A Penalized-Likelihood Image Reconstruction Method for Emission Tomography, Compared to Postsmoothed Maximum-Likelihood With Matched Spatial Resolution

Regularization is desirable for image reconstruction in emission tomography. A powerful regularization method is the penalized-likelihood (PL) reconstruction algorithm (or equivalently, maximum a posteriori reconstruction), where the sum of the likelihood and a noise suppressing penalty term (or Bayesian prior) is optimized. Usually, this approach yields position-dependent resolution and bias. However, for some applications in emission tomography, a shift-invariant point spread function would be advantageous. Recently, a new method has been proposed, in which the penalty term is tuned in every pixel to impose a uniform local impulse response. In this paper, an alternative way to tune the penalty term is presented. We performed positron emission tomography and single photon emission computed tomography simulations to compare the performance of the new method to that of the postsmoothed maximum-likelihood (ML) approach, using the impulse response of the former method as the postsmoothing filter for the latter. For this experiment, the noise properties of the PL algorithm were not superior to those of postsmoothed ML reconstruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85948/1/Fessler65.pd

Comparison between post-smoothed maximum-likelihood and penalized-likelihood for image reconstruction with uniform spatial resolution

Regularization is desirable for image reconstruction in emission tomography. One of the most powerful regularization techniques is the penalized-likelihood reconstruction algorithm (or equivalently, maximum-a-posteriori reconstruction), where the sum of the likelihood and a noise suppressing penalty term (or Bayesian prior) is optimized. Usually, this approach yields position dependent resolution and bias. However, for some applications in emission tomography, a shift invariant point spread function would be advantageous. Recently, a new method has been proposed, in which the penalty term is tuned in every pixel in order to impose a uniform local impulse response. In this paper, an alternative way to tune the penalty term is presented. The performance of the new method is compared to that of the post-smoothed maximum-likelihood approach, using the impulse response of the former method as the post-smoothing filter for the latter. For this experiment, the noise properties of the penalized-likelihood algorithm were not superior to those of post-smoothed maximum-likelihood reconstruction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85974/1/Fessler179.pd

Kaluza-Klein towers for spinors in warped spaces

All the boundary conditions compatible with the reduction of a five dimensional spinor field of bulk mass $M$ in a compactified warped space to a four dimensional brane are derived from the hermiticity conditions of the relevant operator. The possible presence of metric singularities is taken into account. Examples of resulting Kaluza-Klein spinor towers are given for a representative set of values for the basic parameters of the model and of the parameters describing the allowed boundary conditions, within the hypothesis that there exists one-mass-scale-only, the Planck mass. In many cases, the lowest mass in the tower is small and very sensitive to the parameters while the other masses are much higher and become more regularly spaced. In these cases, if a basic fermion of the standard model (lepton or quark) happens to be the lowest mass of a Kaluza-Klein tower, the other masses would be much larger and weakly dependent on the fermion which defines the tower.Comment: 39 page

Multi-operator brackets acting thrice

We generalize an identity, first found by Bremner, for the action of three nested Nambu brackets.Comment: Added references and detailed proof of main result, conforming to journal versio

811-1 Evolution of Left Ventricular Function, Myocardial Perfusion and Metabolism in Infarct Patients After Coronary Thrombolysis

Follow-up of regional myocardial blood flow, metabolism and function was studied in a population of thrombolysed patients. Fifty one patients with an acute myocardial infarction were prospectively enrolled. All patients received thrombolytic therapy within 6 hours after the onset of symptoms. Coronary angiography, 2D-echocardiography and 13NH3/18FDG PET were performed 5 days after the acute event. Three months after the infarction, 2D-echocardiography and 13NH3/18FDG PET studies were repeated.Thirty six patients (62% with TIMI III, 7% with TIMI II) revealed a concordant decrease of flow and metabolism in the infarct area (PET match). Fifteen patients (33% with TIMI III, 13% with TIMI II) revealed a decrease of flow with preservation of metabolism (PET mismatch). Twelve patients received further treatment (PTCA or CAGB) after the first PET scan. Myocardial blood flow improved significantly in both match (71±17ml/min/l00g at 3 months versus 60±17ml/min/100 g at 5 days, p<0.01) and mismatch groups (71±26ml/min/l00 g at 3 months versus 63 ±18ml/min/100 g at 5 days, p<0.05). Blood flow in remote areas did not change significantly (84±18mllmin/l 00 g at 3 months versus 82±19ml/min/l 00 gat 5 days, p=NS). In 4 patients with a match pattern at 5 days, a mismatch pattern had developed 3 months after the acute event.Functional follow-up was performed in 30 patients, 23 with a match pattern and 7 with a mismatch pattern. A variable outcome was observed: In 3 out of 7 mismatch areas contractility did not improve. On the contrary, 9 out of 23 match areas revealed functional improvement.It can be concluded that in this population of early thrombolysed patients, few mismatches were observed (29%). Flow values improved significantly in both match and mismatch groups 3 months after the acute event. In some patients, a mismatch pattern was found after 3 months, suggesting the need for further treatment. Functional outcome was variable, probably due to a variety of pathophysiologic processes such as stunning shortly after reperfusion with functional improvement after 3 months, reocclusion or progression of coronary artery disease resulting in reinfarction or hibernation