Medical Image Reconstruction Research Articles

Fundamentals of Medical Imaging

P. Suetens New York, NY: Cambridge University Press, 253 pages, $135 I would highly recommend this book for medical imaging scientists and for anyone who is interested in learning the basic building blocks of medical image reconstruction and formation. This book is intended to be used as a

Reconstruction of Large, Irregularly Sampled Multidimensional Images. A Tensor-Based Approach

Many practical applications require the reconstruction of images from irregularly sampled data. The spline formalism offers an attractive framework for solving this problem; the currently available methods, however, are hard to deploy for large-scale interpolation problems in dimensions greater than two (3-D, 3-D+time) because of an exponential increase of their computational cost (curse of dimensionality). Here, we revisit the standard regularized least-squares formulation of the interpolation problem, and propose to perform the reconstruction in a uniform tensor-product B-spline basis as an alternative to the classical solution involving radial basis functions. Our analysis reveals that the underlying multilinear system of equations admits a tensor decomposition with an extreme sparsity of its one dimensional components. We exploit this property for implementing a parallel, memory-efficient system solver. We show that the computational complexity of the proposed algorithm is essentially linear in the number of measurements and that its dependency on the number of dimensions is significantly less than that of the original sparse matrix-based implementation. The net benefit is a substantial reduction in memory requirement and operation count when compared to standard matrix-based algorithms, so that even 4-D problems with millions of samples become computationally feasible on desktop PCs in reasonable time. After validating the proposed algorithm in 3-D and 4-D, we apply it to a concrete imaging problem: the reconstruction of medical ultrasound images (3-D+time) from a large set of irregularly sampled measurements, acquired by a fast rotating ultrasound transducer.

A Fast Compressed Sensing Approach to 3D MR Image Reconstruction

The problem of high-resolution image volume reconstruction from reduced frequency acquisition sequences has drawn significant attention from the scientific community because of its practical importance in medical diagnosis. To address this issue, several reconstruction strategies have been recently proposed, which aim to recover the missing information either by exploiting the spatio-temporal correlations of the image series, or by imposing suitable constraints on the reconstructed image volume. The main contribution of this paper is to combine both these strategies in a compressed sensing framework by exploiting the gradient sparsity of the image volume. The resulting constrained 3D minimization problem is then solved using a penalized forward-backward splitting approach that leads to a convergent iterative two-step procedure. In the first step, the updating rule accords with the sequential nature of the data acquisitions, in the second step a truly 3D filtering strategy exploits the spatio-temporal correlations of the image sequences. The resulting NFCS-3D algorithm is very general and suitable for several kinds of medical image reconstruction problems. Moreover, it is fast, stable and yields very good reconstructions, even in the case of highly undersampled image sequences. The results of several numerical experiments highlight the optimal performance of the proposed algorithm and confirm that it is competitive with state of the art algorithms.

Bayesian Image Restoration for Medical Images Using Radon Transform

We propose an image reconstruction algorithm using Bayesian inference for Radon transformed observation data, which often appears in the field of medical image reconstruction known as computed tomography (CT). In order to apply our Bayesian reconstruction method, we introduced several hyper-parameters that control the ratio between prior information and the fidelity of the observation process. Since the quality of the reconstructed image is influenced by the estimation accuracy of these hyper-parameters, we propose an inference method for them based on the marginal likelihood maximization principle as well as the image reconstruction method. We are able to demonstrate a reconstruction result superior to that obtained using the conventional filtered back projection method.

Medical image reconstruction techniques

Medical image reconstruction techniques

Parallel medical image reconstruction: from graphics processing units (GPU) to Grids

We present and compare a variety of parallelization approaches for a real-world case study on modern parallel and distributed computer architectures. Our case study is a production-quality, time-intensive algorithm for medical image reconstruction used in computer tomography (PET). We parallelize this algorithm for the main kinds of contemporary parallel architectures: shared-memory multiprocessors, distributed-memory clusters, graphics processing units (GPU) using the CUDA framework, the Cell processor and, finally, how various architectures can be accessed in a distributed Grid environment. The main contribution of the paper, besides the parallelization approaches, is their systematic comparison regarding four important criteria: performance, programming comfort, accessibility, and cost-effectiveness. We report results of experiments on particular parallel machines of different architectures that confirm the findings of our systematic comparison.

3-D Reconstruction of Medical Image Using Wavelet Transform and Snake Model

Medical i mage segmentation is a n important step in 3-D reconstruction , and 3-D reconstruction from medical images is an important application of computer graphics and biomedicine image processing. A n improved image segmentation method which is suitable for 3-D reconstruction is presented i n this paper. A 3-D reconstruction algorithm is used to reconstruct the 3-D model from medical images. R ough edge is obtained by multi-scale wavelet transform at f irst. With the rough edge, improved gradient vector flow s nake model is used and the object contour in the image is found. In the experiment s , we reconstruct 3-D model s of kidney , liver and brain putamen . The performances of the experiments indicate that the new algorithm can produce accurate 3-D reconstruction.

A self-adaptive projection method for solving the multiple-sets split feasibility problem

The multiple-sets split feasibility problem, a generalization and extension of the split feasibility problem, has a variety of specific applications in real world, such as medical care, image reconstruction and signal processing. It can be a model for many inverse problems where constraints are imposed on the solutions in the domain of a linear operator as well as in the operator's range. Censor et al (2005 Inverse Problems 21 2171–84) proposed a method for solving the multiple-sets split feasibility problem, whose efficiency depends heavily on step size, a fixed constant related to the Lipschitz constant of ∇p(x) (see the definition in section 1). To estimate the Lipschitz constant is a very difficult, if not an impossible task. On the other hand, even if we know the Lipschitz constant, a method with fixed step size may be slow. In this paper, we propose a new method for solving the multiple-sets split feasibility problem by adopting variable step sizes, which chooses suitable step sizes self-adaptively, based on the information from the current iterate. It thus avoids the difficult task of estimating the Lipschitz constant, while the efficiency is enhanced greatly. We prove the global convergence of the new method and report our numerical results, which are promising.

Auxiliary contour algorithm for 3D reconstruction of medical slice images

An improved 3D reconstruction algorithm of multiple contours was presented in the paper in view of contour bifurcation in the process of contour reconstruction.By constructing auxiliary contours,the connection of multiple contours was converted to single contour and the defection of using multiple contours to 3D reconstruction was improved.The three keratinization of characteristic point using the acceptable surface was implemented,the rough surface in the process of reconstruction according to the curvature's change was fitted,and 3D reconstruction of medical slice images was realized.The experimental results show that the proposed algorithm can shorten the time of volume data structure,ensure the correction of reconstruction objects and accelerate the speed of the whole surface reconstruction at the same time.

Guest Editorial Fully 3-D Reconstruction of Medical Images

The 11 papers in this special issue focus on 3-D reconstruction of medical images. Two main classes of reconstructive algorithms are covered in this issue: analytic and iterative. The papers are briefly summarized here.

On Iterative Bayes Algorithms for Emission Tomography

In this paper we formulate a new approach to medical image reconstruction from projections in emission tomography. This approach conceptually differs from the traditional methods such as filtered backprojection, maximum likelihood or maximum penalized likelihood. Similar to the Richardson-Lucy algorithm ([1], [2]), our method develops directly from the Bayes formula with the final result being an iterative algorithm, for which the maximum likelihood expectation-maximization of [3] (or [4]) is a special case. Although there are different ways to enforce smoothness in the reconstructions using this method, in this paper we opt to focus only on the way which smoothes the camera bin measurements before reconstruction. In fact, this method can be explicated as maximizing a special penalized log-likelihood function. Its theoretical properties are also analyzed in the paper.

3D shape reconstruction of medical images using a perspective shape-from-shading method

A 3D shape reconstruction approach for medical images using a shape-from-shading (SFS) method was proposed in this paper. A new reflectance map equation of medical images was analyzed with the assumption that the Lambertian reflectance surface was irradiated by a point light source located at the light center and the image was formed under perspective projection. The corresponding static Hamilton–Jacobi (H–J) equation of the reflectance map equation was established. So the shape-from-shading problem turned into solving the viscosity solution of the static H–J equation. Then with the conception of a viscosity vanishing approximation, the Lax–Friedrichs fast sweeping numerical method was used to compute the viscosity solution of the H–J equation and a new iterative SFS algorithm was gained. Finally, experiments on both synthetic images and real medical images were performed to illustrate the efficiency of the proposed SFS method.

Computational foundations of image interpolation algorithms

Image interpolation is an important image processing operation applied in diverse areas ranging from computer graphics, rendering, editing, medical image reconstruction, to online image viewing. Image interpolation techniques are referred in literature by many terminologies, such as image resizing, image resampling, digital zooming, image magnification or enhancement, etc. Basically, an image interpolation algorithm is used to convert an image from one resolution (dimension) to another resolution without loosing the visual content in the picture. Image interpolation algorithms can be grouped in two categories, non-adaptive and adaptive. The computational logic of an adaptive image interpolation technique is mostly dependent upon the intrinsic image features and contents of the input image whereas computational logic of a non-adaptive image interpolation technique is fixed irrespective of the input image features. In this paper, we review the progress of both non-adaptive and adaptive image interpolation techniques. We also proposed a new algorithm for image interpolation in discrete wavelet transform domain and shown its efficacy. We describe the underlying computational foundations of all these algorithms and their implementation techniques. We present some experimental results to show the impact of these algorithms in terms of image quality metrics and computational requirements for implementation.

Computational foundations of image interpolation algorithms

Image interpolation is an important image processing operation applied in diverse areas ranging from computer graphics, rendering, editing, medical image reconstruction, to online image viewing. Image interpolation techniques are referred in literature by many terminologies, such as image resizing, image resampling, digital zooming, image magnification or enhancement, etc. Basically, an image interpolation algorithm is used to convert an image from one resolution (dimension) to another resolution without loosing the visual content in the picture. Image interpolation algorithms can be grouped in two categories, non-adaptive and adaptive. The computational logic of an adaptive image interpolation technique is mostly dependent upon the intrinsic image features and contents of the input image whereas computational logic of a non-adaptive image interpolation technique is fixed irrespective of the input image features. In this paper, we review the progress of both non-adaptive and adaptive image interpolation techniques. We also proposed a new algorithm for image interpolation in discrete wavelet transform domain and shown its efficacy. We describe the underlying computational foundations of all these algorithms and their implementation techniques. We present some experimental results to show the impact of these algorithms in terms of image quality metrics and computational requirements for implementation.

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Special issue on volumetric reconstruction of medical images

Local tomography property of residual minimization reconstruction with planar integral data

Residual minimization with the well-known conjugate gradient (CG) algorithm has been applied to medical image reconstruction for years. The main advantage of this method is its fast convergence rate. In this paper, we point out that this method has another property-local tomography, when this image reconstruction method is applied to planar integral projections. By local tomography we mean the following: The object is relatively large, the entire object is not sufficiently measured, and the projections are truncated due to a small detector size. However, a small region-of-interest (ROI) is sufficiently measured. The small ROI is able to be exactly reconstructed. This local tomographic property is found for planar integral data only and is not found for line-integral measurements. Iterative local tomography has been applied to cos/spl alpha//r weighted planar integral data through computer simulations and phantom experiments. An efficient projector that models the cos/spl alpha//r weighting factor is also developed.