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Deep neural networks for medical image reconstruction are traditionally trained using high-quality ground-truth images as training targets. Recent work on Noise2Noise (N2N) has shown the potential of using multiple noisy measurements of the same object as an alternative to having a ground-truth. However, existing N2N-based methods are not suitable for learning from the measurements of an object undergoing nonrigid deformation. This paper addresses this issue by proposing the deformation-compensated learning (DeCoLearn) method for training deep reconstruction networks by compensating for object deformations. A key component of DeCoLearn is a deep registration module, which is jointly trained with the deep reconstruction network without any ground-truth supervision. We validate DeCoLearn on both simulated and experimentally collected magnetic resonance imaging (MRI) data and show that it significantly improves imaging quality.

Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is used to account for multiple scattering and regularization is used to enforce prior constraints on the object. In this paper, we propose a powerful alternative to this optimization-based view of image reconstruction by designing and training a deep convolutional neural network that can invert multiple scattered measurements to produce a high-quality image of the refractive index. Our results on both simulated and experimental datasets show that the proposed approach is substantially faster and achieves higher imaging quality compared to the state-of-the-art methods based on optimization.

Multi-modal sensing is increasingly becoming important in a number of applications, providing new capabilities and processing challenges. In this paper, we explore the benefit of combining a low-resolution depth sensor with a high-resolution optical video sensor, in order to provide a high-resolution depth map of the scene. We propose a new formulation that is able to incorporate temporal information and exploit the motion of objects in the video to significantly improve the results over existing methods. In particular, our approach exploits the space-time redundancy in the depth and intensity using motion-adaptive low-rank regularization. We provide experiments to validate our approach and confirm that the quality of the estimated high-resolution depth is improved substantially. Our approach can be a first component in systems using vision techniques that rely on high-resolution depth information.

Total variation (TV) is a one of the most popular regularizers for stabilizing the solution of ill-posed inverse problems. This paper proposes a novel proximal-gradient algorithm for minimizing TV regularized least-squares cost functionals. Unlike traditional methods that require nested iterations for computing the proximal step of TV, our algorithm approximates the latter with several simple proximals that have closed form solutions. We theoretically prove that the proposed parallel proximal method achieves the TV solution with arbitrarily high precision at a global rate of converge that is equivalent to the fast proximal-gradient methods. The results in this paper have the potential to enhance the applicability of TV for solving very large-scale imaging inverse problems.

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies continuous-domain signals as solutions of linear stochastic differential equations. Accordingly, we show that the class of admissible priors for the discretized version of the signal is confined to the family of infinitely divisible distributions. Our estimators not only cover the well-studied methods of Tikhonov and l1-type regularizations as particular cases, but also open the door to a broader class of sparsity-promoting regularization schemes that are typically nonconvex. We provide an algorithm that handles the corresponding nonconvex problems and illustrate the use of our formalism by applying it to deconvolution, magnetic resonance imaging, and X-ray tomographic reconstruction problems. Finally, we compare the performance of estimators associated with models of increasing sparsity.