Mission Statement

The Institute for Biomedical Imaging (IBI) was founded in 2014 by Tobias Knopp and is a joint research department of the University Medical Center Hamburg-Eppendorf (UKE) and the Hamburg University of Technology (TUHH). Medical imaging is the non-invasive imaging of sections of the human body and plays an important role in the diagnosis, treatment and post-treatment of diseases. Effective, safe and high quality imaging is essential for many medical decisions and can prevent unnecessary medical procedures. Our research interests lie in the field of tomographic imaging, with a focus on Magnetic Resonance Imaging (MRI) and the young imaging technique Magnetic Particle Imaging (MPI).  In particular, we are working on the hardware development of MPI systems, the research of new signal processing, image reconstruction and image processing algorithms, and the evaluation of medical applicability. In close cooperation with our clinical partners at the UKE, we also conduct translational research with the goal of bringing state-of-the-art acquisition and reconstruction methods into clinical routine.

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Paper published in SIAM J. SCI. COMPUT.

Our paper "NFFT.jl: Generic and Fast Julia Implementation of the Nonequidistant Fast Fourier Transform" has been published in SIAM Journal on Scientific Computing.

The nonequidistant fast Fourier transform (NFFT) is an extension of the famous fast Fourier transform (FFT) that can be applied to nonequidistantly sampled data in time/space or frequency domain. It is an approximative algorithm that allows one to control the approximation error in such a way that machine precision is reached while keeping the algorithmic complexity in the same order as a regular FFT. The NFFT plays a major role in many signal processing applications and has been intensively studied from a theoretical and computational perspective. The fastest CPU implementations of the NFFT are implemented in the low-level programming languages C and C++ and require a compromise between code generalizability, code readability, and code efficiency. The programming language Julia promises new opportunities in optimizing these three conflicting goals. In this work we show that Julia indeed allows one to develop an NFFT implementation which is completely generic and dimension-agnostic and requires about two to three times less code than the other famous libraries NFFT3 and FINUFFT while still being one of the fastest NFFT implementations developed to date.

The entire methodology is described in the paper "NFFT.jl: Generic and Fast Julia Implementation of the Nonequidistant Fast Fourier Transform" by Tobias Knopp, Marija Boberg, and Mirco Grosser, which you can find here. The Julia package NFFT.jl is available on GitHub.