Abstract: Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. I will first talk about a multigrid-based optimization framework we proposed to reduce the computational burdens of large-scale ptychographic reconstruction, by exploiting the hierarchy in the data and sample domain. I will also discuss some ongoing work by examining the ptychography problem from a stochastic perspective.