Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

Piccolomini, Elena Loli; Coli, Vanna Lisa; Morotti, Elena; Zanni, Luca

doi:10.1007/s10589-017-9961-2

Cited by 14 publications

(25 citation statements)

References 38 publications

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“…2. Perform a backtracking on the computed direction d (k) starting with η = 1: The update of the scaling matrix D k+1 is performed through a splitting of the gradient of the objective function in its positive and negative parts as in 14 and the definition of ρ k+1 is aimed at avoiding restrictive bounds on the diagonal entries of D k+1 in the initial phase of the iterative process and satisfying the SGP convergence conditions 19 by asymptotically forcing D k+1 towards the identity matrix. The update of the steplength α k+1 is obtained by using an alternate Barzilai-Borwein strategy; in particular, we use adaptive alternations of the two classical Barzilai-Borwein rules proposed in 29 and applied also in 14 .…”

Section: Methodsmentioning

confidence: 99%

“…In this work, we propose to solve (1) by an accelerated gradient scheme belonging to the class of Scaled Gradient Projection (SGP) methods 18,19 . The SGP methods have been recently applied in low-sampled X-rays cone beam CT (CBCT) image reconstruction, with very good results in terms of image accuracy 13,14,20 . In particular, in 14 the authors proposed a SGP method for X-rays CT image reconstruction and applied it to a phantom simulation using a geometry different from DBT limited angles.…”

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confidence: 99%

“…The SGP methods have been recently applied in low-sampled X-rays cone beam CT (CBCT) image reconstruction, with very good results in terms of image accuracy 13,14,20 . In particular, in 14 the authors proposed a SGP method for X-rays CT image reconstruction and applied it to a phantom simulation using a geometry different from DBT limited angles. Since SGP showed a very fast convergence in the first iterations, we choose a similar approach also for our DBT application.…”

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confidence: 99%

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GPU acceleration of a model-based iterative method for Digital Breast Tomosynthesis

Cavicchioli

Piccolomini

et al. 2020

Sci Rep

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Digital Breast Tomosynthesis (DBT) is a modern 3D Computed Tomography X-ray technique for the early detection of breast tumors, which is receiving growing interest in the medical and scientific community. Since DBT performs incomplete sampling of data, the image reconstruction approaches based on iterative methods are preferable to the classical analytic techniques, such as the Filtered Back Projection algorithm, providing fewer artifacts. In this work, we consider a Model-Based Iterative Reconstruction (MBIR) method well suited to describe the DBT data acquisition process and to include prior information on the reconstructed image. We propose a gradient-based solver named Scaled Gradient Projection (SGP) for the solution of the constrained optimization problem arising in the considered MBIR method. Even if the SGP algorithm exhibits fast convergence, the time required on a serial computer for the reconstruction of a real DBT data set is too long for the clinical needs. In this paper we propose a parallel SGP version designed to perform the most expensive computations of each iteration on Graphics Processing Unit (GPU). We apply the proposed parallel approach on three different GPU boards, with computational performance comparable with that of the boards usually installed in commercial DBT systems. The numerical results show that the proposed GPU-based MBIR method provides accurate reconstructions in a time suitable for clinical trials. Digital Breast Tomosynthesis (DBT) is a quite recent 3D Computed Tomography (CT) technique providing a volumetric breast reconstruction as a stack of 2D images, each representing a cross-sectional slice of the breast itself 1. When compared with traditional 2D mammography, DBT has the advantage of separating the breast anatomical tissues, which can be overlapped in a mammography, and this generally reduces false negative diagnosis. At the same time, since the DBT source emits X-rays only from a small number of angles in an arc trajectory, DBT provides a low radiation dose comparable to the radiation dose used in a standard mammography. For this reason, DBT is appealing to the medical and scientific community as a breast screening routine 2,3. Until a few years ago, the introduction of DBT in a clinical setting has been slowed down by the absence of efficient algorithms for image reconstruction from a limited number of projections. It is well known that the traditional Filtered Back Projection (FBP) 4 analytic algorithm amplifies noise and artifacts in the case of low-sampled data 3. Iterative algorithms are known to perform better than FBP in the case of tomosynthesis data, but they require computational times incompatible with a clinical use 3,5 , since in clinical DBT examinations the breast reconstruction must be provided in 40 to 60 seconds. Nevertheless, the recent advent of low cost parallel architectures, such as Graphics Processing Units (GPUs), has provided the chance for a remarkable reduction of the image reconstruction time, making iterative methods a realistic alterna...

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Section: Methodsmentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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GPU acceleration of a model-based iterative method for Digital Breast Tomosynthesis

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Piccolomini

et al. 2020

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“…In order to take into account the existence of some background emission, 10 −10 was added to all pixels of the blurred image; obviously, the vector b in D KL (x) was set as b = 10 −10 e. where N exact and N background are the total number of photons in the exact image to be recovered and in the background term, respectively. Therefore, the intensities of the reference images were pre-scaled to get noisy and blurred images with Signal to Noise Ratio (SNR) equal to 35 The regularization parameter λ was set by trial and error, taking into account the double goal of minimizing the relative error of the restored image with respect to the original image and getting visual satisfaction. Its values are reported in Table 1.…”

Section: Numerical Experimentsmentioning

confidence: 99%

ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

Serafino

Landi

Viola

2020

Applied Mathematics and Computation

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We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback-Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback-Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole sequence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality.

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“…This strategy is used in several reconstruction methods (Kim et al, 2014;Nien and Fessler, 2015;Zheng, Ravishankar, Long, and Fessler, 2018). Piccolomini, Coli, Morotti, and Zanni (2018) use the diagonally scaled gradient method of Bonettini et al (2008) to reconstruct CT images in the context of incomplete data. However, in cylindrical coordinates, widely different voxel sizes make A badly scaled, and diagonal scaling is no longer appropriate.…”

Section: Motivation and Previous Workmentioning

confidence: 99%

Scaled projected-directions methods with application to transmission tomography

2020

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Statistical image reconstruction in X-Ray computed tomography yields large-scale regularized linear least-squares problems with nonnegativity bounds, where the memory footprint of the operator is a concern. Discretizing images in cylindrical coordinates results in significant memory savings, and allows parallel operator-vector products without on-the-fly computation of the operator, without necessarily decreasing image quality. However, it deteriorates the conditioning of the operator. We improve the Hessian conditioning by way of a blockcirculant scaling operator and we propose a strategy to handle nondiagonal scaling in the context of projected-directions methods for bound-constrained problems. We describe our implementation of the scaling strategy using two algorithms: TRON, a trust-region method with exact second derivatives, and L-BFGS-B, a linesearch method with a limited-memory quasi-Newton Hessian approximation. We compare our approach with one where a change of variable is made in the problem. On two reconstruction problems, our approach converges faster than the change of variable approach, and achieves much tighter accuracy in terms of optimality residual than a first-order method.

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Reconstruction of 3D X-ray CT images from reduced sampling by a scaled gradient projection algorithm

Cited by 14 publications

References 38 publications

GPU acceleration of a model-based iterative method for Digital Breast Tomosynthesis

GPU acceleration of a model-based iterative method for Digital Breast Tomosynthesis

ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

Scaled projected-directions methods with application to transmission tomography

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