PROJECTED MULTI-AGENT CONSENSUS EQUILIBRIUM (PMACE) FOR DISTRIBUTED RECONSTRUCTION WITH APPLICATION TO PTYCHOGRAPHY

Multi-Agent Consensus Equilibrium (MACE) formulates an inverse imaging problem as a balance among multiple update agents such as data-fitting terms and denoisers. However, each such agent operates on a separate copy of the full image, leading to redundant memory use and slow convergence when each agent affects only a small subset of the full image.

In this dissertation, we extend MACE to Projected Multi-Agent Consensus Equilibrium (PMACE), in which each agent updates only a projected component of the full image, thus greatly reducing memory use for some applications. We describe PMACE in terms of an equilibrium problem and an equivalent fixed point problem and show that in most cases the PMACE equilibrium is not the solution of an optimization problem.

To demonstrate the value of PMACE, we apply it to the problem of ptychography, a technique for reconstructing a sample from diffraction patterns generated by coherent X-ray illumination at overlapping spots. In our PMACE formulation, each spot corresponds to a separate data-fitting agent, with the final solution found as an equilibrium among all the agents. The resulting PMACE reconstruction algorithm generates more accurate reconstructions at a lower computational cost than existing ptychography algorithms, especially when the spots are sparsely sampled.

Additionally, we extend PMACE for blind ptychographic reconstruction to address challenges posed by unknown and partially coherent illumination probes. Our approach jointly estimates the complex transmittance image and probe functions, enabling localized probe refinement and supporting dynamic integration of additional probe modes. Our approach offers a robust and computationally efficient solution for ptychographic reconstruction, effectively estimating both object transmittance and probe functions within a unified framework.

Through experimental simulations and validations using both synthetic and real measurements, we demonstrate that our method consistently outperforms existing approaches in terms of reconstruction quality and convergence rate.