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The proximal gradient algorithm for minimizing the sum of a smooth and a nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may…

Effective image deblurring typically relies on large and fully paired datasets of blurred and corresponding sharp images. However, obtaining such accurately aligned data in the real world poses a number of difficulties, limiting the…

This paper presents a simple and effective visual prompting method for adapting pre-trained models to downstream recognition tasks. Our method includes two key designs. First, rather than directly adding together the prompt and the image,…

Blind image deblurring is a challenging low-level vision task that involves estimating the unblurred image when the blur kernel is unknown. In this paper, we present a self-supervised multi-scale blind image deblurring method to jointly…

Primal-Dual Hybrid Gradient (PDHG) and Alternating Direction Method of Multipliers (ADMM) are two widely-used first-order optimization methods. They reduce a difficult problem to simple subproblems, so they are easy to implement and have…

The data consistency for the physical forward model is crucial in inverse problems, especially in MR imaging reconstruction. The standard way is to unroll an iterative algorithm into a neural network with a forward model embedded. The…

Conditional diffusion probabilistic models can model the distribution of natural images and can generate diverse and realistic samples based on given conditions. However, oftentimes their results can be unrealistic with observable color…

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…

Motion blur is a fundamental problem in computer vision as it impacts image quality and hinders inference. Traditional deblurring algorithms leverage the physics of the image formation model and use hand-crafted priors: they usually produce…

Neural networks have become a prominent approach to solve inverse problems in recent years. Amongst the different existing methods, the Deep Image/Inverse Priors (DIPs) technique is an unsupervised approach that optimizes a highly…

This paper proposes a novel approach to image deblurring and digital zooming using sparse local models of image appearance. These models, where small image patches are represented as linear combinations of a few elements drawn from some…

Many application domains, spanning from computational photography to medical imaging, require recovery of high-fidelity images from noisy, incomplete or partial/compressed measurements. State of the art methods for solving these inverse…

In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…

Deep neural networks have been applied successfully to a wide variety of inverse problems arising in computational imaging. These networks are typically trained using a forward model that describes the measurement process to be inverted,…

In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…

Non-convex gradient descent is a common approach for estimating a low-rank $n\times n$ ground truth matrix from noisy measurements, because it has per-iteration costs as low as $O(n)$ time, and is in theory capable of converging to a…

Variational regularization models are one of the popular and efficient approaches for image restoration. The regularization functional in the model carries prior knowledge about the image to be restored. The prior knowledge, in particular…

Most image deblurring methods assume an over-simplistic image formation model and as a result are sensitive to more realistic image degradations. We propose a novel variational framework, that explicitly handles pixel saturation, noise,…

Training deep neural networks has become a common approach for addressing image restoration problems. An alternative for training a "task-specific" network for each observation model is to use pretrained deep denoisers for imposing only the…

We present a practical implementation of an optimal first-order method, due to Nesterov, for large-scale total variation regularization in tomographic reconstruction, image deblurring, etc. The algorithm applies to $\mu$-strongly convex…