Biomedical subjects

D S Lalush

Publications and source records attributed to D S Lalush.

8 recordsLinked to original sources

PubMed2000

Fast maximum entropy approximation in SPECT using the RBI-MAP algorithm.

In this work, we present a method for approximating constrained maximum entropy (ME) reconstructions of SPECT data with modifications to a block-iterative maximum a posteriori (MAP) algorithm. Maximum likelihood (ML)-based reconstruction algorithms require some form of noise smoothing. Constrained ME provides a more formal method of noise smoothing without requiring the user to select parameters. In the context of SPECT, constrained ME seeks the minimum-information image estimate among those whose projections are a given distance from the noisy measured data, with that distance determined by the magnitude of the Poisson noise. Images that meet the distance criterion are referred to as feasible images. We find that modeling of all principal degrading factors (attenuation, detector response, and scatter) in the reconstruction is critical because feasibility is not meaningful unless the projection model is as accurate as possible. Because the constrained ME solution is the same as a MAP solution for a particular value of the MAP weighting parameter, beta, the constrained ME solution can be found with a MAP algorithm if the correct value of beta is found. We show that the RBI-MAP algorithm, if used with a dynamic scheme for estimating beta, can approximate constrained ME solutions in 20 or fewer iterations. We compare results for various methods of achieving feasible images on a simulation of Tl-201 cardiac SPECT data. Results show that the RBI-MAP ME approximation provides images and quantitative estimates close to those from a slower algorithm that gives the true ME solution. Also, we find that the ME results have higher spatial resolution and greater high-frequency noise content than a feasibility-based stopping rule, feasibility-based low-pass filtering, and a quadratic Gibbs prior with beta selected according to the feasibility criterion. We conclude that fast ME approximation is possible using either RBI-MAP with the dynamic procedure or a feasibility-based stopping rule, and that such reconstructions may be particularly useful in applications where resolution is critical.

Algorithms↗

PubMed2000

Performance of ordered-subset reconstruction algorithms under conditions of extreme attenuation and truncation in myocardial SPECT.

UNLABELLED: We studied the bias and variance characteristics of the ordered-subset expectation maximization (OSEM) and rescaled block-iterative EM (RBIEM) iterative reconstruction algorithms in myocardial SPECT under extreme, but realistic, conditions. METHOD: We used the 2-dimensional mathematic cardiac torso phantom to simulate 2 patient anatomies: a large male with a raised diaphragm and a female with large breast size, approximating extreme cases of attenuation conditions found in the clinic. For each anatomy, realistic 201Tl projection data were simulated for a 180 degrees acquisition arc. Three cases of truncation for a 90 degrees-configured dual detector system were simulated: no truncation, moderate truncation, and extreme truncation. For each case, an ensemble of 250 noise simulations was generated, and each noisy dataset was reconstructed with the OSEM and RBIEM algorithms. The reconstructions modeled only the effects of nonuniform attenuation and used a range of subset configurations. Over the ensemble, we computed means and variances of activity in 8 regions of interest (ROIs) in the heart as a function of iteration. RESULTS: Under conditions of no truncation and moderate truncation, the results from OSEM and RBIEM were very close to those from maximum-likelihood EM (MLEM); in all cases, the difference in ROI means was <2.5%. For extreme truncation, the errors increased to as much as 11% with OSEM, but these were no greater than the errors for MLEM under the same conditions. The OSEM algorithm with 2 views per subset was found to result in much higher variance of ROI estimates for the same bias as compared with RBIEM or OSEM with 4 or more views per subset. CONCLUSION: The OSEM and RBIEM algorithms are at least as robust to highly attenuating patients and truncation as MLEM algorithm and can be adequate substitutes for MLEM, even in extreme cases. Clinical users should apply the smallest number of subsets that can be accommodated by allowable processing time to reduce image noise and variance in quantitative estimates.

Algorithms↗

PubMed1999

Fourier rebinning applied to multiplanar circular-orbit cone-beam SPECT.

We study the application of Fourier rebinning methods to dual-planar cone-beam SPECT. Dual-planar cone-beam SPECT involves the use of a pair of dissimilar cone-beam collimators on a dual-camera SPECT system. Each collimator has its focus in a different axial plane. While dual-planar data is best reconstructed with fully three-dimensional (3-D) iterative methods, these methods are slow and have prompted a search for faster reconstruction techniques. Fourier rebinning was developed to estimate equivalent parallel projections from 3-D PET data, but it simply expresses a relationship between oblique projections taken in planes not perpendicular to the axis of rotation and direct projections taken in those that are. We find that it is possible to put cone-beam data in this context as well. The rebinned data can then be reconstructed using either filtered backprojection (FBP) or parallel iterative algorithms such as OS-EM. We compare the Feldkamp algorithm and fully 3-D OSEM reconstruction with Fourier-rebinned reconstructions on realistically-simulated Tc-99m HMPAO brain SPECT data. We find that the Fourier-rebinned reconstructions exhibit much less image noise and lower variance in region-of-interest (ROI) estimates than Feldkamp. Also, Fourier-rebinning followed by OSEM with nonuniform attenuation correction exhibits less bias in ROI estimates than Feldkamp with Chang attenuation correction. The Fourier-rebinned ROI estimates exhibit bias and variance comparable to those from fully 3-D OSEM and require considerably less processing time. However, in areas off the axis of rotation, the axial-direction resolution of FORE-reconstructed images is poorer than that of images reconstructed with 3-D OSEM. We conclude that Fourier rebinning is a practical and potentially useful approach to reconstructing data from dual-planar circular-orbit cone-beam systems.

Brain↗

PubMed1998

Block-iterative techniques for fast 4D reconstruction using a priori motion models in gated cardiac SPECT.

We introduce a fast block-iterative maximum a posteriori (MAP) reconstruction algorithm and apply it to four-dimensional reconstruction of gated SPECT perfusion studies. The new algorithm, called RBI-MAP, is based on the rescaled block iterative EM (RBI-EM) algorithm. We develop RBI-MAP based on similarities between the RBI-EM, ML-EM and MAP-EM algorithms. RBI-MAP requires far fewer iterations than MAP-EM, and so should result in acceleration similar to that obtained from using RBI-EM or OS-EM as opposed to ML-EM. When complex four-dimensional clique structures are used in the prior, however, evaluation of the smoothing prior dominates the processing time. We show that a simple scheme for updating the prior term in the heart region only for RBI-MAP results in savings in processing time of a factor of six over MAP-EM. The RBI-MAP algorithm incorporating 3D collimator-detector response compensation is demonstrated on a simulated 99mTc gated perfusion study. Results of RBI-MAP are compared with RBI-EM followed by a 4D linear filter. For the simulated study, we find that RBI-MAP provides consistently higher defect contrast for a given degree of noise smoothing than does filtered RBI-EM. This is an indication that RBI-MAP smoothing does less to degrade resolution gained from 3D detector response compensation than does a linear filter. We conclude that RBI-MAP can provide smooth four-dimensional reconstructions with good visualization of heart structures in clinically realistic processing times.

Algorithms↗

PubMed1995

A fast and stable maximum a posteriori conjugate gradient reconstruction algorithm.

We have derived a maximum a posteriori (MAP) approach for iterative reconstruction based on a weighted least-squares conjugate gradient (WLS-CG) algorithm. The WLS-CG algorithm has been shown to have initial convergence rates up to 10x faster than the maximum-likelihood expectation maximization (ML-EM) algorithm, but WLS-CG suffers from rapidly increasing image noise at higher iteration numbers. In our MAP-CG algorithm, the increasing noise is controlled by a Gibbs smoothing prior, resulting in stable, convergent solutions. Our formulation assumes a Gaussian noise model for the likelihood function. When a linear transformation of the pixel space is performed (the "relaxation" acceleration method), the MAP-CG algorithm obtains a low-noise, stable solution (one that does not change with further iterations) in 10-30 iterations, compared to 100-200 iterations for MAP-EM. Each iteration of MAP-CG requires approximately the same amount of processing time as one iteration of ML-EM or MAP-EM. We show that the use of an initial image estimate obtained from a single iteration of the Chang method helps the algorithm to converge faster when acceleration is not used, but does not help when acceleration is applied. While both the WLS-CG and MAP-CG methods suffer from the potential for obtaining negative pixel values in the iterated image estimates, the use of the Gibbs prior substantially reduces the number of pixels with negative values and restricts them to regions of little or no activity. We use SPECT data from simulated hot-sphere phantoms and from patient studies to demonstrate the advantages of the MAP-CG algorithm. We conclude that the MAP-CG algorithm requires 10%-25% of the processing time of EM techniques, and provides images of comparable or superior quality.

Algorithms↗

PubMed1994

Improving the convergence of iterative filtered backprojection algorithms.

Several authors have proposed variations of the iterative filtered backprojection (IFBP) reconstruction algorithms claiming fast initial convergence rates. We have found that these algorithms are trying to minimize an unusual squared-error criterion in a suboptimal way. As a result, existing IFBP algorithms are inefficient in the minimization of the criterion, and may become unstable at higher iteration numbers. We show that existing IFBP algorithms can be modified to use the steepest descent technique by simply optimizing the step size at each iteration. Further gains in convergence rates can be achieved with conjugate gradient IFBP algorithms derived from the same criterion. The steepest descent and conjugate gradient IFBP algorithms are guaranteed to converge, unlike some IFBP algorithms, and will do so in fewer iterations than existing IFBP algorithms.

Algorithms↗

PubMed1993

A generalized Gibbs prior for maximum a posteriori reconstruction in SPECT.

In this paper, we introduce a Gibbs prior for use in MAP (maximum a posteriori) reconstruction in SPECT. This new prior, with three parameters, is able to approximate the results of previously-proposed priors with two parameters, as well as a continuum of others. Also, it allows the user increased flexibility in selecting the properties to be emphasized in the final reconstructed image estimate. The additional flexibility offered by the new prior is important in addressing the problem of selecting a prior and its associated parameters in a clinical situation. The paper demonstrates the importance of the derivative potential function (DPF) of the Gibbs distribution in determining which properties will be emphasized in the iterated image estimates. The effects of each of the three parameters are demonstrated on reconstructions from acquired SPECT data. We conclude that the parameters must be chosen carefully with consideration for the object distribution and the relative requirements for low-contrast detail, smoothing and edge sharpness in the reconstructed image.

Algorithms↗

PubMedDate not supplied

Quantitative myocardial perfusion SPECT.

In recent years, there has been much interest in the clinical application of attenuation compensation to myocardial perfusion single photon emission computed tomography (SPECT) with the promise that accurate quantitative images can be obtained to improve clinical diagnoses. The different attenuation compensation methods that are available create confusion and some misconceptions. Also, attenuation-compensated images reveal other image-degrading effects including collimator-detector blurring and scatter that are not apparent in uncompensated images. This article presents basic concepts of the major factors that degrade the quality and quantitative accuracy of myocardial perfusion SPECT images, and includes a discussion of the various image reconstruction and compensation methods and misconceptions and pitfalls in implementation. The differences between the various compensation methods and their performance are demonstrated. Particular emphasis is directed to an approach that promises to provide quantitative myocardial perfusion SPECT images by accurately compensating for the 3-dimensional (3-D) attenuation, collimator-detector response, and scatter effects. With advances in the computer hardware and optimized implementation techniques, quantitatively accurate and high-quality myocardial perfusion SPECT images can be obtained in clinically acceptable processing time. Examples from simulation, phantom, and patient studies are used to demonstrate the various aspects of the investigation. We conclude that quantitative myocardial perfusion SPECT, which holds great promise to improve clinical diagnosis, is an achievable goal in the near future.

Algorithms↗