Compressed sensing of spatial electron paramagnetic resonance 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.

Partial Acquisition of Spectral Projections Accelerates Four-dimensional Spectral-spatial EPR Imaging for Mouse Tumor Models: A Feasibility Study

PURPOSE

Our study aimed to accelerate the acquisition of four-dimensional (4D) spectral-spatial electron paramagnetic resonance (EPR) imaging for mouse tumor models. This advancement in EPR imaging should reduce the acquisition time of spectroscopic mapping while reducing quality degradation for mouse tumor models.

PROCEDURES

EPR spectra under magnetic field gradients, called spectral projections, were partially measured. Additional spectral projections were later computationally synthesized from the measured spectral projections. Four-dimensional spectral-spatial images were reconstructed from the post-processed spectral projections using the algebraic reconstruction technique (ART) and assessed in terms of their image qualities. We applied this approach to a sample solution and a mouse Hs766T xenograft model of human-derived pancreatic ductal adenocarcinoma cells to demonstrate the feasibility of our concept. The nitroxyl radical imaging agent 2H,15N-DCP was exogenously infused into the mouse xenograft model.

RESULTS

The computation code of 4D spectral-spatial imaging was tested with numerically generated spectral projections. In the linewidth mapping of the sample solution, we achieved a relative standard uncertainty (standard deviation/| mean |) of 0.76 μT/45.38 μT = 0.017 on the peak-to-peak first-derivative EPR linewidth. The qualities of the linewidth maps and the effect of computational synthesis of spectral projections were examined. Finally, we obtained the three-dimensional linewidth map of 2H,15N-DCP in a Hs766T tumor-bearing leg in vivo.

CONCLUSION

We achieved a 46.7% reduction in the acquisition time of 4D spectral-spatial EPR imaging without significantly degrading the image quality. A combination of ART and partial acquisition in three-dimensional raster magnetic field gradient settings in orthogonal coordinates is a novel approach. Our approach to 4D spectral-spatial EPR imaging can be applied to any subject, especially for samples with less variation in one direction.

Accurate reconstruction of 4D spectral-spatial images from sparse-view data in continuous-wave EPRI

In continuous-wave electron paramagnetic resonance imaging (CW EPRI), data are collected generally at densely sampled views sufficient for achieving accurate reconstruction of a four dimensional spectral-spatial (4DSS) image by use of the conventional filtered-backprojection (FBP) algorithm. It is desirable to minimize the scan time by collection of data only at sparsely sampled views, referred to as sparse-view data. Interest thus remains in investigation of algorithms for accurate reconstruction of 4DSS images from sparse-view data collected for potentially enabling fast data acquisition in CW EPRI. In this study, we investigate and demonstrate optimization-based algorithms for accurate reconstruction of 4DSS images from sparse-view data. Numerical studies using simulated and real sparse-view data acquired in CW EPRI are conducted that reveal, in terms of image visualization and physical-parameter estimation, the potential of the algorithms developed for yielding accurate 4DSS images from sparse-view data in CW EPRI. The algorithms developed may be exploited for enabling sparse-view scans with minimized scan time in CW EPRI for yielding 4DSS images of quality comparable to, or better than, that of the FBP reconstruction from data collected at densely sampled views.

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.

Ultrafast multiple paramagnetic species EPR imaging using a total variation based model

An EPR spectrum or an EPR sinogram for imaging contains information about all the paramagnetic species that are in the analyzed sample. When only one species is present, an image of its spatial repartition can be reconstructed from the sinogram by using the well-known Filtered Back-Projection (FBP). However, in the case of several species, the FBP does not allow the reconstruction of the images of each species from a standard acquisition. One has to use for this spectral-spatial imaging whose acquisition can be very long. A new approach, based on Total Variation minimization, is proposed in order to efficiently extract the spatial repartitions of all the species present in a sample from standard imaging data and therefore drastically reduce the acquisition time. Experiments have been carried out on Tetrathiatriarylmethyl, nitroxide and DPPH.

4D-image reconstruction directly from limited-angular-range data in continuous-wave electron paramagnetic resonance imaging

OBJECTIVE

We investigate and develop optimization-based algorithms for accurate reconstruction of four-dimensional (4D)-spectral-spatial (SS) images directly from data collected over limited angular ranges (LARs) in continuous-wave (CW) electron paramagnetic resonance imaging (EPRI).

METHODS

Basing on a discrete-to-discrete data model devised in CW EPRI employing the Zeeman-modulation (ZM) scheme for data acquisition, we first formulate the image reconstruction problem as a convex, constrained optimization program that includes a data fidelity term and also constraints on the individual directional total variations (DTVs) of the 4D-SS image. Subsequently, we develop a primal-dual-based DTV algorithm, simply referred to as the DTV algorithm, to solve the constrained optimization program for achieving image reconstruction from data collected in LAR scans in CW-ZM EPRI.

RESULTS

We evaluate the DTV algorithm in simulated- and real-data studies for a variety of LAR scans of interest in CW-ZM EPRI, and visual and quantitative results of the studies reveal that 4D-SS images can be reconstructed directly from LAR data, which are visually and quantitatively comparable to those obtained from data acquired in the standard, full-angular-range (FAR) scan in CW-ZM EPRI.

CONCLUSION

An optimization-based DTV algorithm is developed for accurately reconstructing 4D-SS images directly from LAR data in CW-ZM EPRI. Future work includes the development and application of the optimization-based DTV algorithm for reconstructions of 4D-SS images from FAR and LAR data acquired in CW EPRI employing schemes other than the ZM scheme.

SIGNIFICANCE

The DTV algorithm developed may be exploited potentially for enabling and optimizing CW EPRI with minimized imaging time and artifacts by acquiring data in LAR scans.

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.

Redox-Sensitive Mapping of a Mouse Tumor Model Using Sparse Projection Sampling of Electron Paramagnetic Resonance

Aims: This work aimed to establish an accelerated imaging system for redox-sensitive mapping in a mouse tumor model using electron paramagnetic resonance (EPR) and nitroxyl radicals. Results: Sparse sampling of EPR spectral projections was demonstrated for a solution phantom. The reconstructed three-dimensional (3D) images with filtered back-projection (FBP) and compressed sensing image reconstruction were quantitatively assessed for the solution phantom. Mouse xenograft models of a human-derived pancreatic ductal adenocarcinoma cell line, MIA PaCa-2, were also measured for redox-sensitive mapping with the sparse sampling technique. Innovation: A short-lifetime redox-sensitive nitroxyl radical (¹⁵N-labeled perdeuterated Tempone) could be measured to map the decay rates of the EPR signals for the mouse xenograft models. Acceleration of 3D EPR image acquisition broadened the choices of nitroxyl radical probes with various redox sensitivities to biological environments. Conclusion: Sparse sampling of EPR spectral projections accelerated image acquisition in the 3D redox-sensitive mapping of mouse tumor-bearing legs fourfold compared with conventional image acquisition with FBP. Antioxid. Redox Signal. 36, 57-69.

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.

Algebraic reconstruction of 3D spatial EPR images from high numbers of noisy projections: An improved image reconstruction technique for high resolution fast scan EPR imaging

A novel method for reconstructing 3D spatial EPR images from large numbers of noisy projections was developed that minimizes mean square error between the experimental projections and those from the reconstructed image. The method utilizes raw projection data and zero gradient spectrum to account for EPR line shape and hyperfine structure of the paramagnetic probe without the need for deconvolution techniques that are poorly suited for processing of high noise projections. A numerical phantom was reconstructed for method validation. Reconstruction time for the matrix of 128³ voxels and 16,384 noiseless projections was 4.6 min for a single iteration. The algorithm converged quickly, reaching R² ~ 0.99975 after the very first iteration. An experimental phantom sample with nitroxyl radical was measured. With 16,384 projections and a field gradient of 8 G/cm, resolutions of 0.4 mm were achieved for a cubical area of 25 × 25 × 25 mm³. Reconstruction was sufficiently fast and memory efficient making it suitable for applications with large 3D matrices and fully determined system of equations. The developed algorithm can be used with any gradient distribution and does not require adjustable filter parameters that makes for simple application. A thorough analysis of the strengths and limitations of this method for 3D spatial EPR imaging is provided.

Development of a fast-scan EPR imaging system for highly accelerated free radical imaging

PURPOSE

In continuous wave EPR imaging, the acquisition of high-quality images was previously limited by the requisite long acquisition times of each image projection that was typically greater than 1 second. To accelerate the process of image acquisition facilitating greater numbers of projections and higher image resolution, instrumentation was developed to greatly accelerate the magnetic field scan that is used to obtain each EPR image projection.

METHODS

A low-inductance solenoidal coil for field scanning was used along with a spherical solenoid air core magnet, and scans were driven by triangular symmetric waves, allowing forward and reverse spectrum acquisition as rapid as 3.8 ms. The uniform distribution of projections was used to optimize the contribution of projections for 3D image reconstruction.

RESULTS

Using this fast-scan EPR system, high-quality EPR images of phantoms and perfused rat hearts were performed using trityl or nanoparticulate LiNcBuO (lithium octa-n-butoxy-substituted naphthalocyanine) probes with fast-scan EPR imaging at L-band, achieving spatial resolutions of up to 250 micrometers in 1 minute.

CONCLUSION

Fast-scan EPR imaging can greatly facilitate the efficient and precise mapping of the spatial distribution of free radical and other paramagnetic probes in living systems.

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.

Fast backprojection-based reconstruction of spectral-spatial EPR images from projections with the constant sweep of a magnetic field

In this paper, we introduce a procedure for the reconstruction of spectral-spatial EPR images using projections acquired with the constant sweep of a magnetic field. The application of a constant field-sweep and a predetermined data sampling rate simplifies the requirements for EPR imaging instrumentation and facilitates the backprojection-based reconstruction of spectral-spatial images. The proposed approach was applied to the reconstruction of a four-dimensional numerical phantom and to actual spectral-spatial EPR measurements. Image reconstruction using projections with a constant field-sweep was three times faster than the conventional approach with the application of a pseudo-angle and a scan range that depends on the applied field gradient. Spectral-spatial EPR imaging with a constant field-sweep for data acquisition only slightly reduces the signal-to-noise ratio or functional resolution of the resultant images and can be applied together with any common backprojection-based reconstruction algorithm.

Accelerated dynamic EPR imaging using fast acquisition and compressive recovery

Electron paramagnetic resonance (EPR) allows quantitative imaging of tissue redox status, which provides important information about ischemic syndromes, cancer and other pathologies. For continuous wave EPR imaging, however, poor signal-to-noise ratio and low acquisition efficiency limit its ability to image dynamic processes in vivo including tissue redox, where conditions can change rapidly. Here, we present a data acquisition and processing framework that couples fast acquisition with compressive sensing-inspired image recovery to enable EPR-based redox imaging with high spatial and temporal resolutions. The fast acquisition (FA) allows collecting more, albeit noisier, projections in a given scan time. The composite regularization based processing method, called spatio-temporal adaptive recovery (STAR), not only exploits sparsity in multiple representations of the spatio-temporal image but also adaptively adjusts the regularization strength for each representation based on its inherent level of the sparsity. As a result, STAR adjusts to the disparity in the level of sparsity across multiple representations, without introducing any tuning parameter. Our simulation and phantom imaging studies indicate that a combination of fast acquisition and STAR (FASTAR) enables high-fidelity recovery of volumetric image series, with each volumetric image employing less than 10 s of scan. In addition to image fidelity, the time constants derived from FASTAR also match closely to the ground truth even when a small number of projections are used for recovery. This development will enhance the capability of EPR to study fast dynamic processes that cannot be investigated using existing EPR imaging techniques.

Fast dynamic electron paramagnetic resonance (EPR) oxygen imaging using low-rank tensors

Hypoxic tumors are resistant to radiotherapy, motivating the development of tools to image local oxygen concentrations. It is generally believed that stable or chronic hypoxia is the source of resistance, but more recent work suggests a role for transient hypoxia. Conventional EPR imaging (EPRI) is capable of imaging tissue pO2in vivo, with high pO2 resolution and 1mm spatial resolution but low imaging speed (10min temporal resolution for T1-based pO2 mapping), which makes it difficult to investigate the oxygen changes, e.g., transient hypoxia. Here we describe a new imaging method which accelerates dynamic EPR oxygen imaging, allowing 3D imaging at 2 frames per minute, fast enough to image transient hypoxia at the "speed limit" of observed pO2 change. The method centers on a low-rank tensor model that decouples the tradeoff between imaging speed, spatial coverage/resolution, and number of inversion times (pO2 accuracy). We present a specialized sparse sampling strategy and image reconstruction algorithm for use with this model. The quality and utility of the method is demonstrated in simulations and in vivo experiments in tumor bearing mice.

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.