ConvexAD: differentiable phase retrieval with geometric regularization for high-strain, low-signal Bragg coherent diffraction imaging
Bragg Coherent Diffraction Imaging (BCDI) relies on phase retrieval (PR), a non-convex, ill-posed inverse problem whose conditioning is degraded by factors like noise, partial coherence, and strain or crystallographic defects in the imaged nanocrystal. Conventional approaches, including alternating projections and deep learning methods, represent the object on a dense voxel grid, which is prone to amplitude-phase mixing and becomes increasingly ill-posed under these factors, often preventing reliable three-dimensional mapping of the particle's shape and strain. Here we present ConvexAD, a gradient descent PR model that parametrizes the object shape as a convex polyhedron, built by the intersection of half-spaces and enforces flat amplitude within it by construction. This geometric regularization eliminates amplitude-phase mixing and reduces the number of trainable parameters, hence facilitating the convergence of the PR. Implemented in JAX for native GPU acceleration and forward-model flexibility, ConvexAD is validated on simulated and experimental BCDI data, where it outperforms conventional and deep learning assisted PR at high strain, low signal, and reduced coherence, extending the conditions under which quantitative BCDI reconstruction is achievable.