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Unpaired image denoising has achieved promising development over the last few years. Regardless of the performance, methods tend to heavily rely on underlying noise properties or any assumption which is not always practical. Alternatively,…

Neural networks have shown tremendous potential for reconstructing high-resolution images in inverse problems. The non-convex and opaque nature of neural networks, however, hinders their utility in sensitive applications such as medical…

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Discrete inverse problems correspond to solving a system of equations in a stable way with respect to noise in the data. A typical approach to enforce uniqueness and select a meaningful solution is to introduce a regularizer. While for most…

Deep learning had already demonstrated its power in medical images, including denoising, classification, segmentation, etc. All these applications are proposed to automatically analyze medical images beforehand, which brings more…

Low rank regularization, in essence, involves introducing a low rank or approximately low rank assumption for matrix we aim to learn, which has achieved great success in many fields including machine learning, data mining and computer…

Near-infrared imaging can capture haze-free near-infrared gray images and visible color images, according to physical scattering models, e.g., Rayleigh or Mie models. However, there exist serious discrepancies in brightness and image…

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…

Regularization-based image restoration has remained an active research topic in computer vision and image processing. It often leverages a guidance signal captured in different fields as an additional cue. In this work, we present a general…

We study the 2-D super-resolution multi-reference alignment (SR-MRA) problem: estimating an image from its down-sampled, circularly-translated, and noisy copies. The SR-MRA problem serves as a mathematical abstraction of the structure…

This paper proposes a novel method for automatic MRI denoising that exploits last advances in deep learning feature regression and self-similarity properties of the MR images. The proposed method is a two-stage approach. In the first stage,…

The denoising of magnetic resonance (MR) images is a task of great importance for improving the acquired image quality. Many methods have been proposed in the literature to retrieve noise free images with good performances. Howerever, the…

Artificial neural networks perform state-of-the-art in an ever-growing number of tasks, and nowadays they are used to solve an incredibly large variety of tasks. There are problems, like the presence of biases in the training data, which…

Image denoising is an essential tool in computational photography. Standard denoising techniques, which use deep neural networks at their core, require pairs of clean and noisy images for its training. If we do not possess the clean…

Deep neural networks have been proved efficient for medical image denoising. Current training methods require both noisy and clean images. However, clean images cannot be acquired for many practical medical applications due to naturally…

Learning-based image reconstruction models, such as those based on the U-Net, require a large set of labeled images if good generalization is to be guaranteed. In some imaging domains, however, labeled data with pixel- or voxel-level label…

The recent development of diffusion models has led to significant progress in solving inverse problems by leveraging these models as powerful generative priors. However, challenges persist due to the ill-posed nature of such problems, often…

This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…

This work proposes a learning-based statistical refinement method for improving the denoising results of a given denoiser without knowing the precise noise distribution or accessing clean images or calibration data. While there are many…

The characteristic feature of inverse problems is their instability with respect to data perturbations. In order to stabilize the inversion process, regularization methods have to be developed and applied. In this work we introduce and…