IBI: Further Software

Further Software

Several software packages developed at our institute are either suitable for both MPI and MRI or neither. These software packages are grouped in different GitHub organizations or under the account of Tobias Knopp.

The packages AbstractImageReconstruction.jl and RegularizedLeastSquares.jl contain code that is used by both MPIReco.jl and MRIReco.jl. The former contains an abstract interface for tomographic image reconstruction algorithms and code that stores and simplifies working with reconstruction algorithm parameters. The latter contains several solvers that can solve large linear systems using regularization techniques and nonlinear problem formulations.

The RedPitayaDAQServer repository contains software for use with RedPitaya's STEMlab 125-14 devices. These devices together with our software allow continuous and parallel generation and acquisition of analog signals with sampling rates up to 15.625 MH/z. In addition, multiple RedPitayas can be synchronized to form a cluster. These clusters are responsible for the analog signal handling in many of our hardware projects.

The Julia package NFFT.jl provides an implementation of the nonequidistant Fast-Fourier Transform, that is completely generic and dimension-agnostic, requiring about two to three times less code than the well-known libraries NFFT3 and FINUFFT while still being one of the fastest NFFT implementations developed to date.

The Julia package SphericalHarmonicExpansions.jl provides methods to numerically handle real spherical harmonic expansions and their coefficients. These methods together with the Julia package MPISphericalHarmonics.jl are used in our magnetic field characterization project to investigate the magnetic fields of MPI devices.

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[183062]

Title: NFFT.jl: Generic and Fast Julia Implementation of the Nonequidistant Fast Fourier Transform.

Written by: T. Knopp, M. Boberg, and M. Grosser

in: <em>SIAM Journal on Scientific Computing</em>. (2023).

Volume: <strong>45</strong>. Number: (3),

on pages: C179-C205

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DOI: 10.1137/22M1510935

URL: https://arxiv.org/abs/2208.00049

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Note: article, opensoftware, openaccess, generalsoftware

Abstract: 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.

Further Software

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