Optimizing sparse sampling for 2D electronic spectroscopy.

We present a new data acquisition concept using optimized non-uniform sampling and compressed sensing reconstruction in order to substantially decrease the acquisition times in action-based multidimensional electronic spectroscopy. For this we acquire a regularly sampled reference data set at a fixed population time and use a genetic algorithm to optimize a reduced non-uniform sampling pattern. We then apply the optimal sampling for data acquisition at all other population times. Furthermore, we show how to transform two-dimensional (2D) spectra into a joint 4D time-frequency von Neumann representation. This leads to increased sparsity compared to the Fourier domain and to improved reconstruction. We demonstrate this approach by recovering transient dynamics in the 2D spectrum of a cresyl violet sample using just 25% of the originally sampled data points.