  We present energy-resolved photoelectron momentum maps for orbital tomography
that have been collected with a novel and efficient time-of-flight momentum
microscopy setup. This setup is combined with a 0.5 MHz table-top femtosecond
extreme-ultraviolet light source, which enables unprecedented speed in data
collection and paves the way towards time-resolved orbital imaging experiments
in the future. Moreover, we take a significant step forward in the data
analysis procedure for orbital imaging, and present a sparsity-driven approach
to the required phase retrieval problem, which uses only the number of non-zero
pixels in the orbital. Here, no knowledge of the object support is required,
and the sparsity number can easily be determined from the measured data. Used
in the relaxed averaged alternating reflections algorithm, this sparsity
constraint enables fast and reliable phase retrieval for our experimental as
well as noise-free and noisy simulated photoelectron momentum map data.
