Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional (2D) variant of compressed sensing for multidimensional electronic spectroscopy and apply it to experimental data. For the model system of atomic rubidium vapor, we find that compressed sensing provides significantly better resolution of 2D spectra than a conventional discrete Fourier transform from the same experimental data. We believe that by combining powerful resolution with ease of use, compressed sensing can be a powerful tool for the analysis and interpretation of ultrafast spectroscopy data.
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