Tomographic reconstruction of stack plume based on sparse optimization

Compressed sensing (CS) enables accurate CT image reconstruction from low-dose measurements, due to the sparsifiable feature of most CT images using total variation (TV). The CS reconstruction is formulated as either a constrained problem to minimize the TV objective within a small data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning. In this work, we propose an optimization algorithm for cone-beam CT (CBCT) CS reconstruction which overcomes the above two drawbacks. The data tolerance is well estimated using the measured data, as most of the projection errors are from Poisson noise. We adopt the TV optimization framework with data fidelity as constraints. To accelerate the convergence, we first convert such a constrained optimization using a barrier method into a similar form to the conventional TV-regularization reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection. The proposed algorithm is referred to as Accelerated Barrier Optimization for CS (ABOCS). As demonstrated on Shepp-Logan and head phantoms, ABOCS achieves consistent performances using the same parameters on scans with different datasets, while the TV-regularization method needs a large-scale tuning on the penalty weight. ABOCS also requires less computation time than ASDPOCS in Matlab by more than 10 times. ABOCS is further accelerated on GPU to reconstruct a 3D Shepp-Logan volume of 256×256×256 voxels in less than 20 mins using 10% projections, and the image quality is comparable to that of the full-view FDK reconstruction. We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter setting for different datasets.

Recent advances in compressed sensing (CS) enable accurate CT image reconstruction from highly undersampled and noisy projection measurements, due to the sparsifiable feature of most CT images using total variation (TV). These novel reconstruction methods have demonstrated advantages in clinical applications where radiation dose reduction is critical, such as onboard cone-beam CT (CBCT) imaging in radiation therapy. The image reconstruction using CS is formulated as either a constrained problem to minimize the TV objective within a small and fixed data fidelity error, or an unconstrained problem to minimize the data fidelity error with TV regularization. However, the conventional solutions to the above two formulations are either computationally inefficient or involved with inconsistent regularization parameter tuning, which significantly limit the clinical use of CS-based iterative reconstruction. In this paper, we propose an optimization algorithm for CS reconstruction which overcomes the above two drawbacks. The data fidelity tolerance of CS reconstruction can be well estimated based on the measured data, as most of the projection errors are from Poisson noise after effective data correction for scatter and beam-hardening effects. We therefore adopt the TV optimization framework with a data fidelity constraint. To accelerate the convergence, we first convert such a constrained optimization using a logarithmic barrier method into a form similar to that of the conventional TV regularization based reconstruction but with an automatically adjusted penalty weight. The problem is then solved efficiently by gradient projection with an adaptive Barzilai-Borwein step-size selection scheme. The proposed algorithm is referred to as accelerated barrier optimization for CS (ABOCS), and evaluated using both digital and physical phantom studies. ABOCS directly estimates the data fidelity tolerance from the raw projection data. Therefore, as demonstrated in both digital Shepp-Logan and physical head phantom studies, consistent reconstruction performances are achieved using the same algorithm parameters on scans with different noise levels and∕or on different objects. On the contrary, the penalty weight in a TV regularization based method needs to be fine-tuned in a large range (up to seven times) to maintain the reconstructed image quality. The improvement of ABOCS on computational efficiency is demonstrated in the comparisons with adaptive-steepest-descent-projection-onto-convex-sets (ASD-POCS), an existing CS reconstruction algorithm also using constrained optimization. ASD-POCS alternatively minimizes the TV objective using adaptive steepest descent (ASD) and the data fidelity error using projection onto convex sets (POCS). For similar image qualities of the Shepp-Logan phantom, ABOCS requires less computation time than ASD-POCS in MATLAB by more than one order of magnitude. We propose ABOCS for CBCT reconstruction. As compared to other published CS-based algorithms, our method has attractive features of fast convergence and consistent parameter settings for different datasets. These advantages have been demonstrated on phantom studies.

Isotropic and anisotropic filtering norm-minimization: A generalization of the TV and TGV minimizations using NESTA

In this paper, we deal with the signal recovery problem in compressed sensing, that is, the problem of estimating the original signal from its linear measurements. Recovery algorithms can be mainly classified into two types, optimization based algorithms and statistical modeling based algorithms. Basis pursuit (BP) or basis pursuit denoising (BPDN) is one of the most widely used optimization based recovery algorithms, that minimizes the $\ell_{1}$ norm of the signal or its coefficients in some basis under the constraint that its linear transform is equal to or close to the observation signal. There are various extensions of those algorithms depending on the problem structure. When the original signal is an image, the objective function is often the sum of the $\ell_{1}$ norm of the coefficients of the signal in some basis and a total variation (TV) of the image. It can be considered that it requires the image to be sparse in both the specific transform domain and finite differences at the same time. In this paper, we propose a statistical model that represents those sparsities and the signal recovery algorithm based on the variational method. One of the advantages of the statistical approach is that we can utilize the posterior information of the original signal and it is known that it can be used to construct the compressed sensing measurements adaptively. The proposed recovery algorithm and adaptive construction of the compressed sensing measurements are validated on numerical experiments.

A Lagrange barrier approach for the minimum concave cost supply problem via a logarithmic descent direction algorithm

We explore the use of the recently proposed ‘total nuclear variation’ (TVN) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued images and has the advantage of encouraging common edge locations and a shared gradient direction among image channels. We show how it can be incorporated into a general, data-constrained reconstruction framework and derive update equations based on the first-order, primal-dual algorithm of Chambolle and Pock. Early simulation studies based on the numerical XCAT phantom indicate that the inter-channel coupling introduced by the TVN leads to better preservation of image features at high levels of regularization, compared to independent, channel-by-channel TV reconstructions.

The aim of this work is to develop a compressed sensing (CS) based optimization for in- verse treatment planning in radiation therapy. This approach is applied to the example of brachytherapy where fast optimization is essential during intra-operative treatment planning. In this thesis, a novel approach is presented that allows real-time intra-operative plan- ning for the first time. The standard inverse treatment problem is reformulated to resemble a CS problem. Highly specific solvers are developed and incorporated into a novel treatment planning system. By incorporating biological models and clinically important dosimetric criteria, the objective functions become more realistic. Being approximately two orders of magnitude faster than state-of-the-art methods, the CS based approach is proven to return the same or better quality in plans. The inherit sparsity approach in CS allows to decrease the amount of needles by up to 25% reducing the intervention time and the probability of side effects. In addition, the new objective functions further simplify the treatment planning. The novel CS based strategy and solvers can also be applied to other modalities in radi- ation therapy, e.g. intensity-modulated radiation therapy. The incorporation of sparse solution is a novel and promising paradigm for optimization in medical physics.

Three-dimensional reconstruction of abdominal aortic aneurysm is the key technology to improve the success rate of surgical and reduce complications. However, the outer contour of abdominal aortic aneurysm(AAA)is fuzzy, which make it difficult for recent existing method to obtain its accurate segmentation performance and high reconstruction accuracy. In this paper, an improved compressive sensing reconstruction algorithm is proposed, which defines a differentiable and convex total variation (TV) function as an optimization goal function and further reduces the number of projections and improve the quality of reconstructed images. Our proposed algorithm improves the speed and stability of the reconstruction algorithm in three-dimensional reconstruction of abdominal aortic aneurysm. The experimental results show that the proposed model can be used for 3D modeling in 3-D printing to improve the accuracy of endovascular repair and the adaptability of the stent, which is suitable for the application of bioengineering medicine.

In limited-angle tomography, the system of imaging equations is underdetermined, and a naïve reconstruction may not have any practical values. Additional information is needed to augment the data so that a useful image can be reconstructed. This additional information is usually implemented as a Bayesian term in the objective function for an iterative optimization procedure. The state-of-the-art augmented information is the total variation (TV) norm of the image. The TV norm enforces a smooth image with sharp edges. The novelty of this paper is a new Bayesian term that is in the form of a neural network. This neural network is a classifier trained by images reconstructed by full and limited-angle projections. The impact of the proposed method is that the information provided by the neural network contains more features of the images than the TV norm and better reconstruction is expected. Computer simulations are carried out and presented.

In limited-angle tomography, the system of imaging equations is underdetermined, and a naïve reconstruction may not have any practical values. Additional information is needed to augment the data so that a useful image can be reconstructed. This additional information is usually implemented as a Bayesian term in the objective function for an iterative optimization procedure. The state-of-the-art augmented information is the total variation (TV) norm of the image. The TV norm enforces a smooth image with sharp edges. The novelty of this paper is a new Bayesian term that is in the form of a neural network. This neural network is a classifier trained by images reconstructed by full and limited-angle projections. The impact of the proposed method is that the information provided by the neural network contains more features of the images than the TV norm and better reconstruction is expected. Computer simulations are carried out and presented.

Accelerating Dynamic Magnetic Resonance Imaging (MRI) for Lung Tumor Tracking Based on Low-Rank Decomposition in the Spatial–Temporal Domain: A Feasibility Study Based on Simulation and Preliminary Prospective Undersampled MRI

In deep exploration, we often use high-noise and high-resolution astronomical images because of long distance transmission, cosmic noise interference, or other disturbances. Designing an effective method for high-noise astronomical image denoising plays a crucial role in this field. The famous compressed sensing (CS) has shown to be a successful technique for high-resolution image reconstruction. CS is employed to solve the denoising problem in high-noise astronomical images, and a CS reconstruction model and a CS curvelet soft thresholding (NCCST) reconstruction algorithm are proposed simultaneously. In image denoising, the <italic>l</italic>₁-norm reconstruction model based on CS cannot fully consider the internal structure of the image, thus affecting the reconstruction quality. Combined with the <italic>l</italic>₁-norm reconstruction model and group sparse total variation method, the CS reconstruction model is first established. In this framework, the NCCST algorithm uses an adaptive curvelet adjustment operator proposed to select the sparse coefficients in the stage of image sparsity transform, and then a descending VisuShrink threshold is adopted to pick out these reconstructed astronomical image coefficients in each iteration. The experimental results demonstrate that the algorithm proposed can reconstruct clear images from high-noise and high-resolution astronomical images. Meanwhile, it can preserve more astronomical image details, edges, and textures. Even at a low-compression sampling ratio, this algorithm can achieve superior reconstruction performance. The proposed algorithm can be applied in the satellite receiving station to quickly and accurately reconstruct high-resolution astronomical images with high quality.

Coronary vessel wall magnetic resonance (MR) imaging is important for heart disease diagnosis but often suffers long scan time. Compressed sensing (CS) has been previously used to accelerate MR imaging by reconstructing an MR image from undersampled k-space data using a regularization framework. However, the widely used regularizations in the current CS methods often lead to smoothing effects and thus are unable to reconstruct the coronary vessel walls with sufficient resolution. To address this issue, a novel block-weighted total variation regularization is presented to accelerate the coronary vessel wall MR imaging. The proposed regularization divides the image into two parts: a region-of-interest (ROI) which contains the coronary vessel wall, and the other region with less concerned features. Different penalty weights are given to the two regions. As a result, the small details within ROI do not suffer from over-smoothing while the noise outside the ROI can be significantly suppressed. Results with both numerical simulations and in vivo experiments demonstrated that the proposed method can reconstruct the coronary vessel wall from undersampled k-space data with higher qualities than the conventional CS with the total variation or the edge-preserved total variation.

Due to the ocean observation and detection requirements, as well as the construction of ocean defense system engineering, collecting and transmitting a large number of acoustic signals are prerequisite for subsequent processing and analysis. Massive detection data bring a big challenge for transmission lines and underwater processors. The detection acoustic signals can be compressed for storage and reconstructed for processing. In this paper, data compression methods are proposed based on wavelet transform and compressed sensing, the two algorithms are applied and compared for acoustic signal compression. The empirical mode decomposition algorithm is applied for pro-processing. Multilayer wavelet compression is used for getting a compressed acoustic signals. Gradient projection is used for sparse reconstruction. The experimental results show that both methods can perform well in acoustic signal compression, retain the main characteristics of the original acoustic signal, and greatly reduce signals to be transmitted and processed. Wavelet compression is faster in calculation. Compressed sensing is able to achieve a higher compression ratio.

ABSTRACTThis study newly demonstrates a compressed sensing (CS)-based reconstruction scheme for computed tomography (CT) with a translational trajectory. CT with a translational trajectory has many potential applications in the field of non-destructive testing (NDT) and medicine. For example, in the X-ray inspection of a large civil engineering structure, the movements of the source and detector are strictly limited, and a simple straight CT trajectory is preferable. This method could also be applied in X-ray inspection lines in factories and airports. In the medical field, this method would complement the tomosynthesis in mammography. When using a translational trajectory, the dispersion of the fan- or cone-beam creates projection data with the angular information of the sample object. However, the angular information inevitably becomes insufficient when using a translational trajectory, which degrades the reconstruction accuracy. In this case, CS is considered suitable for reconstruction because it has been successfully used for reconstructions from sparse-view and limited-angle data. For reconstruction from the translational trajectory projection, a new concept of directional difference (DD) regularization was proposed. An algorithm was developed based on the alternating direction method of multipliers (ADMM) algorithm to solve the regularization problem. Numerical reconstruction experiments from noisy projection data were conducted and the results were compared with those from other reconstruction methods. The convergence performance of the total variation (TV), DD, and mixed TV-DD regularization methods were examined. The proposed DD and TV-DD methods showed better performance than the TV only regularization. Reconstruction from Monte-Carlo simulated projection data was also demonstrated.