(PRiMA) Phase retrieval in mathematics and applications

In many applications within science and engineering, the phases of the signal measurements are lost in the measurement process or are too noisy to be used for the signal reconstruction. This problem is known as the phase retrieval problem. Even though it has been studied for decades, a significant gap still remains between the assumptions and the models commonly used in theoretical studies and the measurement and reconstruction procedures and limitations arising in applications. The purpose of this workshop is to bring together practitioners in the area of phase retrieval and researchers in mathematical signal processing to address the question:

What are the limitations of the existing phase retrieval methods, and how can we develop a new mathematical toolbox for addressing them and creating more efficient and accurate reconstruction methods?

During the workshop, the participants will use their joint expertise to evaluate the gap between theory and practice in phase retrieval and work towards bridging it by identifying the most important open problems in phaseless reconstruction and ptychography. The following topics will be discussed during the workshop from both applied and theoretical sides:

Topic 1: Obtaining theoretical guarantees for phase retrieval with structured, application-relevant measurements.
Topic 2: Study of the accuracy of the reconstruction methods under different, application-relevant noise models.
Topic 3: Data-driven phase retrieval methods and incorporation of (learned or model-based) priors into reconstruction methods. 
Topic 4: Estimation of the sample properties from phaseless measurements.