Context fusion network with multi-scale-aware skip connection and twin-split attention for liver tumor segmentation.

Manually annotating liver tumor contours is a time-consuming and labor-intensive task for clinicians. Therefore, automated segmentation is urgently needed in clinical diagnosis. However, automatic segmentation methods face certain challenges due to heterogeneity, fuzzy boundaries, and irregularity of tumor tissue. In this paper, a novel deep learning-based approach with multi-scale-aware (MSA) module and twin-split attention (TSA) module is proposed for tumor segmentation. The MSA module can bridge the semantic gap and reduce the loss of detailed information. The TSA module can recalibrate the channel response of the feature map. Eventually, we can count tumors based on the segmentation results from a 3D perspective for cancer grading. Extensive experiments conducted on the LiTS2017 dataset show the effectiveness of the proposed method by achieving a Dice index of 85.97% and a Jaccard index of 81.56% over the state of the art. In addition, the proposed method also achieved a Dice index of 83.67% and a Jaccard index of 80.11% in 3Dircadb dataset verification, which further reflects its robustness and generalization ability.

RFPNet: Reorganizing feature pyramid networks for medical image segmentation.

Medical image segmentation is a crucial step in clinical treatment planning. However, automatic and accurate medical image segmentation remains a challenging task, owing to the difficulty in data acquisition, the heterogeneity and large variation of the lesion tissue. In order to explore image segmentation tasks in different scenarios, we propose a novel network, called Reorganization Feature Pyramid Network (RFPNet), which uses alternately cascaded Thinned Encoder-Decoder Modules (TEDMs) to construct semantic features in various scales at different levels. The proposed RFPNet is composed of base feature construction module, feature pyramid reorganization module and multi-branch feature decoder module. The first module constructs the multi-scale input features. The second module first reorganizes the multi-level features and then recalibrates the responses between integrated feature channels. The third module weights the results obtained from different decoder branches. Extensive experiments conducted on ISIC2018, LUNA2016, RIM-ONE-r1 and CHAOS datasets show that RFPNet achieves Dice scores of 90.47%, 98.31%, 96.88%, 92.05% (Average between classes) and Jaccard scores of 83.95%, 97.05%, 94.04%, 88.78% (Average between classes). In quantitative analysis, RFPNet outperforms some classical methods as well as state-of-the-art methods. Meanwhile, the visual segmentation results demonstrate that RFPNet can excellently segment target areas from clinical datasets.

A spectral interior CT by a framelet-based reconstruction algorithm.

Reducing radiation dose is an important goal in medical computed tomography (CT), for which interior tomography is an effective approach. There have been interior reconstruction algorithms for monochromatic CT, but in reality, X-ray sources are polychromatic. Using a polychromatic acquisition model and motivated by framelet-based image processing algorithms, in this paper, we propose an interior reconstruction algorithm to obtain an image with spectral information assuming only one scan with a current energy-integrating detector. This algorithm is a new nonlinear iterative method by minimizing a special functional under a polychromatic acquisition model for X-ray CT, where the attenuation coefficients are energy-dependent. Experimental results validate that our algorithm can effectively reduce the beam-hardening artifacts and metal artifacts. It also produces color overlays which are useful in tumor identification and quantification.

A framelet-based iterative maximum-likelihood reconstruction algorithm for spectral CT.

Standard computed tomography (CT) cannot reproduce spectral information of an object. Hardware solutions include dual-energy CT which scans the object twice in different x-ray energy levels, and energy-discriminative detectors which can separate lower and higher energy levels from a single x-ray scan. In this paper, we propose a software solution and give an iterative algorithm that reconstructs an image with spectral information from just one scan with a standard energy-integrating detector. The spectral information obtained can be used to produce color CT images, spectral curves of the attenuation coefficient µ(r, E)at points inside the object, and photoelectric images, which are all valuable imaging tools in cancerous diagnosis. Our software solution requires no change on hardware of a CT machine. With the Shepp-Logan phantom, we have found that although the photoelectric and Compton components were not perfectly reconstructed, their composite effect was very accurately reconstructed as compared to the ground truth and the dual-energy CT counterpart. This means that our proposed method has an intrinsic benefit in beam hardening correction and metal artifact reduction. The algorithm is based on a nonlinear polychromatic acquisition model for x-ray CT. The key technique is a sparse representation of iterations in a framelet system. Convergence of the algorithm is studied. This is believed to be the first application of framelet imaging tools to a nonlinear inverse problem.

Gel'fand-Graev's reconstruction formula in the 3D real space.

PURPOSE: Gel'fand and Graev performed classical work on the inversion of integral transforms in different spaces [Gel'fand and Graev, Funct. Anal. Appl. 25(1) 1-5 (1991)]. This paper discusses their key results for further research and development. METHODS: The Gel'fand-Graev inversion formula reveals a fundamental relationship between projection data and the Hilbert transform of an image to be reconstructed. This differential backprojection (DBP)∕backprojection filtration (BPF) approach was rediscovered in the CT field, and applied in important applications such as reconstruction from truncated projections, interior tomography, and limited-angle tomography. Here the authors present the Gel'fand-Graev inversion formula in a 3D setting assuming the 1D x-ray transform. RESULTS: The pseudodifferential operator is a powerful theoretical tool. There is a fundamental mathematical link between the Gel'fand-Graev formula and the DBP (or BPF) approach in the case of the 1D x-ray transform in a 3D real space. CONCLUSIONS: This paper shows the power of mathematics for tomographic imaging and the value of a pure theoretical finding, which may appear quite irrelevant to daily healthcare at the first glance.

A scheme for multisource interior tomography.

Currently, x-ray computed tomography (CT) requires source scanning so that projections can be collected from various orientations for image reconstruction. Limited by the scanning time, the temporal resolution of CT is often inadequate when rapid dynamics is involved in an object to be reconstructed. To meet this challenge, here the authors propose a scheme of multisource interior tomography for ultrafast imaging that reconstructs a relatively small region of interest (ROI). Specifically, such a ROI is irradiated in parallel with narrow x-ray beams defined by many source-detector pairs for data acquisition. This ROI can be then reconstructed using the interior tomography approach. To demonstrate the merits of this approach, the authors report interior reconstruction from in vivo lung CT data at a much reduced radiation dose, which is roughly proportional to the ROI size. The results suggest a scheme for ultrafast tomography (such as with a limited number of sources and in a scanning mode) to shorten data acquisition time and to suppress motion blurring.

Exact interior reconstruction from truncated limited-angle projection data.

Using filtered backprojection (FBP) and an analytic continuation approach, we prove that exact interior reconstruction is possible and unique from truncated limited-angle projection data, if we assume a prior knowledge on a subregion or subvolume within an object to be reconstructed. Our results show that (i) the interior region-of-interest (ROI) problem and interior volume-of-interest (VOI) problem can be exactly reconstructed from a limited-angle scan of the ROI/VOI and a 180 degree PI-scan of the subregion or subvolume and (ii) the whole object function can be exactly reconstructed from nontruncated projections from a limited-angle scan. These results improve the classical theory of Hamaker et al. (1980).

Interior Reconstruction Using the Truncated Hilbert Transform via Singular Value Decomposition.

The state-of-the-art technology for theoretically exact local computed tomography (CT) is to reconstruct an object function using the truncated Hilbert transform (THT) via the projection onto convex sets (POCS) method, which is iterative and computationally expensive. Here we propose to reconstruct the object function using the THT via singular value decomposition (SVD). First, we review the major steps of our algorithm. Then, we implement the proposed SVD method and perform numerical simulations. Our numerical results indicate that our approach runs two orders of magnitude faster than the iterative approach and produces an excellent region-of-interest (ROI) reconstruction that was previously impossible, demonstrating the feasibility of localized pre-clinical and clinical CT as a new direction for research on exact local image reconstruction. Finally, relevant issues are discussed.

Lambda tomography with discontinuous scanning trajectories.

Lambda tomography (LT) is a well-known local reconstruction technology to reduce the radiation dose or accommodate a limited imaging geometry. After a theoretical analysis of the so-called Calderon operator (CO), the necessary conditions for exact LT reconstruction are presented in terms of the 2D and 3D COs. Based on our previous results on LT, a general scheme is proposed to construct exact LT formulae in terms of the 2D CO with multiple segment trajectories. Every 2D formula has a corresponding 3D cone-beam formula in the Feldkamp framework in terms of the 2D CO which was illustrated in a triple-segment case. Our simulation results verify the correctness and demonstrate the merits of the proposed scheme.

Approximate and exact cone-beam reconstruction with standard and non-standard spiral scanning.

The long object problem is practically important and theoretically challenging. To solve the long object problem, spiral cone-beam CT was first proposed in 1991, and has been extensively studied since then. As a main feature of the next generation medical CT, spiral cone-beam CT has been greatly improved over the past several years, especially in terms of exact image reconstruction methods. Now, it is well established that volumetric images can be exactly and efficiently reconstructed from longitudinally truncated data collected along a rather general scanning trajectory. Here we present an overview of some key results in this area.

Exact interior reconstruction with cone-beam CT.

Using the backprojection filtration (BPF) and filtered backprojection (FBP) approaches, respectively, we prove that with cone-beam CT the interior problem can be exactly solved by analytic continuation. The prior knowledge we assume is that a volume of interest (VOI) in an object to be reconstructed is known in a subregion of the VOI. Our derivations are based on the so-called generalized PI-segment (chord). The available projection onto convex set (POCS) algorithm and singular value decomposition (SVD) method can be applied to perform the exact interior reconstruction. These results have many implications in the CT field and can be extended to other tomographic modalities, such as SPECT/PET, MRI.

A general local reconstruction approach based on a truncated hilbert transform.

Exact image reconstruction from limited projection data has been a central topic in the computed tomography (CT) field. In this paper, we present a general region-of-interest/volume-of-interest (ROI/VOI) reconstruction approach using a truly truncated Hilbert transform on a line-segment inside a compactly supported object aided by partial knowledge on one or both neighboring intervals of that segment. Our approach and associated new data sufficient condition allows the most flexible ROI/VOI image reconstruction from the minimum account of data in both the fan-beam and cone-beam geometry. We also report primary numerical simulation results to demonstrate the correctness and merits of our finding. Our work has major theoretical potentials and innovative practical applications.

Practical cone-beam lambda tomography.

As a potentially important technology for medical x-ray computed tomography (CT), lambda tomography (LT) is to reconstruct a gradient-like image only from local projection data. Based on our recently derived exact fan-beam LT formula, [H. Y. Gu and G. Wang, Int. J. Biomed. Imaging 2006(1), 1-9 (2006)] here we propose a practical cone-beam LT algorithm for LT reconstruction from local data collected along an arbitrary smooth three-dimensional curve. A key step in our algorithm is to determine an appropriate vector perpendicular to the line connecting the x-ray source and an image point. The algorithm is implemented assuming an equispatial planar detector and a nonstandard spiral trajectory. The numerical simulation results demonstrate the merits of our method.

Local ROI Reconstruction via Generalized FBP and BPF Algorithms along More Flexible Curves.

We study the local region-of-interest (ROI) reconstruction problem, also referred to as the local CT problem. Our scheme includes two steps: (a) the local truncated normal-dose projections are extended to global dataset by combining a few global low-dose projections; (b) the ROI are reconstructed by either the generalized filtered backprojection (FBP) or backprojection-filtration (BPF) algorithms. The simulation results show that both the FBP and BPF algorithms can reconstruct satisfactory results with image quality in the ROI comparable to that of the corresponding global CT reconstruction.

Exact BPF and FBP algorithms for nonstandard saddle curves.

A hot topic in cone-beam CT research is exact cone-beam reconstruction from a general scanning trajectory. Particularly, a nonstandard saddle curve attracts attention, as this construct allows the continuous periodic scanning of a volume-of-interest (VOI). Here we evaluate two algorithms for reconstruction from data collected along a nonstandard saddle curve, which are in the filtered backprojection (FBP) and backprojection filtration (BPF) formats, respectively. Both the algorithms are implemented in a chord-based coordinate system. Then, a rebinning procedure is utilized to transform the reconstructed results into the natural coordinate system. The simulation results demonstrate that the FBP algorithm produces better image quality than the BPF algorithm, while both the algorithms exhibit similar noise characteristics.

Computed tomography simulation with superquadrics.

Accurate and efficient simulation of an x-ray transform for representative structures plays an important role in research and development of x-ray CT, for the evaluation and improvement of CT image reconstruction algorithms, in particular. Superquadrics are a family of three-dimensional objects, which can be used to model a variety of anatomical structures. In this paper, we propose an algorithm for the computation of x-ray transforms for superellipsoids and tori with a monochromatic x-ray. Their usefulness is demonstrated by projection and reconstruction of a superquadric-based thorax phantom. Our work indicates that superquadric modeling provides a more realistic visualization than quadratic modeling, and a faster computation than spline methods.

A general exact reconstruction for cone-beam CT via backprojection-filtration.

In this paper, we prove a generalized backprojection-filtration formula for exact cone-beam image reconstruction with an arbitrary scanning locus. Our proof is independent of the shape of the scanning locus, as long as the object is contained in a region where there is a chord through any interior point. As special cases, this generalized formula can be applied with cone-beam scanning along nonstandard spiral and saddle curves, as well as in an n-PI window setting. The algorithmic implementation and numerical results are described to support the correctness of our general claim.

A backprojection-filtration algorithm for nonstandard spiral cone-beam CT with an n-PI-window.

For applications in bolus-chasing computed tomography (CT) angiography and electron-beam micro-CT, the backprojection-filtration (BPF) formula developed by Zou and Pan was recently generalized by Ye et al to reconstruct images from cone-beam data collected along a rather flexible scanning locus, including a nonstandard spiral. A major implication of the generalized BPF formula is that it can be applied for n-PI-window-based reconstruction in the nonstandard spiral scanning case. In this paper, we design an n-PI-window-based BPF algorithm, and report the numerical simulation results with the 3D Shepp-Logan phantom and Defrise disk phantom. The proposed BPF algorithm consists of three steps: cone-beam data differentiation, weighted backprojection and inverse Hilbert filtration. Our simulated results demonstrate the feasibility and merits of the proposed algorithm.

Filtered backprojection formula for exact image reconstruction from cone-beam data along a general scanning curve.

Recently, Katsevich proved a filtered backprojection formula for exact image reconstruction from cone-beam data along a helical scanning locus, which is an important breakthrough since 1991 when the spiral cone-beam scanning mode was proposed. In this paper, we prove a generalized Katsevich's formula for exact image reconstruction from cone-beam data collected along a rather flexible curve. We will also give a general condition on filtering directions. Based on this condition, we suggest a natural choice of filtering directions, which is more convenient than Katsevich's choice and can be applied to general scanning curves. In the derivation, we use analytical techniques instead of geometric arguments. As a result, we do not need the uniqueness of the PI lines. In fact, our formula can be used to reconstruct images on any chord as long as a scanning curve runs from one endpoint of the chord to the other endpoint. This can be considered as a generalization of Orlov's classical theorem. Specifically, our formula can be applied to (i) nonstandard spirals of variable radii and pitches (with PI- or n-PI-windows), and (ii) saddlelike curves.