Three-dimensional dental X-ray imaging by combination of panoramic and projection data

Hyvönen, Nuutti; Kalke, Martti; Lassas, Matti; Setala, H.; Siltanen, Samuli

doi:10.3934/ipi.2010.4.257

Cited by 14 publications

(9 citation statements)

References 32 publications

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“…CT scans are being used to study organs such as the heart, and objects that are highly dynamic, implying that a slightly longer scan time introduces a lot of blurring into the image [25,7]. Further, the limited angle setting can help limit the area of the scan only to a region of interest like in healthcare applications such as breast [26], and dental [13] tomography. It can also support applications involving objects that have physical constraints restricting the angles from which they can be scanned, for example in electron microscopy [30,28].…”

Section: Need For Limited Angle Scansmentioning

confidence: 99%

Lose the Views: Limited Angle CT Reconstruction via Implicit Sinogram Completion

Anirudh

Kim

Thiagarajan

et al. 2018

2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition

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Computed Tomography (CT) reconstruction is a fundamental component to a wide variety of applications ranging from security, to healthcare. The classical techniques require measuring projections, called sinograms, from a full 180°view of the object. However, obtaining a full-view is not always feasible, such as when scanning irregular objects that limit flexibility of scanner rotation. The resulting limited angle sinograms are known to produce highly artifact-laden reconstructions with existing techniques. In this paper, we propose to address this problem using CTNet -a system of 1D and 2D convolutional neural networks, that operates directly on a limited angle sinogram to predict the reconstruction. We use the x-ray transform on this prediction to obtain a "completed" sinogram, as if it came from a full 180°view. We feed this to standard analytical and iterative reconstruction techniques to obtain the final reconstruction. We show with extensive experimentation on a challenging real world dataset that this combined strategy outperforms many competitive baselines. We also propose a measure of confidence for the reconstruction that enables a practitioner to gauge the reliability of a prediction made by CTNet. We show that this measure is a strong indicator of quality as measured by the PSNR, while not requiring ground truth at test time. Finally, using a segmentation experiment, we show that our reconstruction also preserves the 3D structure of objects better than existing solutions.

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Section: Need For Limited Angle Scansmentioning

confidence: 99%

Lose the Views: Limited Angle CT Reconstruction via Implicit Sinogram Completion

Anirudh

Kim

Thiagarajan

et al. 2018

2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition

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“…From the one side, the use of particularly suitable directions in real applications could be prevented by some physical or mechanical constraints. It occurs, for instance, in electron microscopy [6], digital breast tomosynthesis [20] or dental tomography [15,18], where limited angle reconstructions based on truncated sinogram are exploited.…”

Section: Local Uniquenessmentioning

confidence: 99%

A geometrical characterization of regions of uniqueness and applications to discrete tomography

Dulio¹,

Frosini²,

Pagani³

2015

Inverse Problems

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In the reconstruction problem of Discrete Tomography, projections are considered from a finite set S of lattice directions. Employing a limited number of projections implies that the injectivity of the Radon transform is lost, and, in general, images consistent with a given set of projections form a huge class. In order to lower the number of allowed solutions, one usually tries to include in the problem some a priori information. This suggests that modeling the tomographic reconstruction problem as a linear system of equations is preferable.In this paper we propose to restrict the usual notion of uniqueness, related to the solutions of the linear system, and to provide, for each set S, a geometrical characterization of the shape of a lattice subset, say region of uniqueness (ROU), forming a partial, fast reconstructible, solution.Any selected set S intrinsically determines its ROU inside an arbitrary lattice grid. For instance, trivially, if |S| = 1, the ROU is represented by two rectangles having sizes equal to the absolute values of the entries of the unique direction in S, and placed at two opposite corners of the chosen grid. Surprisingly, if |S| = 2, the problem becomes much more complicated.Our purpose is to provide a geometrical characterization of the ROU. This is based on a double Euclidean division algorithm (DEDA), which runs in polynomial time. It turns out that the ROU is delimited by a zigzag profile obtained by means of numerical relations among the entries of the employed directions. According to different inputs in DEDA, the shape of the ROU can change consistently, as it can be easily observed from the provided examples. Moreover, after selecting a region of interest (ROI) from a given phantom, we exploit DEDA to reconstruct the part of the ROI which falls in the ROU and, with a few further a priori knowledge, even parts of the ROI which are outside the ROU.

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“…Limited-angle tomography refers to a case when this is not fulfilled. Such problems arise naturally in many applications, like digital breast tomosynthesis [60,6], dental tomography [43,44], electron tomography [68,63], transmission x-ray microscopy [42], nondestructive testing [66,71], geophysical prospecting [84], etc. This missing data significantly amplifies the instability in the corresponding reconstruction problem [21,58].…”

Section: Introductionmentioning

confidence: 99%

Deep Microlocal Reconstruction for Limited-Angle Tomography

Andrade-Loarca¹,

Kutyniok²,

Öktem³

et al. 2021

Preprint

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We present a deep learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a recently developed digital wavefront set extractor as well as the well-known microlocal canonical relation for the Radon transform. We use the wavefront set information about x-ray data to improve the reconstruction by requiring that the underlying neural networks simultaneously extract the correct ground truth wavefront set and ground truth image. As a necessary theoretical step, we identify the digital microlocal canonical relations for deep convolutional residual neural networks. We find strong numerical evidence for the effectiveness of this approach.

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Three-dimensional dental X-ray imaging by combination of panoramic and projection data

Cited by 14 publications

References 32 publications

Lose the Views: Limited Angle CT Reconstruction via Implicit Sinogram Completion

Lose the Views: Limited Angle CT Reconstruction via Implicit Sinogram Completion

A geometrical characterization of regions of uniqueness and applications to discrete tomography

Deep Microlocal Reconstruction for Limited-Angle Tomography

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