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Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…
In this work, a method for obtaining pixel-wise error bounds in Bayesian regularization of inverse imaging problems is introduced. The proposed method employs estimates of the posterior variance together with techniques from conformal…
In the practical applications of computed tomography imaging, the projection data may be acquired within a limited-angle range and corrupted by noises due to the limitation of scanning conditions. The noisy incomplete projection data…
Ill-posed imaging inverse problems remain challenging due to the ambiguity in mapping degraded observations to clean images. Diffusion-based generative priors have recently shown promise, but typically rely on computationally intensive…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
This paper addresses the solution of inverse problems in imaging given an additional reference image. We combine a modification of the discrete geodesic path model for image metamorphosis with a variational model,actually the $L^2$-$TV$…
The recent emergence of diffusion models has significantly advanced the precision of learnable priors, presenting innovative avenues for addressing inverse problems. Since inverse problems inherently entail maximum a posteriori estimation,…
Image recovery from compressive measurements requires a signal prior for the images being reconstructed. Recent work has explored the use of deep generative models with low latent dimension as signal priors for such problems. However, their…
This paper presents an uncalibrated deep neural network framework for the photometric stereo problem. For training models to solve the problem, existing neural network-based methods either require exact light directions or ground-truth…
Inverse problems have many applications in science and engineering. In Computer vision, several image restoration tasks such as inpainting, deblurring, and super-resolution can be formally modeled as inverse problems. Recently, methods have…
Generation of photo-realistic images, semantic editing and representation learning are a few of many potential applications of high resolution generative models. Recent progress in GANs have established them as an excellent choice for such…
Image reconstruction is an inverse problem that solves for a computational image based on sampled sensor measurement. Sparsely sampled image reconstruction poses addition challenges due to limited measurements. In this work, we propose an…
A wide range of systems exhibit high dimensional incomplete data. Accurate estimation of the missing data is often desired, and is crucial for many downstream analyses. Many state-of-the-art recovery methods involve supervised learning…
Indirect image registration is a promising technique to improve image reconstruction quality by providing a shape prior for the reconstruction task. In this paper, we propose a novel hybrid method that seeks to reconstruct high quality…
Single-image reflection removal is a highly ill-posed problem, where existing methods struggle to reason about the composition of corrupted regions, causing them to fail at recovery and generalization in the wild. This work reframes an…
This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…
Ill-posed inverse problems are commonplace in biomedical image processing. Their solution typically requires imposing prior knowledge about the latent ground truth. While this regularizes the problem to an extent where it can be solved, it…
We present the first diffusion-based framework that can learn an unknown distribution using only highly-corrupted samples. This problem arises in scientific applications where access to uncorrupted samples is impossible or expensive to…
Limited angle CT reconstruction is an under-determined linear inverse problem that requires appropriate regularization techniques to be solved. In this work we study how pre-trained generative adversarial networks (GANs) can be used to…
Beamforming in ultrasound imaging has significant impact on the quality of the final image, controlling its resolution and contrast. Despite its low spatial resolution and contrast, delay-and-sum is still extensively used nowadays in…