source spectra and the detector response functions. For four special types of X-ray detectors, the sign of this factor stays the same over the integration range. Therefore, when these four types of detectors are used for imaging non-K-edge materials, the ME X-ray transform is globally invertible. The same framework can be used to study an arbitrary ME X-ray imaging system, for example, when K-edge materials are present. Furthermore, the ML estimator we presented is an unbiased, efficient estimator and can be used for a wide range of scenes. Conclusions: We have provided a framework to study the invertibility of an arbitrary ME X-ray transform and proved the global invertibility for four types of systems. K E Y W O R D Sinvertibility, multi-energy X-ray imaging, spectral X-ray imaging, X-rayThis is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

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Multi-step material decomposition for spectral computed tomography

Cited by 22 publications

References 45 publications

Spectral Signatures of X-ray Scatter Using Energy-Resolving Photon-Counting Detectors

Spectral Signatures of X-ray Scatter Using Energy-Resolving Photon-Counting Detectors

ADJUST: A Dictionary-Based Joint Reconstruction and Unmixing Method for Spectral Tomography

Invertibility of multi‐energy X‐ray transform

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