Entropy Maximization Algorithm for Positron Emission Tomography

The expectation maximization (EM) algorithm is extensively used for tomographic image reconstruction based on Positron Emission Tomography (PET) modality. The EM algorithm gives good reconstructed images compared to those created by deterministic methods such as Filtered Back Projection (FBP) and Convolution Back projection (CBP). However, the computational complexity of EM-based algorithm is high due to the iterative nature of the algorithm. Prior knowledge of the estimate has been added to the basic EM algorithm to improve image quality as well as to reduce the number of iterations required for an acceptable image quality. We have developed an algorithm which produces better quality images in much lesser number of iterations, thereby speeding up the image reconstruction task. of observing the measured data given the emission parameter A. We have addressed this problem in a much general form via entropy maximization (maximizing the information content) associated with the emission process rather than maximizing the likelihood function. This generalized form enables us to determine the form of prior knowledge about the object being imaged, which is not possible till now by any other means. Once prior knowledge about the object is known, then one can hope to have a reconstructed image of better quality. Section 11 presents the entropy maximization and its relevance to PET. In section III, we bring out the form of the prior distribution. Section lV gives the implementation details. Section V discusses the results from the point of view of both quality of the image and the speed of reconstruction. Section VI concludes the paper.