# Spurious minimizers in non uniform Fourier sampling optimization

arXiv: https://arxiv.org/abs/2207.10323 · HTML: https://mlsanity.com/paper/2207.10323/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jul 2022.

## Built on by (most cited first, 2 of 2)

- [Artificial Intelligence for Neuro MRI Acquisition: A Review](https://mlsanity.com/paper/2406.05982/) (2024)
- [Unsupervised Complex Semi-Binary Matrix Factorization for Activation Sequence Recovery of Quasi-Stationary Sources](https://mlsanity.com/paper/2310.02295/) (2023)

## Abstract (arXiv)

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 first effect and illustrate experimentally the benefits of using stochastic gradient algorithms with a variable metric.