High-speed quantitative phase and amplitude imaging methods have led to numerous biological discoveries. For general samples, phase retrieval from a single-diffraction pattern has been an algorithmic and experimental challenge. Here we present a quantitative phase and amplitude imaging method applying an efficient support constraint to yield a rapid algorithmic convergence due to the removal of the twin image and spatial shift ambiguities. Compared to previous complex-valued imaging, our method is lenslet-free and relies neither on assumption based on sample sparsity nor interferometric measurements. Our method provides a robust method for imaging in materials and biological science, while its rapid imaging capability will benefit the investigation of dynamical processes.