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Author |
Zeegers, M.T.; Kadu, A.; van Leeuwen, T.; Batenburg, K.J. |
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Title |
ADJUST : a dictionary-based joint reconstruction and unmixing method for spectral tomography |
Type |
A1 Journal article |
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Year  |
2022 |
Publication |
Inverse problems |
Abbreviated Journal |
Inverse Probl |
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Volume |
38 |
Issue |
12 |
Pages |
125002-125033 |
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Keywords |
A1 Journal article; Electron microscopy for materials research (EMAT) |
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Abstract |
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 compared to other state-of-the-art methods. Additionally, we address the robustness of ADJUST against limited and noisy measurement patterns. The demonstration of the proposed approach on a spectral micro-CT dataset shows its potential for real-world applications. Code is available at https://github.com/mzeegers/ADJUST. |
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Wos |
000868885200001 |
Publication Date |
2022-09-20 |
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Edition |
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ISSN |
0266-5611 |
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Additional Links |
UA library record; WoS full record |
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Impact Factor |
2.1 |
Times cited |
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Open Access |
Not_Open_Access |
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Notes |
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Approved |
Most recent IF: 2.1 |
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Call Number |
UA @ admin @ c:irua:191536 |
Serial |
7280 |
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Author |
Kadu, A.; van Leeuwen, T.; Batenburg, K.J. |
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Title |
CoShaRP : a convex program for single-shot tomographic shape sensing |
Type |
A1 Journal article |
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Year |
2021 |
Publication |
Inverse Problems |
Abbreviated Journal |
Inverse Probl |
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Volume |
37 |
Issue |
10 |
Pages |
105005 |
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Keywords |
A1 Journal article; Electron microscopy for materials research (EMAT) |
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Abstract |
We introduce single-shot x-ray tomography that aims to estimate the target image from a single cone-beam projection measurement. This linear inverse problem is extremely under-determined since the measurements are far fewer than the number of unknowns. Moreover, it is more challenging than conventional tomography, where a sufficiently large number of projection angles forms the measurements, allowing for a simple inversion process. However, single-shot tomography becomes less severe if the target image is only composed of known shapes. This paper restricts analysis to target image function that can be decomposed into known compactly supported non-negative-valued functions termed shapes. Hence, the shape prior transforms a linear ill-posed image estimation problem to a non-linear problem of estimating the roto-translations of the shapes. We circumvent the non-linearity by using a dictionary of possible roto-translations of the shapes. We propose a convex program CoShaRP, to recover the dictionary coefficients successfully. CoShaRP relies on simplex-type constraints and can be solved quickly using a primal-dual algorithm. The numerical experiments show that CoShaRP recovers shape stably from moderately noisy measurements. |
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Wos |
000691743700001 |
Publication Date |
2021-07-23 |
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Abbreviated Series Title |
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ISSN |
0266-5611 |
ISBN |
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Additional Links |
UA library record; WoS full record |
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Impact Factor |
1.62 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 1.62 |
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Call Number |
UA @ admin @ c:irua:181617 |
Serial |
6859 |
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