Segmentation of tomographic data without image reconstruction

Geometric tomography (GT), a technique for processing tomographic projections in order to reconstruct the external and internal boundaries of objects, is presented. GT does not necessitate the reconstruction of an image of the slice of the object. It is shown that the segmentation can be performed directly with the raw data, the sinogram produced with the scanner, and that those segmented shapes can be geometrically transformed into reconstructed shapes in the usual space. If one is interested in only the boundaries of the objects, they do not need to reconstruct an image, and therefore the method needs much less computation than those using traditional computed tomography techniques. Experimental results are presented for both synthesized and real data, leading to subpixel positioning of the reconstructed boundaries. GT gives its best results for sparse, highly contrasted objects such as bones or blood vessels in angiograms, it allows ;on the fly' processing of the data, and real time tracking of the object boundaries.     

Efficient framework for model-based tomographic image reconstruction using wavelet packets

The use of model-based algorithms in tomographic imaging offers many advantages over analytical inversion methods. However, the relatively high computational complexity of model-based approaches often restricts their efficient implementation. In practice, many modern imaging modalities, such as computed-tomography, positron-emission tomography, or optoacoustic tomography, normally use a very large number of pixels/voxels for image reconstruction. Consequently, the size of the forward-model matrix hinders the use of many inversion algorithms. In this paper, we present a new framework for model-based tomographic reconstructions, which is based on a wavelet-packet representation of the imaged object and the acquired projection data. The frequency localization property of the wavelet-packet base leads to an approximately separable model matrix, for which reconstruction at each spatial frequency band is independent and requires only a fraction of the projection data. Thus, the large model matrix is effectively separated into a set of smaller matrices, facilitating the use of inversion schemes whose complexity is highly nonlinear with respect to matrix size. The performance of the new methodology is demonstrated for the case of 2-D optoacoustic tomography for both numerically generated and experimental data.     

A Hankel transform approach to tomographic image reconstruction

A relatively unexplored algorithm is developed for reconstructing a two-dimensional image from a finite set of its sampled projections. The algorithm, referred to as the Hankel-transform-reconstruction (HTR) algorithm, is polar-coordinate based. The algorithm expands the polar-form Fourier transform F(r,theta) of an image into a Fourier series in theta calculates the appropriately ordered Hankel transform of the coefficients of this series, giving the coefficients for the Fourier series of the polar-form image f(p,phi); resolves this series, giving a polar-form reconstruction; and interpolates this reconstruction to a rectilinear grid. The HTR algorithm is outlined, and it is shown that its performance compares favorably to the popular convolution-backprojection algorithm.     

Spatial resolution properties of motion-compensated tomographic image reconstruction methods

Many motion-compensated image reconstruction (MCIR) methods have been proposed to correct for subject motion in medical imaging. MCIR methods incorporate motion models to improve image quality by reducing motion artifacts and noise. This paper analyzes the spatial resolution properties of MCIR methods and shows that nonrigid local motion can lead to nonuniform and anisotropic spatial resolution for conventional quadratic regularizers. This undesirable property is akin to the known effects of interactions between heteroscedastic log-likelihoods (e.g., Poisson likelihood) and quadratic regularizers. This effect may lead to quantification errors in small or narrow structures (such as small lesions or rings) of reconstructed images. This paper proposes novel spatial regularization design methods for three different MCIR methods that account for known nonrigid motion. We develop MCIR regularization designs that provide approximately uniform and isotropic spatial resolution and that match a user-specified target spatial resolution. Two-dimensional PET simulations demonstrate the performance and benefits of the proposed spatial regularization design methods.     

Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction

Fourier-based forward and back-projection methods can reduce computation in iterative tomographic image reconstruction. Recently, an optimized nonuniform fast Fourier transform (NUFFT) approach was shown to yield accurate parallel-beam projections. In this paper, we extend the NUFFT approach to describe an O (N2 log N) projector/backprojector pair for fan-beam transmission tomography. Simulations and experiments with real CT data show that fan-beam Fourier-based forward and back-projection methods can reduce computation for iterative reconstruction while still providing accuracy comparable to their O (N3) space-based counterparts.     

Iterative tomographic image reconstruction using Fourier-based forward and back-projectors

Iterative image reconstruction algorithms play an increasingly important role in modern tomographic systems, especially in emission tomography. With the fast increase of the sizes of the tomographic data, reduction of the computation demands of the reconstruction algorithms is of great importance. Fourier-based forward and back-projection methods have the potential to considerably reduce the computation time in iterative reconstruction. Additional substantial speed-up of those approaches can be obtained utilizing powerful and cheap off-the-shelf fast Fourier transform (FFT) processing hardware. The Fourier reconstruction approaches are based on the relationship between the Fourier transform of the image and Fourier transformation of the parallel-ray projections. The critical two steps are the estimations of the samples of the projection transform, on the central section through the origin of Fourier space, from the samples of the transform of the image, and vice versa for back-projection. Interpolation errors are a limitation of Fourier-based reconstruction methods. We have applied min-max optimized Kaiser-Bessel interpolation within the nonuniform FFT (NUFFT) framework and devised ways of incorporation of resolution models into the Fourier-based iterative approaches. Numerical and computer simulation results show that the min-max NUFFT approach provides substantially lower approximation errors in tomographic forward and back-projection than conventional interpolation methods. Our studies have further confirmed that Fourier-based projectors using the NUFFT approach provide accurate approximations to their space-based counterparts but with about ten times faster computation, and that they are viable candidates for fast iterative image reconstruction.     

Pose estimation of known objects during transmission tomographic image reconstruction

We address the problem of image formation in transmission tomography when metal objects of known composition and shape, but unknown pose, are present in the scan subject. Using an alternating minimization (AM) algorithm, derived from a model in which the detected data are viewed as Poisson-distributed photon counts, we seek to eliminate the streaking artifacts commonly seen in filtered back projection images containing high-contrast objects. We show that this algorithm, which minimizes the I-divergence (or equivalently, maximizes the log-likelihood) between the measured data and model-based estimates of the means of the data, converges much faster when knowledge of the high-density materials (such as brachytherapy applicators or prosthetic implants) is exploited. The algorithm incorporates a steepest descent-based method to find the position and orientation (collectively called the pose) of the known objects. This pose is then used to constrain the image pixels to their known attenuation values, or, for example, to form a mask on the "missing" projection data in the shadow of the objects. Results from two-dimensional simulations are shown in this paper. The extension of the model and methods used to three dimensions is outlined.     

A wavelet-based method for multiscale tomographic reconstruction

The authors represent the standard ramp filter operator of the filtered-back-projection (FBP) reconstruction in different bases composed of Haar and Daubechies compactly supported wavelets. The resulting multiscale representation of the ramp-filter matrix operator is approximately diagonal. The accuracy of this diagonal approximation becomes better as wavelets with larger numbers of vanishing moments are used. This wavelet-based representation enables the authors to formulate a multiscale tomographic reconstruction technique in which the object is reconstructed at multiple scales or resolutions. A complete reconstruction is obtained by combining the reconstructions at different scales. The authors' multiscale reconstruction technique has the same computational complexity as the FBP reconstruction method. It differs from other multiscale reconstruction techniques in that (1) the object is defined through a one-dimensional multiscale transformation of the projection domain, and (2) the authors explicitly account for noise in the projection data by calculating maximum a posteriori probability (MAP) multiscale reconstruction estimates based on a chosen fractal prior on the multiscale object coefficients. The computational complexity of this maximum a posteriori probability (MAP) solution is also the same as that of the FBP reconstruction. This result is in contrast to commonly used methods of statistical regularization, which result in computationally intensive optimization algorithms.     

Improved tomographic reconstruction in seven-pinhole imaging

Cardiac emission tomography using a seven-pinhole collimator has received only little appreciation as a diagnostic imaging technique. The main reasons are the limited angular sampling of the seven-pinhole device and the difficulties encountered in properly positioning the patient relative to the collimator/camera system. In order to overcome these problems, we have developed a modified ART3 algorithm for reconstruction of the radioactivity distribution in the heart. The method is very appropriate for seven-pinhole tomography, as demonstrated by the quality of the reconstructions, by the excellent point source resolution of the system response, and by a comparison to two other suitable reconstruction techniques, viz., SMART and SIRT.     

Human observer confidence in image quality assessment

Mean opinion scores obtained from subjective quality assessment are widely used as a ground truth for the development of predictive quality models. The underlying variance between observer ratings is typically quantified using confidence intervals, which do not provide any direct insight into the underlying causes of the disagreement. For better understanding of human visual quality perception and to develop more accurate models, it is important to identify the factors that impact on the variations in quality ratings. This work considers one such factor: observer confidence. This consideration is motivated by the view that quality assessment is a difficult task and hence quality ratings are provided with varying levels of confidence. The first goal of this paper is to analyse the results of an experiment to determine association between observer confidence and image quality judgement. Secondly, models are developed that aim to predict mean observer confidence as a complementary measure to the widely used mean opinion scores. It is shown that there is indeed a strong interrelation between quality perception and confidence, resulting in predictive models of high accuracy.     

DCT-based complexity regularization for EM tomographic reconstruction.

This paper introduces a simple algorithm for tomographic reconstruction based on the use of a complexity regularization term. The regularization is formulated in the discrete cosine transform (DCT) domain by promoting a low-noise reconstruction having a high sparsity in the frequency domain. The resulting algorithm simply alternates between a maximum-likelihood (ML) expectation-maximization (EM) update and a decreasing sparsity constraint in the DCT domain. Applications to SPECT reconstruction and comparisons with a classical estimator using the best available regularization terms are given in order to illustrate the potential of our reconstruction technique.     

Adaptive wavelet graph model for Bayesian tomographic reconstruction

We introduce an adaptive wavelet graph image model applicable to Bayesian tomographic reconstruction and other problems with nonlocal observations. The proposed model captures coarse-to-fine scale dependencies in the wavelet tree by modeling the conditional distribution of wavelet coefficients given overlapping windows of scaling coefficients containing coarse scale information. This results in a graph dependency structure which is more general than a quadtree, enabling the model to produce smooth estimates even for simple wavelet bases such as the Haar basis. The inter-scale dependencies of the wavelet graph model are specified using a spatially nonhomogeneous Gaussian distribution with parameters at each scale and location. The parameters of this distribution are selected adaptively using nonlinear classification of coarse scale data. The nonlinear adaptation mechanism is based on a set of training images. In conjunction with the wavelet graph model, we present a computationally efficient multiresolution image reconstruction algorithm. This algorithm is based on iterative Bayesian space domain optimization using scale recursive updates of the wavelet graph prior model. In contrast to performing the optimization over the wavelet coefficients, the space domain formulation facilitates enforcement of pixel positivity constraints. Results indicate that the proposed framework can improve reconstruction quality over fixed resolution Bayesian methods.     

Regularization in tomographic reconstruction using thresholding estimators

In tomographic medical devices such as single photon emission computed tomography or positron emission tomography cameras, image reconstruction is an unstable inverse problem, due to the presence of additive noise. A new family of regularization methods for reconstruction, based on a thresholding procedure in wavelet and wavelet packet (WP) decompositions, is studied. This approach is based on the fact that the decompositions provide a near-diagonalization of the inverse Radon transform and of prior information in medical images. A WP decomposition is adaptively chosen for the specific image to be restored. Corresponding algorithms have been developed for both two-dimensional and full three-dimensional reconstruction. These procedures are fast, noniterative, and flexible. Numerical results suggest that they outperform filtered back-projection and iterative procedures such as ordered-subset-expectation-maximization.     

Multiobjective neural network for image reconstruction

The authors propose a multiobjective neural network model and algorithm for image reconstruction from projections. This model combines the Hopfield model and multiobjective decision making approach. A weighted sum optimisation based neural network algorithm is developed. The dynamic process of the net is based on minimisation of a weighted sum energy function and Euler's iteration and this algorithm is applied to image reconstruction from computer-generated noisy projections and Siemens Somaton DR scanner data, respectively. Reconstructions based on this method are shown to be superior to those based on conventional iterative reconstruction algorithms such as MART (multiplicate algebraic reconstruction technique) and convolution from the point of view of accuracy of reconstruction. Computer simulation using the multiobjective method shows a significant improvement in image quality and convergence behaviour over conventional algorithms     

Multidimensional image reconstruction in astronomy

The goal of this article is to describe a unified approach based on the assumption of additive Gaussian noise and regularization theory that illustrates the flavor of such multidimensional image reconstruction problems and the associated challenges. Efficient iterative methods are described for the solution of these problems. Indeed, a crucial point in the solution to the problems considered in this article is the size of the data set and the need for efficient algorithms.     

Grouped-coordinate ascent algorithms for penalized-likelihoodtransmission image reconstruction

Presents a new class of algorithms for penalized-likelihood reconstruction of attenuation maps from low-count transmission scans. We derive the algorithms by applying to the transmission log-likelihood a version of the convexity technique developed by De Pierro for emission tomography. The new class includes the single-coordinate ascent (SCA) algorithm and Lange's convex algorithm for transmission tomography as special cases. The new grouped-coordinate ascent (GCA) algorithms in the class overcome several limitations associated with previous algorithms. (1) Fewer exponentiations are required than in the transmission maximum likelihood-expectation maximization (ML-EM) algorithm or in the SCA algorithm. (2) The algorithms intrinsically accommodate nonnegativity constraints, unlike many gradient-based methods. (3) The algorithms are easily parallelizable, unlike the SCA algorithm and perhaps line-search algorithms. We show that the GCA algorithms converge faster than the SCA algorithm, even on conventional workstations. An example from a low-count positron emission tomography (PET) transmission scan illustrates the method     

Unique tomographic reconstruction of vector fields using boundarydata

The problem of reconstructing a vector field v(r) from its line integrals (through some domain D) is generally undetermined since v(r) is defined by two component functions. When v(r) is decomposed into its irrotational and solenoidal components, it is shown that the solenoidal part is uniquely determined by the line integrals of v(r). This is demonstrated in a particularly simple manner in the Fourier domain using a vector analog of the well-known projection slice theorem. In addition, under the constraint that v (r) is divergenceless in D, a formula for the scalar potential phi(r) is given in terms of the normal component of v(r) on the boundary D. An important application of vector tomography, i.e., a fluid velocity field from reciprocal acoustic travel time measurements or Doppler backscattering measurements, is considered.     

Biorthogonal wavelet system for high-resolution image reconstruction

High-resolution images are often desired but made impossible because of hardware limitations. For the high-resolution model proposed by Bose and Boo (see Int. J. Imaging Syst. Technol., vol.9, p.294-304, 1998), the iterative wavelet-based algorithm has been shown to perform better than the traditional least square method when the resolution ratio M is two and four. In this paper, we discuss the minimally supported biorthogonal wavelet system that comes from the mathematical model by Bose and Boo and propose a wavelet-based algorithm for arbitrary resolution ratio M/spl ges/2. The numerical results indicate that the algorithm based on our biorthogonal wavelet system performs better in high-resolution image reconstruction than the wavelet-based algorithm in the literature, as well as the common-used least square method.     

Fast spatio-temporal image reconstruction for dynamic PET

In tomographic imaging, dynamic images are typically obtained by reconstructing the frames of a time sequence independently, one by one. A disadvantage of this frame-by-frame reconstruction approach is that it fails to account. For temporal correlations in the signal. Ideally, one should treat the entire image sequence as a single spatio-temporal signal. However, the resulting reconstruction task becomes computationally intensive. Fortunately, as the authors show in this paper, the spatio-temporal reconstruction problem call be greatly simplified by first applying a temporal Karhunen-Loeve (KL) transformation to the imaging equation. The authors show that if the regularization operator is chosen to be separable into space and time components, penalized weighted least squares reconstruction of the entire image sequence is approximately equivalent to frame-by-frame reconstruction in the space-KL domain. By this approach, spatio-temporal reconstruction can be achieved at reasonable computational cost. One can achieve further computational savings by discarding high-order KL components to avoid reconstructing them. Performance of the method is demonstrated through statistical evaluations of the bias-variance tradeoff obtained by computer simulation reconstruction     

Improved image reconstruction techniques for synthetic apertureradiometers

Ripple in excess of that attributable to Gibb's phenomenon has been identified in brightness temperature images created from data collected by synthetic aperture radiometers used for Earth remote sensing. The cause of the excess ripple is identified, and methods for reducing its effect on image quality are proposed