Acceleration of maximum likelihood reconstruction, using frequency amplification and attenuation compensation

A general class of preconditioners for statistical iterative reconstruction of emission computed tomography

A major drawback of statistical iterative image reconstruction for emission computed tomography is its high computational cost. The ill-posed nature of tomography leads to slow convergence for standard gradient-based iterative approaches such as the steepest descent or the conjugate gradient algorithm. In this paper new theory and methods for a class of preconditioners are developed for accelerating the convergence rate of iterative reconstruction. To demonstrate the potential of this class of preconditioners, a preconditioned conjugate gradient (PCG) iterative algorithm for weighted least squares reconstruction (WLS) was formulated for emission tomography. Using simulated positron emission tomography (PET) data of the Hoffman brain phantom, it was shown that the convergence rate of the PCG can reduce the number of iterations of the standard conjugate gradient algorithm by a factor of 2-8 times depending on the convergence criterion.

A non-negative fast multiplicative algorithm in 3D scatter-compensated SPET reconstruction

Single-photon emission tomographic (SPET) reconstruction can be improved, especially for noisy images, by using the iterative expectation-maximization of the maximum-likelihood (EM-ML) algorithm. Its application to clinical routine is, however, hampered by the high number of iterations necessary to achieve acceptable results. Therefore various methods have been developed to accelerate the EM-ML algorithm. In this paper a new accelerated EM-ML-like multiplicative algorithm is proposed for SPET reconstruction. Contrary to some other accelerating methods, it preserves two of the most important properties of the EM-ML, namely pixel positivity inside the patient body and null activity outside. The convergence speed is improved by a factor which can reach 100 in high spatial frequency or low count regions. Good estimates in the low count region are obtained without any smoothing, even at typical routine clinical count rates. The algorithm used in conjunction with the 3D effective one scatter path model provides high-quality SPET images and accurate quantitation.

The approximate inverse and conjugate gradient: non-symmetrical algorithms for fast attenuation correction in SPECT

Hybrid methods have been known for a long time as very efficient algorithms for attenuation correction in single-photon emission computed tomography, but only recently have efforts been made to formulate them with more rigorous mathematics. This has allowed us to explain their efficiency in terms of approximate inversion, and to establish a convergence condition. The present study focuses on the convergence problem and emphasizes the question of symmetry. Hybrid method operators are not symmetrical; therefore the convergence condition is not easily verified. New schemes based on a modified conjugate gradient method are presented. Convergence is proved and performances are shown to be at least as good as the standard hybrid schemes on perfect and noisy simulated data.