Titel Deelnemers "Decomposition algebras and axial algebras" "Tom De Medts, Simon F. Peacock, Sergey Shpectorov, Michiel Van Couwenberghe" "Decomposition algebras and axial algebras" "Michiel Van Couwenberghe" "Modules over axial algebras" "Tom De Medts, Michiel Van Couwenberghe" "Non-associative Frobenius algebras for simply laced Chevalley groups" "Tom De Medts, Michiel Van Couwenberghe" "Spatially Variant Ultrasound Attenuation Mapping using a Regularized Linear Least-Squares Approach" "Jan D'hooge, Alexander Bertrand" "Quantitative ultrasound methods aim to estimate the acoustic properties of the underlying medium, such as the attenuation and backscatter coefficients, and have applications in various areas including tissue characterization. In practice, tissue heterogeneity makes the coefficient estimation challenging. In this work, we propose a computationally efficient algorithm to map spatial variations of the attenuation coefficient. Our proposed approach adopts a fast, linear least-squares strategy to fit the signal model to data from pulse-echo measurements. As opposed to existing approaches, we directly estimate the attenuation map, that is, the local attenuation coefficient at each axial location by solving a joint estimation problem. In particular, we impose a physical model that couples all these local estimates and combine it with a smooth regularization to obtain a smooth map. Compared to the conventional spectral log difference method and the more recent ALGEBRA approach, we demonstrate that the attenuation estimates obtained by our method are more accurate and better correlate with the ground-truth attenuation profiles over a wide range of spatial and contrast resolutions." "The cylindrical Fourier transform" "Fred Brackx, Nele De Schepper, Franciscus Sommen" "In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that fixed vector. For this Fourier kernel we now substitute a new Clifford-Fourier kernel such that, again for a fixed vector in the image space, its phase is constant on co-axial cylinders w.r.t. that fixed vector. The point is that when restricting to dimension two this new cylindrical Fourier transform coincides with the earlier introduced Clifford-Fourier transform.We are now faced with the following situation: in dimension greater than two we have a first Clifford-Fourier transform with elegant properties but no kernel in closed form, and a second cylindrical one with a kernel in closed form but more complicated calculation formulae. In dimension two both transforms coincide. The paper concludes with the calculation of the cylindrical Fourier spectrum of an L2-basis consisting of generalized Clifford-Hermite functions."