Spurious minimizers in non uniform Fourier sampling optimization. (1st October 2022)

• Record Type: Journal Article
• Authors: Gossard, Alban; de Gournay, Frédéric; Weiss, Pierre
• Is Part Of: Inverse problems. Volume 38:Number 10(2022)
• Publication Date: 2022-10-01
• Subjects: spurious minimizers -- non-uniform Fourier transform -- data-driven optimization -- MRI reconstruction -- Fourier sampling; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac86c1
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing optimal non Cartesian Fourier sampling patterns is a difficult nonconvex problem by bringing to light two optimization issues. The first one is the existence of a combinatorial number of spurious minimizers for a generic class of signals. The second one is a vanishing gradient effect for the high frequencies. We conclude the paper by showing how using large datasets can mitigate the first effect and illustrate experimentally the benefits of using stochastic gradient algorithms with a variable metric.