Signal retrieval from a series of indirect measurements is a common task in many imaging, metrology and characterization platforms in science and engineering. Because most of the indirect measurement processes are well-described by physical models, signal retrieval can be solved with an iterative optimization that enforces measurement consistency and prior knowledge on the signal. These iterative processes are time-consuming and only accommodate a linear measurement process and convex signal constraints. Recently, neural networks have been widely adopted to supersede iterative signal retrieval methods by approximating the inverse mapping of the measurement model. However, networks with deterministic processes have failed to distinguish signal ambiguities in an ill-posed measurement system, and retrieved signals often lack consistency with the measurement. In this work we introduce a variational generative model to capture the distribution of all possible signals, given a particular measurement. By exploiting the known measurement model in the variational generative framework, our signal retrieval process resolves the ambiguity in the forward process, and learns to retrieve signals that satisfy the measurement with high fidelity in a variety of linear and nonlinear ill-posed systems, including ultrafast pulse retrieval, coded aperture compressive video sensing and image retrieval from Fresnel hologram.
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