My research lies in the intersection of computational mathematics and data sciences. I focus on signal/image recovery from a limited number of measurements, where ``limited'' refers to the fact that the amount of data that can be taken or transmitted is restricted by technical or economic constraints. In this scenario, additional information and reasonable assumptions are often required to recover useful information from the insufficient amount of data. Over the years, I have developed efficient computational tools for data-driven applications ranging from phase retrieval to hyperspectral imaging and seismic data completion. I specifically focus on exploiting sparsity, low-rankness, and tensor structures to analyze high-dimensional data.