Retrospective correction of Rigid and Non-Rigid MR motion artifacts using GANs

Motion artifacts are a primary source of magnetic resonance (MR) image quality deterioration with strong repercussions on diagnostic performance. Currently, MR motion correction is carried out either prospectively, with the help of motion tracking systems, or retrospectively by mainly utilizing computationally expensive iterative algorithms. In this paper, we utilize a new adversarial framework, titled MedGAN, for the joint retrospective correction of rigid and non-rigid motion artifacts in different body regions and without the need for a reference image. MedGAN utilizes a unique combination of non-adversarial losses and a new generator architecture to capture the textures and fine-detailed structures of the desired artifact-free MR images. Quantitative and qualitative comparisons with other adversarial techniques have illustrated the proposed model performance.Comment: 5 pages, 2 figures, under review for the IEEE International Symposium for Biomedical Image

G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Ito's type

We introduce a notion of nonlinear expectation --G--expectation-- generated by a nonlinear heat equation with infinitesimal generator G. We first discuss the notion of G-standard normal distribution. With this nonlinear distribution we can introduce our G-expectation under which the canonical process is a G--Brownian motion. We then establish the related stochastic calculus, especially stochastic integrals of Ito's type with respect to our G--Brownian motion and derive the related Ito's formula. We have also give the existence and uniqueness of stochastic differential equation under our G-expectation. As compared with our previous framework of g-expectations, the theory of G-expectation is intrinsic in the sense that it is not based on a given (linear) probability space.Comment: Submited to Proceedings Abel Symposium 2005, Dedicated to Professor Kiyosi Ito for His 90th Birthda

Classical and quantum q-deformed physical systems

On the basis of the non-commutative q-calculus, we investigate a q-deformation of the classical Poisson bracket in order to formulate a generalized q-deformed dynamics in the classical regime. The obtained q-deformed Poisson bracket appears invariant under the action of the q-symplectic group of transformations. In this framework we introduce the q-deformed Hamilton's equations and we derive the evolution equation for some simple q-deformed mechanical systems governed by a scalar potential dependent only on the coordinate variable. It appears that the q-deformed Hamiltonian, which is the generator of the equation of motion, is generally not conserved in time but, in correspondence, a new constant of motion is generated. Finally, by following the standard canonical quantization rule, we compare the well known q-deformed Heisenberg algebra with the algebra generated by the q-deformed Poisson bracket.Comment: 9 pages, accepted for publication in "The European Physical Journal C

Microscopic Transport Theory of Nuclear Processes

We formulate a microscopic theory of the decay of a compound nucleus through fission which generalizes earlier microscopic approaches of fission dynamics performed in the framework of the adiabatic hypothesis. It is based on the constrained Hartree-Fock-Bogoliubov procedure and the Generator Coordinate Method, and requires an effective nucleon-nucleon interaction as the only input quantity. The basic assumption is that the slow evolution of the nuclear shape must be treated explicitely, whereas the rapidly time-dependent intrinsic excitations can be treated by statistical approximations. More precisely, we introduce a reference density which represents the slow evolution of the nuclear shape by a reduced density matrix and the state of intrinsic excitations by a canonical distribution at each given shape of the nucleus. The shape of the nuclear density distribution is described by parameters ("generator coordinates"), not by "superabundant" degrees of freedom introduced in addition to the complete set of nucleonic degrees of freedom. We first derive a rigorous equation of motion for the reference density and, subsequently, simplify this equation on the basis of the Markov approximation. The temperature which appears in the canonical distribution is determined by the requirement that, at each time t, the reference density should correctly reproduce the mean excitation energy at given values of the shape parameters. The resulting equation for the "local" temperature must be solved together with the equations of motion obtained for the reduced density matrix.Comment: 33 pages, accepted in Nucl. Phys.

Continuous Facial Motion Deblurring

We introduce a novel framework for continuous facial motion deblurring that restores the continuous sharp moment latent in a single motion-blurred face image via a moment control factor. Although a motion-blurred image is the accumulated signal of continuous sharp moments during the exposure time, most existing single image deblurring approaches aim to restore a fixed number of frames using multiple networks and training stages. To address this problem, we propose a continuous facial motion deblurring network based on GAN (CFMD-GAN), which is a novel framework for restoring the continuous moment latent in a single motion-blurred face image with a single network and a single training stage. To stabilize the network training, we train the generator to restore continuous moments in the order determined by our facial motion-based reordering process (FMR) utilizing domain-specific knowledge of the face. Moreover, we propose an auxiliary regressor that helps our generator produce more accurate images by estimating continuous sharp moments. Furthermore, we introduce a control-adaptive (ContAda) block that performs spatially deformable convolution and channel-wise attention as a function of the control factor. Extensive experiments on the 300VW datasets demonstrate that the proposed framework generates a various number of continuous output frames by varying the moment control factor. Compared with the recent single-to-single image deblurring networks trained with the same 300VW training set, the proposed method show the superior performance in restoring the central sharp frame in terms of perceptual metrics, including LPIPS, FID and Arcface identity distance. The proposed method outperforms the existing single-to-video deblurring method for both qualitative and quantitative comparisons

Geometrical and physical interpretation of evolution governed by general complex algebra

AbstractIn this paper we explore a geometrical and physical matter of the evolution governed by the generator of General Complex Algebra, GC2. The generator of this algebra obeys a quadratic polynomial equation. It is shown that the geometrical image of the GC2-number is given by a straight line fixed by two given points on Euclidean plane. In this representation the straight line possesses the norm and the argument. The motion of the straight line conserving the norm of the line is described by evolution equation governed by the generator of the GC2-algebra. This evolution is depicted on the Euclidean plane as rotational motion of the straight line around the semicircle to which this line is tangent. Physical interpretation is found within the framework of the relativistic dynamics where the quadratic polynomial is formed by mass-shell equation. In this way we come to a new representation for the momenta of the relativistic particle