Related papers: On the Development of a Coupled Non-linear Telegra…

In SPECT image reconstruction, limited-angle (LA) conditions lead to a loss of frequency components, which distort the reconstructed tomographic image along directions corresponding to the non-collected projection angle range. Although…

This paper introduces a novel variational approach for image compression motivated by recent PDE-based approaches combining edge detection and Laplacian inpainting. The essential feature is to encode the image via a sparse vector field,…

Blind image restoration is a non-convex problem which involves restoration of images from an unknown blur kernel. The factors affecting the performance of this restoration are how much prior information about an image and a blur kernel are…

In recent years, deep learning-based image compression, particularly through generative models, has emerged as a pivotal area of research. Despite significant advancements, challenges such as diminished sharpness and quality in…

Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…

Parabolic partial differential equations (PDEs) are in ubiquitous, very effective use to model diffusion processes. However, there are many applications (e.g., such as in hydrology, animal foraging, biology, and light diffusion just do name…

We propose a novel PDE-based anisotropic filter for noise reduction in multicolor images. It is a generalization of Nitzberg & Shiota's (1992) model being a hyperbolic relaxation of the well-known parabolic Perona & Malik's filter (1990).…

Diffusion models have shown significant progress in image translation tasks recently. However, due to their stochastic nature, there's often a trade-off between style transformation and content preservation. Current strategies aim to…

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…

In this paper, we consider a model with tumor microenvironment involving nutrient density, extracellular matrix and matrix-degrading enzymes, which satisfy a coupled system of PDEs with a free boundary. For this coupled parabolic-hyperbolic…

Denoising diffusion models have emerged as the go-to generative framework for solving inverse problems in imaging. A critical concern regarding these models is their performance on out-of-distribution tasks, which remains an under-explored…

The problem of image reconstruction under multiple light scattering is usually formulated as a regularized non-convex optimization. A deep learning architecture, Scattering Decoder (ScaDec), was recently proposed to solve this problem in a…

We present a new nonlinear optimization approach for the sparse reconstruction of single-photon absorption and two-photon absorption coefficients in photoacoustic tomography (PAT). This framework comprises of minimizing an objective…

We introduced Temporally Incremental Disparity Estimation Network (TIDE-Net), a learning-based technique for disparity computation in mono-camera structured light systems. In our hardware setting, a static pattern is projected onto a…

This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…

Denoising diffusion models produce high-fidelity image samples by capturing the image distribution in a progressive manner while initializing with a simple distribution and compounding the distribution complexity. Although these models have…

Transferring visual style between images while preserving semantic correspondence between similar objects remains a central challenge in computer vision. While existing methods have made great strides, most of them operate at global level…

This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…

A unified method for extracting geometric shape features from binary image data using a steady state partial differential equation (PDE) system as a boundary value problem is presented in this paper. The PDE and functions are formulated to…

Many state-of-the-art methods have been proposed for infrared small target detection. They work well on the images with homogeneous backgrounds and high-contrast targets. However, when facing highly heterogeneous backgrounds, they would not…