Compressed Sensing for Reconstructing Coherent Multidimensional Spectra

TL;DR

This paper demonstrates that sparse reconstruction techniques, LASSO and SEMA, can effectively reconstruct multidimensional spectra from significantly less data, with SEMA offering superior accuracy and efficiency.

Contribution

The study introduces the application of LASSO and SEMA to 2D spectroscopy, highlighting SEMA's advantages in accuracy and computational efficiency over LASSO.

Findings

Both methods reconstruct spectra with less data than Fourier-based methods.

SEMA outperforms LASSO in spectral line width and position accuracy.

SEMA enables off-grid component analysis, reducing computational complexity.

Abstract

We apply two sparse reconstruction techniques, the least absolute shrinkage and selection operator (LASSO) and the sparse exponential mode analysis (SEMA), to two-dimensional (2D) spectroscopy. The algorithms are first tested on model data, showing that both are able to reconstruct the spectra using only a fraction of the data required by the traditional Fourier-based estimator. Through the analysis of a sparsely sampled experimental fluorescence detected 2D spectra of LH2 complexes, we conclude that both SEMA and LASSO can be used to significantly reduce the required data, still allowing to reconstruct the multidimensional spectra. Of the two techniques, it is shown that SEMA offers preferable performance, providing more accurate estimation of the spectral line widths and their positions. Furthermore, SEMA allows for off-grid components, enabling the use of a much smaller dictionary than the LASSO, thereby improving both the performance and lowering the computational complexity for reconstructing coherent multidimensional spectra.