The use of deep learning approaches for image reconstruction is of contemporary interest in radiology, especially for approaches that solve inverse problems associated with imaging. In deployment, these models may be exposed to input distributions that are widely shifted from training data, due in part to data biases or drifts. We propose a metric based on local Lipschitz determined from a single trained model that can be used to estimate the model uncertainty for image reconstructions. We demonstrate a monotonic relationship between the local Lipschitz value and Mean Absolute Error and show that this method can be used to provide a threshold that determines whether a given DL reconstruction approach was well suited to the task. Our uncertainty estimation method can be used to identify out-of-distribution test samples, relate information regarding epistemic uncertainties, and guide proper data augmentation. Quantifying uncertainty of learned reconstruction approaches is especially pertinent to the medical domain where reconstructed images must remain diagnostically accurate.
Image reconstruction plays a critical role in the implementation of all contemporary imaging modalities across the physical and life sciences including optical, MRI, CT, PET, and radio astronomy. During an image acquisition, the sensor encodes an intermediate representation of an object in the sensor domain, which is subsequently reconstructed into an image by an inversion of the encoding function. Image reconstruction is challenging because analytic knowledge of the inverse transform may not exist a priori, especially in the presence of sensor non-idealities and noise. Thus, the standard reconstruction approach involves approximating the inverse function with multiple ad hoc stages in a signal processing chain whose composition depends on the details of each acquisition strategy, and often requires expert parameter tuning to optimize reconstruction performance. We present here a unified framework for image reconstruction, AUtomated TransfOrm by Manifold APproximation (AUTOMAP), which recasts image reconstruction as a data-driven, supervised learning task that allows a mapping between sensor and image domain to emerge from an appropriate corpus of training data. We implement AUTOMAP with a deep neural network and exhibit its flexibility in learning reconstruction transforms for a variety of MRI acquisition strategies, using the same network architecture and hyperparameters. We further demonstrate its efficiency in sparsely representing transforms along low-dimensional manifolds, resulting in superior immunity to noise and reconstruction artifacts compared with conventional handcrafted reconstruction methods. In addition to improving the reconstruction performance of existing acquisition methodologies, we anticipate accelerating the discovery of new acquisition strategies across modalities as the burden of reconstruction becomes lifted by AUTOMAP and learned-reconstruction approaches.