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1

A L 1 Minimization Strategy for Robust Joint Activity and Attenuation Estimation in Positron Emission Tomography

Presotto Luca

Fundamenta Informaticae

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2020

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Vol. 172, nr 2

187--202

EN

Positron Emission Tomography image reconstruction needs a map of photon attenuation probability to provide the correct solution. This map is generally provided by an independent imaging modality. However, it might suffer for artifacts due to patient motion in sequential systems or from intrinsic limitation of the second modality (e.g.: bones that cannot be identified in MR images). It has been shown that such map can be estimated from the PET data themselves, but the solution to this problem has much worse conditioning than the tomographic problem. In this work we propose a new algorithm based on the use of multiple L1 regularization terms in the attenuation sub-problem, to incorporate prior knowledge. We also chose optimal maximizers for both sub-problems: preconditioned gradient descent for the emission one and split-Bregman for the attenuation one. The algorithm was then tested using digital phantom simulations. The proposed algorithm proved to provide accurate quantification over a large range of strength of the regularization terms. The algorithm is also able to reconstruct objects outside of the region where the problem is uniquely determined and it is able to fix the undetermined global scaling factor of joint attenuation and emission estimation. Thanks to the maximizers chosen, the algorithm is computationally less expensive than the current standard.

2

New estimate for the curvature of an order-convex set and related questions

Ramazanov Ali B.

Control and Cybernetics

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2020

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Vol. 49, No. 2

233--240

EN

It is well known that in discrete optimization problems, gradient (local) algorithms do not always guarantee an optimal solution. Therefore, the problem arises of finding the accuracy of the gradient algorithm. This is a fairly well-known problem and numerous publications have been devoted to it. In establishing accuracy, various approaches are used. One of these approaches is to obtain guaranteed estimates of the accuracy of the gradient algorithm in terms of the curvature of the admissible domain. With this approach, it is required to find the curvatures of the admissible region. Since finding the exact value of curvature is a difficult problem to solve, curvature estimates in terms of more or less simply calculated parameters of the problem are relevant. A new improved bound for the curvature of an order-convex set is found and is presented in this paper in terms of the steepness and parameters of strict convexity of the function.

3

Rotundity, smoothness and duality

Penot J.-P.

Control and Cybernetics

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2003

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Vol. 32, no 4

711-733

EN

The duality between smoothness and rotundity of functions is studied in a nonlinear abstract framework. Here smoothness is enlarged to subdifferentiability properties and rotundity is formulated by means of approximation properties.

4

Koherentna analiza korelacyjna niestacjonarnych sygnałów zmodulowanych

Jaworski I., Zakrzewski Z.

Kwartalnik Elektroniki i Telekomunikacji

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2000

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Vol. 46, nr 3

355-400

PL

Omówiono koherentną metodę estymacji charakterystyk niestacjonarnych sygnałów zmodulowanych. Rozpatrzono własności estymatorów wartości oczekiwanej, funkcji autokorelacji i ich komponentów Fouriera, które zostały obliczone na podstawie uśrednienia próbek co okres korelowania realizacji pojedyńczej. Zostały wprowadzone wyrażenia asymptotyczne na obciążenia i wariancje estymatorów. Otrzymano zależności charakterystyk sygnałów amplitudowo i fazowo zmodulowanych.

EN

oherentr estimation method of nonstationary modulated signals is considered. The properties of the estimates of mean, correlation function and Fourier components was analysed. The formulas for biases variances of estimates was received.