Tensor Framelet Research Articles

Ultra-Low Dose 4D-CBCT Image Reconstruction Via Joint Sparse and Nonlocal Regularization

4D cone-beam CT (4D-CBCT) is becoming an indispensable tool in cancer radiotherapy, image-guided interventions, and many other clinical applications. However, excessive radiation exposure presents a major concern for its widespread clinical applications due to its prolonged scanning duration. While intense efforts have been made in the development of 4D-CBCT under sparse-view projections, few progress has been made to address the noise problem in ultra-low dose 4D-CBCT when the projection data are also subject to photon starvation. The purpose of this work is to establish a joint sparse and nonlocal regularization approach for improved 4D-CBCT image quality with order of magnitude less radiation dose as compared to the existing techniques. To address the under-sampling problem in 4D-CBCT, we adopted the spatiotemporal tensor framelet (STF) regularization model to characterize the spatiotemporal sparse property of patient anatomy by effective use of inter-phase correlation of the projections. To simultaneously tackle the imaging noise problem caused by photon starvation, the spatiotemporal nonlocal total variation (SNTV) regularization model was also incorporated to take into account the spatiotemporal nonlocal self-recursive property of anatomical structures in 4D images. The proposed joint STF-SNTV regularization model in conjunction with the projection data fidelity constraint was optimized via the Bregman operator splitting technique. The proposed approach was evaluated first using dynamic digital phantoms and then using physical experiment data in the low-dose context of both sparse and noisy projections. Root mean squared error (RMSE), signal-to-noise ratio (SNR), and contrast-to-noise ratio (CNR) were utilized to quantitatively evaluate the reconstructed image quality. With at least one order of magnitude less radiation dose, the presented joint regularization approach achieved improved image quality in terms of noise suppression when comparing with the existing STF regularization approach. Our approach also outperformed the existing SNTV approach in terms of resolution and detail preservation. Simulation studies showed that the improvement over the STF approach is 22.41% in RMSE and 10.07% in SNR; the improvement over the SNTV approach is 51.32% in RMSE and 34.32% in SNR. While for the experimental data, the improvement over the STF is 4.42% in CNR, and the improvement over the SNTV is 14.51% in CNR. All quantitative metrics indicated the superior performance of the proposed method. The presented approach is not only effective in suppressing the view-aliasing artifacts due to angular under-sampling, but also superior in suppressing noise artifacts caused by photon starvation. With improved image quality and reduced imaging dose, our approach represents a significant step forward in 4D-CBCT guided radiation therapy.

Low-dose 4D cone-beam CT via joint spatiotemporal regularization of tensor framelet and nonlocal total variation

Excessive radiation exposure is still a major concern in 4D cone-beam computed tomography (4D-CBCT) due to its prolonged scanning duration. Radiation dose can be effectively reduced by either under-sampling the x-ray projections or reducing the x-ray flux. However, 4D-CBCT reconstruction under such low-dose protocols is prone to image artifacts and noise. In this work, we propose a novel joint regularization-based iterative reconstruction method for low-dose 4D-CBCT. To tackle the under-sampling problem, we employ spatiotemporal tensor framelet (STF) regularization to take advantage of the spatiotemporal coherence of the patient anatomy in 4D images. To simultaneously suppress the image noise caused by photon starvation, we also incorporate spatiotemporal nonlocal total variation (SNTV) regularization to make use of the nonlocal self-recursiveness of anatomical structures in the spatial and temporal domains. Under the joint STF–SNTV regularization, the proposed iterative reconstruction approach is evaluated first using two digital phantoms and then using physical experiment data in the low-dose context of both under-sampled and noisy projections. Compared with existing approaches via either STF or SNTV regularization alone, the presented hybrid approach achieves improved image quality, and is particularly effective for the reconstruction of low-dose 4D-CBCT data that are not only sparse but noisy.

SU‐D‐210‐03: Limited‐View Multi‐Source Quantitative Photoacoustic Tomography

Purpose:This work is to investigate a novel limited‐view multi‐source acquisition scheme for the direct and simultaneous reconstruction of optical coefficients in quantitative photoacoustic tomography (QPAT), which has potentially improved signal‐to‐noise ratio and reduced data acquisition time.Methods:Conventional QPAT is often considered in two steps: first to reconstruct the initial acoustic pressure from the full‐view ultrasonic data after each optical illumination, and then to quantitatively reconstruct optical coefficients (e.g., absorption and scattering coefficients) from the initial acoustic pressure, using multi‐source or multi‐wavelength scheme.Based on a novel limited‐view multi‐source scheme here, We have to consider the direct reconstruction of optical coefficients from the ultrasonic data, since the initial acoustic pressure can no longer be reconstructed as an intermediate variable due to the incomplete acoustic data in the proposed limited‐view scheme. In this work, based on a coupled photo‐acoustic forward model combining diffusion approximation and wave equation, we develop a limited‐memory Quasi‐Newton method (LBFGS) for image reconstruction that utilizes the adjoint forward problem for fast computation of gradients. Furthermore, the tensor framelet sparsity is utilized to improve the image reconstruction which is solved by Alternative Direction Method of Multipliers (ADMM).Results:The simulation was performed on a modified Shepp‐Logan phantom to validate the feasibility of the proposed limited‐view scheme and its corresponding image reconstruction algorithms.Conclusion:A limited‐view multi‐source QPAT scheme is proposed, i.e., the partial‐view acoustic data acquisition accompanying each optical illumination, and then the simultaneous rotations of both optical sources and ultrasonic detectors for next optical illumination. Moreover, LBFGS and ADMM algorithms are developed for the direct reconstruction of optical coefficients from the acoustic data.Jing Feng and Hao Gao were partially supported by the NSFC (#11405105), the 973 Program (#2015CB856000) and the Shanghai Pujiang Talent Program (#14PJ1404500).

Limited-view multi-source quantitative photoacoustic tomography

A limited-view scheme is proposed for multi-source quantitative photoacoustic tomography (MS-QPAT), in which the acoustic measurements following each optical illumination are acquired on the partial boundary near the optical source instead of the entire boundary, namely the limited-view MS-QPAT. The proposed limited-view scheme has an improved signal-to-noise ratio when the data are measured near the optical source, and reduces the acquisition time of the imaging system with a single or limited-view acoustic detector. A limited-view MS-QPAT example is to acquire acoustic data following each of 90 optical illuminations, in contrast to acoustic data for each of 90 optical illuminations under the conventional MS-QPAT setting. However, due to the incomplete data, the initial acoustic pressure can no longer be stably reconstructed that serves as an intermediate step in the conventional two-step reconstruction that first reconstructs the initial acoustic pressure and then the optical coefficients. Therefore the direct reconstruction of optical coefficients is considered using the coupled opto-acoustic forward model. The reconstruction algorithm is based on the quasi-Newton method, i.e. limited-memory BFGS with efficient adjoint computations of objective function gradients, and the sparsity-regularized formulation is also considered with tensor framelet sparsity transform and solved by the alternating direction method of multipliers.

A high-resolution photon-counting breast CT system with tensor-framelet based iterative image reconstruction for radiation dose reduction

Both computer simulations and experimental phantom studies were carried out to investigate the radiation dose reduction with tensor framelet based iterative image reconstruction (TFIR) for a dedicated high-resolution spectral breast computed tomography (CT) based on a silicon strip photon-counting detector. The simulation was performed with a 10 cm-diameter water phantom including three contrast materials (polyethylene, 8 mg ml−1 iodine and B-100 bone-equivalent plastic). In the experimental study, the data were acquired with a 1.3 cm-diameter polymethylmethacrylate (PMMA) phantom containing iodine in three concentrations (8, 16 and 32 mg ml−1) at various radiation doses (1.2, 2.4 and 3.6 mGy) and then CT images were reconstructed using the filtered-back-projection (FBP) technique and the TFIR technique, respectively. The image quality between these two techniques was evaluated by the quantitative analysis on contrast-to-noise ratio (CNR) and spatial resolution that was evaluated using the task-based modulation transfer function (MTF). Both the simulation and experimental results indicated that the task-based MTF obtained from TFIR reconstruction with one-third of the radiation dose was comparable to that from the FBP reconstruction for low contrast target. For high contrast target, the TFIR was substantially superior to the FBP reconstruction in terms of spatial resolution. In addition, TFIR was able to achieve a factor of 1.6–1.8 increase in CNR, depending on the target contrast level. This study demonstrates that the TFIR can reduce the required radiation dose by a factor of two-thirds for a CT image reconstruction compared to the FBP technique. It achieves much better CNR and spatial resolution for high contrast target in addition to retaining similar spatial resolution for low contrast target. This TFIR technique has been implemented with a graphic processing unit system and it takes approximately 10 s to reconstruct a single-slice CT image, which can potentially be used in a future multi-slit multi-slice spiral CT system.

SU‐E‐I‐93: Improved Imaging Quality for Multislice Helical CT Via Sparsity Regularized Iterative Image Reconstruction Method Based On Tensor Framelet

Purpose:Inspired by compressive sensing, sparsity regularized iterative reconstruction method has been extensively studied. However, its utility pertinent to multislice helical 4D CT for radiotherapy with respect to imaging quality, dose, and time has not been thoroughly addressed. As the beginning of such an investigation, this work carries out the initial comparison of reconstructed imaging quality between sparsity regularized iterative method and analytic method through static phantom studies using a state‐of‐art 128‐channel multi‐slice Siemens helical CT scanner.Methods:In our iterative method, tensor framelet (TF) is chosen as the regularization method for its superior performance from total variation regularization in terms of reduced piecewise‐constant artifacts and improved imaging quality that has been demonstrated in our prior work. On the other hand, X‐ray transforms and its adjoints are computed on‐the‐fly through GPU implementation using our previous developed fast parallel algorithms with O(1) complexity per computing thread. For comparison, both FDK (approximate analytic method) and Katsevich algorithm (exact analytic method) are used for multislice helical CT image reconstruction.Results:The phantom experimental data with different imaging doses were acquired using a state‐of‐art 128‐channel multi‐slice Siemens helical CT scanner. The reconstructed image quality was compared between TF‐based iterative method, FDK and Katsevich algorithm with the quantitative analysis for characterizing signal‐to‐noise ratio, image contrast, and spatial resolution of high‐contrast and low‐contrast objects.Conclusion:The experimental results suggest that our tensor framelet regularized iterative reconstruction algorithm improves the helical CT imaging quality from FDK and Katsevich algorithm for static experimental phantom studies that have been performed.

TH‐E‐17A‐02: High‐Pitch and Sparse‐View Helical 4D CT Via Iterative Image Reconstruction Method Based On Tensor Framelet

Purpose:4D CT is routinely performed during radiation therapy treatment planning of thoracic and abdominal cancers. Compared with the cine mode, the helical mode is advantageous in temporal resolution. However, a low pitch (∼0.1) for 4D CT imaging is often required instead of the standard pitch (∼1) for static imaging, since standard image reconstruction based on analytic method requires the low‐pitch scanning in order to satisfy the data sufficient condition when reconstructing each temporal frame individually. In comparison, the flexible iterative method enables the reconstruction of all temporal frames simultaneously, so that the image similarity among frames can be utilized to possibly perform high‐pitch and sparse‐view helical 4D CT imaging. The purpose of this work is to investigate such an exciting possibility for faster imaging with lower dose.Methods:A key for highpitch and sparse‐view helical 4D CT imaging is the simultaneous reconstruction of all temporal frames using the prior that temporal frames are continuous along the temporal direction. In this work, such a prior is regularized through the sparsity transform based on spatiotemporal tensor framelet (TF) as a multilevel and high‐order extension of total variation transform. Moreover, GPU‐based fast parallel computing of X‐ray transform and its adjoint together with split Bregman method is utilized for solving the 4D image reconstruction problem efficiently and accurately.Results:The simulation studies based on 4D NCAT phantoms were performed with various pitches (i.e., 0.1, 0.2, 0.5, and 1) and sparse views (i.e., 400 views per rotation instead of standard >2000 views per rotation), using 3D iterative individual reconstruction method based on 3D TF and 4D iterative simultaneous reconstruction method based on 4D TF respectively.Conclusion:The proposed TF‐based simultaneous 4D image reconstruction method enables high‐pitch and sparse‐view helical 4D CT with lower dose and faster speed.

Improved Imaging Quality for Megavoltage CT via a Novel Iterative Reconstruction Method Based on Tensor Framelet

To investigate the feasibility of improving megavoltage CT (MVCT) imaging quality and reducing imaging dose using a novel iterative reconstruction technique based on tensor framelet (TF) for better patient alignment.

Megavoltage CT imaging quality improvement on TomoTherapy via tensor framelet

This work is to investigate the feasibility of improving megavoltage imaging quality for TomoTherapy using a novel reconstruction technique based on tensor framelet, with either full-view or partial-view data. The reconstruction problem is formulated as a least-square L1-type optimization problem, with the tensor framelet for the image regularization, which is a generalization of L1, total variation, and wavelet. The high-order derivatives of the image are simultaneously regularized in L1 norm at multilevel along the x, y, and z directions. This convex formulation is efficiently solved using the Split Bregman method. In addition, a GPU-based parallel algorithm was developed to accelerate image reconstruction. The new method was compared with the filtered backprojection and the total variation based method in both phantom and patient studies with full or partial projection views. The tensor framelet based method improved the image quality from the filtered backprojection and the total variation based method. The new method was robust when only 25% of the projection views were used. It required ∼2 min for the GPU-based solver to reconstruct a 40-slice 1 mm-resolution 350×350 3D image with 200 projection views per slice and 528 detection pixels per view. The authors have developed a GPU-based tensor framelet reconstruction method with improved image quality for the megavoltage CT imaging on TomoTherapy with full or undersampled projection views. In particular, the phantom and patient studies suggest that the imaging quality enhancement via tensor framelet method is prominent for the low-dose imaging on TomoTherapy with up to a 75% projection view reduction.

SU-D-116-02: Super-Resolution Spiral Imaging Via Tensor Framelet: Megavoltage CT On TomoTherapy

Purpose: Spiral computed tomography (CT) acquires the sinogram projection views while the patient couch moves axially. As a Result each projection corresponds to a different “narrow” axial slice. However, limited by the minimal requirement of ∼180‐degree projections, filtered backprojection (FBP) can only reconstruct an axially‐averaged “thick” slice. This work is to investigate the recovery of multiple “narrow” axial slices per rotation for increasing the axial resolution, namely the super‐resolution image reconstruction. Methods: A key that enables the super‐resolution image construction for spiral CT is the utility of the image slice similarity along the axial dimension, since the patient anatomy is often continuous with small variation within a narrow thickness. This prior of axial image coherence and the smoothness of each slice can be conveniently enforced by tensor framelet (TF), in which the image details are characterized by various filters at multilevel. In particular, we apply piecewise‐linear TF that regularizes multilevel first‐order and second‐order gradients for x, y, and z directions in an isotropic fashion. The formulated convex L1‐type optimization problem is efficiently solved by the split Bregman method with GPU accelerated X‐ray transform and its adjoint. Results: The validation of this super‐resolution technique was performed using the setting of megavoltage (MV) CT on TomoTherapy with 1mm in‐plane resolution and the couch speed 8mm per gantry rotation. The simulation results indicated that this TF‐based super‐resolution technique was able to reconstruct multiple slices per rotation, while FBP failed to do so. The experimental results suggested that this technique was able to reconstruct multiple slices with 1mm axial resolution, with new abundant information that was not available otherwise. Conclusion: The super‐resolution concept is introduced for spiral CT to enhance the axial image resolution. TF‐based super‐resolution reconstruction technique provides finer axial slices with 1mm axial resolution and in‐plane resolution for TomoTherapy MVCT. This work is partially supported by NIH/NIBIB grant EB013387.

TH‐C‐103‐10: AIR: Fused Analytical and Iterative Reconstruction Method for Computed Tomography

Purpose: CT image reconstruction techniques can be classified roughly into two categories: analytical reconstruction method and iterative reconstruction method (IR). Analytical methods reconstruct images through analytical formulas, such as filtered backprojection (FBP) in 2D and FDK in 3D, which can be either mathematically exact or approximate. In contrast, IR is often based on the discrete forward model of X‐ray transform and formulated as a minimization problem with certain image regularization, so that the reconstructed image corresponds to the minimizer obtained after iterations. Each method has its own advantages. This work is to investigate the fused analytical and iterative reconstruction method (AIR). Methods: As a 2D example of AIR, FBP is incorporated into tensor framelet (TF) based IR. Specifically, AIR is formulated as a L1‐type optimization problem. The data fidelity term consists of the discrete X‐ray transform with the preconditioner that is specific to FBP. The image regularization term is via TF. The formulated minimization problem is efficiently solved through split Bregman method with GPU‐accelerated X‐ray transform and its adjoint. Results: FBP, IR, and AIR were compared using experimental data that were acquired from a resolution phantom and a contrast phantom with TomoTherapy megavoltage CT. The reconstruction was performed with the regular fully sampled case (100% data) and the low‐dose undersampled case (25% data). Quantitative contrast and resolution evaluations were computed, including the full width at half maximum (FWHM) and the contrast‐to‐noise ratio (CNR). The experimental results suggest that AIR provides better image resolution than FBP or IR, and the reconstructed image contrast from AIR is comparable to that from IR, and better than that from FBP. Conclusion: AIR is proposed with a 2D example of FBP‐based TF‐regularized IR. Its superiority in terms of the resolution and the contrast for either regular or low‐dose scan has been established through experimental studies. This work is partially supported by NIH/NIBIB grant EB013387.

4D cone beam CT via spatiotemporal tensor framelet

On-board 4D cone beam CT (4DCBCT) offers respiratory phase-resolved volumetric imaging, and improves the accuracy of target localization in image guided radiation therapy. However, the clinical utility of this technique has been greatly impeded by its degraded image quality, prolonged imaging time, and increased imaging dose. The purpose of this letter is to develop a novel iterative 4DCBCT reconstruction method for improved image quality, increased imaging speed, and reduced imaging dose. The essence of this work is to introduce the spatiotemporal tensor framelet (STF), a high-dimensional tensor generalization of the 1D framelet for 4DCBCT, to effectively take into account of highly correlated and redundant features of the patient anatomy during respiration, in a multilevel fashion with multibasis sparsifying transform. The STF-based algorithm is implemented on a GPU platform for improved computational efficiency. To evaluate the method, 4DCBCT full-fan scans were acquired within 30 s, with a gantry rotation of 200°; STF is also compared with a state-of-art reconstruction method via spatiotemporal total variation regularization. Both the simulation and experimental results demonstrate that STF-based reconstruction achieved superior image quality. The reconstruction of 20 respiratory phases took less than 10 min on an NVIDIA Tesla C2070 GPU card. The STF codes are available at https://sites.google.com/site/spatiotemporaltensorframelet. By effectively utilizing the spatiotemporal coherence of the patient anatomy among different respiratory phases in a multilevel fashion with multibasis sparsifying transform, the proposed STF method potentially enables fast and low-dose 4DCBCT with improved image quality.