Comparison of parabolic filtration methods for 3D filtered back projection in pulsed EPR imaging

Directional TV algorithm for image reconstruction from sparse-view projections in EPR imaging

Objective.Electron paramagnetic resonance (EPR) imaging is an advanced in vivo oxygen imaging modality. The main drawback of EPR imaging is the long scanning time. Sparse-view projections collection is an effective fast scanning pattern. However, the commonly-used filtered back projection (FBP) algorithm is not competent to accurately reconstruct images from sparse-view projections because of the severe streak artifacts. The aim of this work is to develop an advanced algorithm for sparse reconstruction of 3D EPR imaging.Methods.The optimization based algorithms including the total variation (TV) algorithm have proven to be effective in sparse reconstruction in EPR imaging. To further improve the reconstruction accuracy, we propose the directional TV (DTV) model and derive its Chambolle-Pock solving algorithm.Results.After the algorithm correctness validation on simulation data, we explore the sparse reconstruction capability of the DTV algorithm via a simulated six-sphere phantom and two real bottle phantoms filled with OX063 trityl solution and scanned by an EPR imager with a magnetic field strength of 250 G.Conclusion.Both the simulated and real data experiments show that the DTV algorithm is superior to the existing FBP and TV-type algorithms and a deep learning based method according to visual inspection and quantitative evaluations in sparse reconstruction of EPR imaging.Significance.These insights gained in this work may be used in the development of fast EPR imaging workflow of practical significance.

Directional TV algorithm for fast EPR imaging

Precise radiation guided by oxygen images has demonstrated superiority over the traditional radiation methods. Electron paramagnetic resonance (EPR) imaging has proven to be the most advanced oxygen imaging modality. However, the main drawback of EPR imaging is the long scan time. For each projection, we usually need to collect the projection many times and then average them to achieve high signal-to-noise ratio (SNR). One approach to fast scan is to reduce the repeating time for each projection. While the projections would be noisy and thus the traditional commonly-use filtered backprojection (FBP) algorithm would not be capable of accurately reconstructing images. Optimization-based iterative algorithms may accurately reconstruct images from noisy projections for they may incorporate prior information into optimization models. Based on the total variation (TV) algorithms for EPR imaging, in this work, we propose a directional TV (DTV) algorithm to further improve the reconstruction accuracy. We construct the DTV constrained, data divergence minimization (DTVcDM) model, derive its Chambolle-Pock (CP) solving algorithm, validate the correctness of the whole algorithm, and perform evaluations via simulated and real data. The experimental results show that the DTV algorithm outperforms the existing TV and FBP algorithms in fast EPR imaging. Compared to the standard FBP algorithm, the proposed algorithm may achieve 10 times of acceleration.

EPRI sparse reconstruction method based on deep learning

Electron paramagnetic resonance imaging (EPRI) is an advanced tumor oxygen concentration imaging method. Now, the bottleneck problem of EPRI is that the scanning time is too long. Sparse reconstruction is an effective and fast imaging method, which means reconstructing images from sparse-view projections. However, the EPRI images sparsely reconstructed by the classic filtered back projection (FBP) algorithm often contain severe streak artifacts, which affect subsequent image processing. In this work, we propose a feature pyramid attention-based, residual, dense, deep convolutional network (FRD-Net) to suppress the streak artifacts in the FBP-reconstructed images. This network combines residual connection, attention mechanism, dense connections and introduces perceptual loss. The EPRI image with streak artifacts is used as the input of the network and the output-label is the corresponding high-quality image densely reconstructed by the FBP algorithm. After training, the FRD-Net gets the capability of suppressing streak artifacts. The real data reconstruction experiments show that the FRD-Net can better improve the sparse reconstruction accuracy, compared with three existing representative deep networks.

An iterative reconstruction algorithm without system matrix for EPR imaging

Electron paramagnetic resonance (EPR) imaging is an advanced oxygen imaging modality for oxygen-image guided radiation. The iterative reconstruction algorithm is the research hot-point in image reconstruction for EPR imaging (EPRI) for this type of algorithm may incorporate image-prior information to construct advanced optimization model to achieve accurate reconstruction from sparse-view projections and/or noisy projections. However, the system matrix in the iterative algorithm needs complicated calculation and needs huge memory-space if it is stored in memory. In this work, we propose an iterative reconstruction algorithm without system matrix for EPRI to simplify the whole iterative reconstruction process. The function of the system matrix is to calculate the projections, whereas the function of the transpose of the system matrix is to perform backprojection. The existing projection and backprojection methods are all based on the configuration that the imaged-object remains stationary and the scanning device rotates. Here, we implement the projection and backprojection operations by fixing the scanning device and rotating the object. Thus, the core algorithm is only the commonly-used image-rotation algorithm, while the calculation and store of the system matrix are avoided. Based on the idea of image rotation, we design a specific iterative reconstruction algorithm for EPRI, total variation constrained data divergence minimization (TVcDM) algorithm without system matrix, and named it as image-rotation based TVcDM (R-TVcDM). Through a series of comparisons with the original TVcDM via real projection data, we find that the proposed algorithm may achieve similar reconstruction accuracy with the original one. But it avoids the complicated calculation and store of the system matrix. The insights gained in this work may be also applied to other imaging modalities, for example computed tomography and positron emission tomography.

A balanced total-variation-Chambolle-Pock algorithm for EPR imaging

Total variation (TV) minimization algorithm is an effective algorithm capable of accurately reconstructing images from sparse projection data in a variety of imaging modalities including computed tomography (CT) and electron paramagnetic resonance imaging (EPRI). The data divergence constrained, TV minimization (DDcTV) model and its Chambolle-Pock (CP) solving algorithm have been proposed for CT. However, when the DDcTV-CP algorithm is applied to 3D EPRI, it suffers from slow convergence rate or divergence. We hypothesize that this is due to the magnitude imbalance between the data fidelity term and the TV regularization term. In this work, we propose a balanced TV (bTV) model incorporating a balance parameter and demonstrate its capability to avoid convergence issues for the 3D EPRI application. Simulation and real experiments show that the DDcTV-CP algorithm cannot guarantee convergence but the bTV-CP algorithm may guarantee convergence and achieve fast convergence by use of an appropriate balance parameter. Experiments also show that underweighting the balance parameter leads to slow convergence, whereas overweighting the balance parameter leads to divergence. The iteration-behavior change-law with the variation of the balance parameter is explained by use of the data tolerance ellipse and gradient descent principle. The findings and insights gained in this work may be applied to other imaging modalities and other constrained optimization problems.

Optimization-based image reconstruction from sparsely sampled data in electron paramagnetic resonance imaging

Electron paramagnetic resonance imaging (EPRI) can yield information about the 3-dimensional (3D) spatial distribution of the unpaired-electron-spin density from which the spatial distribution of oxygen concentration within tumor tissue, referred to as the oxygen image or electron paramagnetic resonance (EPR) image in this work, can be derived. Existing algorithms for reconstruction of EPR images often require data collected at a large number of densely sampled projection views, resulting in a prolonged data-acquisition time and consequently numerous practical challenges especially to in vivo animal EPRI. Therefore, a strong interest exists in shortening data-acquisition time through reducing the number of data samples collected in EPRI, and one approach is to acquire data at a reduced number of sparsely distributed projection views from which existing algorithms may reconstruct images with prominent artifacts. In this work, we investigate and develop an optimization-based technique for image reconstruction from data collected at sparsely sampled projection views for reducing scanning time in EPRI. Specifically, we design a convex optimization program in which the EPR image of interest is formulated as a solution and then tailor the Chambolle-Pock (CP) primal-dual algorithm to reconstruct the image by solving the convex optimization program. Using computer-simulated EPRI data from numerical phantoms and real EPRI data collected from physical phantoms, we perform studies on the verification and characterization of the optimization-based technique for EPR image reconstruction. Results of the studies suggest that the technique may yield accurate EPR images from data collected at sparsely distributed projection views, thus potentially enabling fast EPRI with reduced acquisition time.

Investigation of the preconditioner-parameter in the preconditioned Chambolle-Pock algorithm applied to optimization-based image reconstruction

The optimization-based image reconstruction methods have been thoroughly investigated in the field of medical imaging. The Chambolle-Pock (CP) algorithm may be employed to solve these convex optimization image reconstruction programs. The preconditioned CP (PCP) algorithm has been shown to have much higher convergence rate than the ordinary CP (OCP) algorithm. This algorithm utilizes a preconditioner-parameter to tune the implementation of the algorithm to the specific application, which ranges from 0 and 2, but is often set to 1. In this work, we investigated the impact of the preconditioner-parameter on the convergence rate of the PCP algorithm when it is applied to the TV constrained, data-divergence minimization (TVDM) optimization based image reconstruction. We performed the investigations in the context of 2D computed tomography (CT) and 3D electron paramagnetic resonance imaging (EPRI). For 2D CT, we used the Shepp-Logan and two FORBILD phantoms. For 3D EPRI, we used a simulated 6-spheres phantom and a physical phantom. Study results showed that the optimal preconditioner-parameter depends on the specific imaging conditions. Simply setting the parameter equal to 1 cannot guarantee a fast convergence rate. Thus, this study suggests that one should adaptively tune the preconditioner-parameter to obtain the optimal convergence rate of the PCP algorithm.

Three novel accurate pixel-driven projection methods for 2D CT and 3D EPR imaging

OBJECTIVES

This work aims to explore more accurate pixel-driven projection methods for iterative image reconstructions in order to reduce high-frequency artifacts in the generated projection image.

METHODS

Three new pixel-driven projection methods namely, small-pixel-large-detector (SPLD), linear interpolation based (LIB) and distance anterpolation based (DAB), were proposed and applied to reconstruct images. The performance of these methods was evaluated in both two-dimensional (2D) computed tomography (CT) images via the modified FORBILD phantom and three-dimensional (3D) electron paramagnetic resonance (EPR) images via the 6-spheres phantom. Specifically, two evaluations based on projection generation and image reconstruction were performed. For projection generation, evaluation was using a 2D disc phantom, the modified FORBILD phantom and the 6-spheres phantom. For image reconstruction, evaluations were performed using the FORBILD and 6-spheres phantom. During evaluation, 2 quantitative indices of root-mean-square-error (RMSE) and contrast-to-noise-ratio (CNR) were used.

RESULTS

Comparing to the use of ordinary pixel-driven projection method, RMSE of the SPLD based least-square algorithm was reduced from 0.0701 to 0.0384 and CNR was increased from 5.6 to 19.47 for 2D FORBILD phantom reconstruction. For 3D EPRI, RMSE of SPLD was also reduced from 0.0594 to 0.0498 and CNR was increased from 3.88 to 11.58. In addition, visual evaluation showed that images reconstructed in both 2D and 3D images suffered from high-frequency line-shape artifacts when using the ordinary pixel-driven projection method. However, using 3 new methods all suppressed the artifacts significantly and yielded more accurate reconstructions.

CONCLUSIONS

Three proposed pixel-driven projection methods achieved more accurate iterative image reconstruction results. These new and more accurate methods can also be easily extended to other imaging modalities. Among them, SPLD method should be recommended to 3D and four dimensional (4D) EPR imaging.

3D pulse EPR imaging from sparse-view projections via constrained, total variation minimization

Tumors and tumor portions with low oxygen concentrations (pO2) have been shown to be resistant to radiation therapy. As such, radiation therapy efficacy may be enhanced if delivered radiation dose is tailored based on the spatial distribution of pO2 within the tumor. A technique for accurate imaging of tumor oxygenation is critically important to guide radiation treatment that accounts for the effects of local pO2. Electron paramagnetic resonance imaging (EPRI) has been considered one of the leading methods for quantitatively imaging pO2 within tumors in vivo. However, current EPRI techniques require relatively long imaging times. Reducing the number of projection scan considerably reduce the imaging time. Conventional image reconstruction algorithms, such as filtered back projection (FBP), may produce severe artifacts in images reconstructed from sparse-view projections. This can lower the utility of these reconstructed images. In this work, an optimization based image reconstruction algorithm using constrained, total variation (TV) minimization, subject to data consistency, is developed and evaluated. The algorithm was evaluated using simulated phantom, physical phantom and pre-clinical EPRI data. The TV algorithm is compared with FBP using subjective and objective metrics. The results demonstrate the merits of the proposed reconstruction algorithm.