Dynamic mode decomposition (DMD) is a popular approach to analyzing and modeling fluid flows. In practice, datasets are almost always corrupted to some degree by noise. The vanilla DMD is highly noise-sensitive, which is why many algorithmic extensions for improved robustness exist. We introduce a flexible optimization approach that merges available ideas for improved accuracy and robustness. The approach simultaneously identifies coherent dynamics and noise in the data. In tests on the laminar flow past a cylinder, the method displays strong noise robustness and high levels of accuracy.