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Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…
Partial differential equations have recently garnered substantial attention as an image processing framework due to their extensibility, the ability to rigorously engineer and analyse the governing dynamics as well as the ease of…
Feature-preserving mesh denoising has received noticeable attention in visual media, with the aim of recovering high-fidelity, clean mesh shapes from the ones that are contaminated by noise. Existing denoising methods often design smaller…
Monitoring diseases that affect the brain's structural integrity requires automated analysis of magnetic resonance (MR) images, e.g., for the evaluation of volumetric changes. However, many of the evaluation tools are optimized for…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
Sparse representation of 3D images is considered within the context of data reduction. The goal is to produce high quality approximations of 3D images using fewer elementary components than the number of intensity points in the 3D array.…
Differentiable 3D Gaussian splatting has emerged as an efficient and flexible rendering technique for representing complex scenes from a collection of 2D views and enabling high-quality real-time novel-view synthesis. However, its reliance…
Recently, deep learning methods such as the convolutional neural networks have gained prominence in the area of image denoising. This is owing to their proven ability to surpass state-of-the-art classical image denoising algorithms such as…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
In this paper, we propose a novel image denoising algorithm exploiting features from both spatial as well as transformed domain. We implement intensity-invariance based improved grouping for collaborative support-agnostic sparse…
We introduce a model-based iterative method to obtain shear modulus images of tissue using magnetic resonance elastography. The method jointly finds the displacement field that best fits multifrequency tissue displacement data and the…
Dynamic mode decomposition (DMD) represents an effective means for capturing the essential features of numerically or experimentally generated flow fields. In order to achieve a desirable tradeoff between the quality of approximation and…
Denoising diffusion models have recently achieved state-of-the-art performance in many image-generation tasks. They do, however, require a large amount of computational resources. This limits their application to medical tasks, where we…
Sparse depth measurements are widely available in many applications such as augmented reality, visual inertial odometry and robots equipped with low cost depth sensors. Although such sparse depth samples work well for certain applications…
The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…
We present a suite of techniques for jointly optimizing triangle meshes and shading models to match the appearance of reference scenes. This capability has a number of uses, including appearance-preserving simplification of extremely…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
Medical image segmentation is a challenging task, made more difficult by many datasets' limited size and annotations. Denoising diffusion probabilistic models (DDPM) have recently shown promise in modelling the distribution of natural…
Image denoising algorithms have been extensively investigated for medical imaging. To perform image denoising, penalized least-squares (PLS) problems can be designed and solved, in which the penalty term encodes prior knowledge of the…
In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…