3D denoised completion network for deep single-pixel reconstruction of hyperspectral images.

Single-pixel imaging acquires an image by measuring its coefficients in a transform domain, thanks to a spatial light modulator. However, as measurements are sequential, only a few coefficients can be measured in the real-time applications. Therefore, single-pixel reconstruction is usually an underdetermined inverse problem that requires regularization to obtain an appropriate solution. Combined with a spectral detector, the concept of single-pixel imaging allows for hyperspectral imaging. While each channel can be reconstructed independently, we propose to exploit the spectral redundancy between channels to regularize the reconstruction problem. In particular, we introduce a denoised completion network that includes 3D convolution filters. Contrary to black-box approaches, our network combines the classical Tikhonov theory with the deep learning methodology, leading to an explainable network. Considering both simulated and experimental data, we demonstrate that the proposed approach yields hyperspectral images with higher quantitative metrics than the approaches developed for grayscale images.

Technical Note: Relative proton stopping power estimation from virtual monoenergetic images reconstructed from dual-layer computed tomography.

PURPOSE: The objective of this technical note was to investigate the accuracy of proton stopping power relative to water (RSP) estimation using a novel dual-layer, dual-energy computed tomography (DL-DECT) scanner for potential use in proton therapy planning. DL-DECT allows dual-energy reconstruction from scans acquired at a single x-ray tube voltage V by using two-layered detectors. METHODS: Sets of calibration and evaluation inserts were scanned at a DL-DECT scanner in a custom phantom with variable diameter D (0 to 150 mm) at V of 120 and 140 kV. Inserts were additionally scanned at a synchrotron computed tomography facility to obtain comparative linear attenuation coefficients for energies from 50 to 100 keV, and reference RSP was obtained using a carbon ion beam and variable water column. DL-DECT monoenergetic (mono-E) reconstructions were employed to obtain RSP by adapting the Yang-Saito-Landry (YSL) method. The method was compared to reference RSP via the root mean square error (RMSE) over insert mean values obtained from volumetric regions of interest. The accuracy of intermediate quantities such as the relative electron density (RED), effective atomic number (EAN), and the mono-E was additionally evaluated. RESULTS: The lung inserts showed higher errors for all quantities and we report RMSE excluding them. RMSE for µ from DL-DECT mono-E was below 1.9%. For the evaluation inserts at D = 150 mm and V = 140 kV, RED RMSE was 1.0%, while for EAN it was 2.9%. RSP RMSE was below 0.8% for all D and V, which did not strongly affect the results. CONCLUSIONS: In this investigation of RSP accuracy from DL-DECT, we have shown that RMSE below 1% can be achieved. It was possible to adapt the YSL method for DL-DECT and intermediate quantities RED and EAN had comparable accuracy to previous publications.

Extended Joint Sparsity Reconstruction for Spatial and Temporal ERT Imaging.

Electrical resistance tomography (ERT) is an imaging technique to recover the conductivity distribution with boundary measurements via attached electrodes. There are a wide range of applications using ERT for image reconstruction or parameter calculation due to high speed data collection, low cost, and the advantages of being non-invasive and portable. Although ERT is considered a high temporal resolution method, a temporally regularized method can greatly enhance such a temporal resolution compared to frame-by-frame reconstruction. In some of the cases, especially in the industrial applications, dynamic movement of an object is critical. In practice, it is desirable for monitoring and controlling the dynamic process. ERT can determine the spatial conductivity distribution based on previous work, and ERT potentially shows good performance in exploiting temporal information as well. Many ERT algorithms reconstruct images frame by frame, which is not optimal and would assume that the target is static during collection of each data frame, which is inconsistent with the real case. Although spatiotemporal-based algorithms can account for the temporal effect of dynamic movement and can generate better results, there is not that much work aimed at analyzing the performance in the time domain. In this paper, we discuss the performance of a novel spatiotemporal total variation (STTV) algorithm in both the spatial and temporal domain, and Temporal One-Step Tikhonov-based algorithms were also employed for comparison. The experimental results show that the STTV has a faster response time for temporal variation of the moving object. This robust time response can contribute to a much better control process which is the main aim of the new generation of process tomography systems.

Electrical Resistance Tomography for Visualization of Moving Objects Using a Spatiotemporal Total Variation Regularization Algorithm.

Electrical resistance tomography (ERT) has been considered as a data collection and image reconstruction method in many multi-phase flow application areas due to its advantages of high speed, low cost and being non-invasive. In order to improve the quality of the reconstructed images, the Total Variation algorithm attracts abundant attention due to its ability to solve large piecewise and discontinuous conductivity distributions. In industrial processing tomography (IPT), techniques such as ERT have been used to extract important flow measurement information. For a moving object inside a pipe, a velocity profile can be calculated from the cross correlation between signals generated from ERT sensors. Many previous studies have used two sets of 2D ERT measurements based on pixel-pixel cross correlation, which requires two ERT systems. In this paper, a method for carrying out flow velocity measurement using a single ERT system is proposed. A novel spatiotemporal total variation regularization approach is utilised to exploit sparsity both in space and time in 4D, and a voxel-voxel cross correlation method is adopted for measurement of flow profile. Result shows that the velocity profile can be calculated with a single ERT system and that the volume fraction and movement can be monitored using the proposed method. Both semi-dynamic experimental and static simulation studies verify the suitability of the proposed method. For in plane velocity profile, a 3D image based on temporal 2D images produces velocity profile with accuracy of less than 1% error and a 4D image for 3D velocity profiling shows an error of 4%.

Incorporation of Prior Knowledge of Signal Behavior Into the Reconstruction to Accelerate the Acquisition of Diffusion MRI Data.

Diffusion MRI data are generally acquired using hyperpolarized gases during patient breath-hold, which yields a compromise between achievable image resolution, lung coverage, and number of -values. In this paper, we propose a novel method that accelerates the acquisition of diffusion MRI data by undersampling in both the spatial and -value dimensions and incorporating knowledge about signal decay into the reconstruction (SIDER). SIDER is compared with total variation (TV) reconstruction by assessing its effect on both the recovery of ventilation images and the estimated mean alveolar dimensions (MADs). Both methods are assessed by retrospectively undersampling diffusion data sets ( =8) of healthy volunteers and patients with Chronic Obstructive Pulmonary Disease (COPD) for acceleration factors between x2 and x10. TV led to large errors and artifacts for acceleration factors equal to or larger than x5. SIDER improved TV, with a lower solution error and MAD histograms closer to those obtained from fully sampled data for acceleration factors up to x10. SIDER preserved image quality at all acceleration factors, although images were slightly smoothed and some details were lost at x10. In conclusion, we developed and validated a novel compressed sensing method for lung MRI imaging and achieved high acceleration factors, which can be used to increase the amount of data acquired during breath-hold. This methodology is expected to improve the accuracy of estimated lung microstructure dimensions and provide more options in the study of lung diseases with MRI.

Intraventricular vector flow mapping-a Doppler-based regularized problem with automatic model selection.

We propose a regularized least-squares method for reconstructing 2D velocity vector fields within the left ventricular cavity from single-view color Doppler echocardiographic images. Vector flow mapping is formulated as a quadratic optimization problem based on an [Formula: see text]-norm minimization of a cost function composed of a Doppler data-fidelity term and a regularizer. The latter contains three physically interpretable expressions related to 2D mass conservation, Dirichlet boundary conditions, and smoothness. A finite difference discretization of the continuous problem was adopted in a polar coordinate system, leading to a sparse symmetric positive-definite system. The three regularization parameters were determined automatically by analyzing the L-hypersurface, a generalization of the L-curve. The performance of the proposed method was numerically evaluated using (1) a synthetic flow composed of a mixture of divergence-free and curl-free flow fields and (2) simulated flow data from a patient-specific CFD (computational fluid dynamics) model of a human left heart. The numerical evaluations showed that the vector flow fields reconstructed from the Doppler components were in good agreement with the original velocities, with a relative error less than 20%. It was also demonstrated that a perturbation of the domain contour has little effect on the rebuilt velocity fields. The capability of our intraventricular vector flow mapping (iVFM) algorithm was finally illustrated on in vivo echocardiographic color Doppler data acquired in patients. The vortex that forms during the rapid filling was clearly deciphered. This improved iVFM algorithm is expected to have a significant clinical impact in the assessment of diastolic function.

A Novel Prior- and Motion-Based Compressed Sensing Method for Small-Animal Respiratory Gated CT.

Low-dose protocols for respiratory gating in cardiothoracic small-animal imaging lead to streak artifacts in the images reconstructed with a Feldkamp-Davis-Kress (FDK) method. We propose a novel prior- and motion-based reconstruction (PRIMOR) method, which improves prior-based reconstruction (PBR) by adding a penalty function that includes a model of motion. The prior image is generated as the average of all the respiratory gates, reconstructed with FDK. Motion between respiratory gates is estimated using a nonrigid registration method based on hierarchical B-splines. We compare PRIMOR with an equivalent PBR method without motion estimation using as reference the reconstruction of high dose data. From these data acquired with a micro-CT scanner, different scenarios were simulated by changing photon flux and number of projections. Methods were evaluated in terms of contrast-to-noise-ratio (CNR), mean square error (MSE), streak artefact indicator (SAI), solution error norm (SEN), and correction of respiratory motion. Also, to evaluate the effect of each method on lung studies quantification, we have computed the Jaccard similarity index of the mask obtained from segmenting each image as compared to those obtained from the high dose reconstruction. Both iterative methods greatly improved FDK reconstruction in all cases. PBR was prone to streak artifacts and presented blurring effects in bone and lung tissues when using both a low number of projections and low dose. Adopting PBR as a reference, PRIMOR increased CNR up to 33% and decreased MSE, SAI and SEN up to 20%, 4% and 13%, respectively. PRIMOR also presented better compensation for respiratory motion and higher Jaccard similarity index. In conclusion, the new method proposed for low-dose respiratory gating in small-animal scanners shows an improvement in image quality and allows a reduction of dose or a reduction of the number of projections between two and three times with respect to previous PBR approaches.

Investigation of different sparsity transforms for the PICCS algorithm in small-animal respiratory gated CT.

Respiratory gating helps to overcome the problem of breathing motion in cardiothoracic small-animal imaging by acquiring multiple images for each projection angle and then assigning projections to different phases. When this approach is used with a dose similar to that of a static acquisition, a low number of noisy projections are available for the reconstruction of each respiratory phase, thus leading to streak artifacts in the reconstructed images. This problem can be alleviated using a prior image constrained compressed sensing (PICCS) algorithm, which enables accurate reconstruction of highly undersampled data when a prior image is available. We compared variants of the PICCS algorithm with different transforms in the prior penalty function: gradient, unitary, and wavelet transform. In all cases the problem was solved using the Split Bregman approach, which is efficient for convex constrained optimization. The algorithms were evaluated using simulations generated from data previously acquired on a micro-CT scanner following a high-dose protocol (four times the dose of a standard static protocol). The resulting data were used to simulate scenarios with different dose levels and numbers of projections. All compressed sensing methods performed very similarly in terms of noise, spatiotemporal resolution, and streak reduction, and filtered back-projection was greatly improved. Nevertheless, the wavelet domain was found to be less prone to patchy cartoon-like artifacts than the commonly used gradient domain.

Comparison of total variation with a motion estimation based compressed sensing approach for self-gated cardiac cine MRI in small animal studies.

PURPOSE: Compressed sensing (CS) has been widely applied to prospective cardiac cine MRI. The aim of this work is to study the benefits obtained by including motion estimation in the CS framework for small-animal retrospective cardiac cine. METHODS: We propose a novel B-spline-based compressed sensing method (SPLICS) that includes motion estimation and generalizes previous spatiotemporal total variation (ST-TV) methods by taking into account motion between frames. In addition, we assess the effect of an optimum weighting between spatial and temporal sparsity to further improve results. Both methods were implemented using the efficient Split Bregman methodology and were evaluated on rat data comparing animals with myocardial infarction with controls for several acceleration factors. RESULTS: ST-TV with optimum selection of the weighting sparsity parameter led to results similar to those of SPLICS; ST-TV with large relative temporal sparsity led to temporal blurring effects. However, SPLICS always properly corrected temporal blurring, independently of the weighting parameter. At acceleration factors of 15, SPLICS did not distort temporal intensity information but led to some artefacts and slight over-smoothing. At an acceleration factor of 7, images were reconstructed without significant loss of quality. CONCLUSION: We have validated SPLICS for retrospective cardiac cine in small animal, achieving high acceleration factors. In addition, we have shown that motion modelling may not be essential for retrospective cine and that similar results can be obtained by using ST-TV provided that an optimum selection of the spatiotemporal sparsity weighting parameter is performed.

Use of Split Bregman denoising for iterative reconstruction in fluorescence diffuse optical tomography.

Fluorescence diffuse optical tomography (fDOT) is a noninvasive imaging technique that makes it possible to quantify the spatial distribution of fluorescent tracers in small animals. fDOT image reconstruction is commonly performed by means of iterative methods such as the algebraic reconstruction technique (ART). The useful results yielded by more advanced l1-regularized techniques for signal recovery and image reconstruction, together with the recent publication of Split Bregman (SB) procedure, led us to propose a new approach to the fDOT inverse problem, namely, ART-SB. This method alternates a cost-efficient reconstruction step (ART iteration) with a denoising filtering step based on minimization of total variation of the image using the SB method, which can be solved efficiently and quickly. We applied this method to simulated and experimental fDOT data and found that ART-SB provides substantial benefits over conventional ART.