Related papers: Diffusion Tensor Regularization with Metric Double…
Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute 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…
Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This in turn can be achieved by variational regularization…
Denoising diffusion models offer a promising approach to accelerating magnetic resonance imaging (MRI) and producing diagnostic-level images in an unsupervised manner. However, our study demonstrates that even tiny worst-case potential…
The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the…
We present a new inner-outer iterative algorithm for edge enhancement in imaging problems. At each outer iteration, we formulate a Tikhonov-regularized problem where the penalization is expressed in the 2-norm and involves a regularization…
The advancement of imaging devices and countless images generated everyday pose an increasingly high demand on image denoising, which still remains a challenging task in terms of both effectiveness and efficiency. To improve denoising…
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…
When adopting a model-based formulation, solving inverse problems encountered in multiband imaging requires to define spatial and spectral regularizations. In most of the works of the literature, spectral information is extracted from the…
We introduce regularised diffusion--shock (RDS) inpainting as a modification of diffusion--shock inpainting from our SSVM 2023 conference paper. RDS inpainting combines two carefully chosen components: homogeneous diffusion and…
Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…
Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner. One major drawback of optical diffraction tomography is poor…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
While variational methods have been among the most powerful tools for solving linear inverse problems in imaging, deep (convolutional) neural networks have recently taken the lead in many challenging benchmarks. A remaining drawback of deep…
The multilinear normal distribution is a widely used tool in tensor analysis of magnetic resonance imaging (MRI). Diffusion tensor MRI provides a statistical estimate of a symmetric 2nd-order diffusion tensor, for each voxel within an…
Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical…
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…
Image denoising is an important problem in low-level vision and serves as a critical module for many image recovery tasks. Anisotropic diffusion is a wide family of image denoising approaches with promising performance. However, traditional…
Coherent imaging systems, such as medical ultrasound and synthetic aperture radar (SAR), are subject to corruption from speckle due to sub-resolution scatterers. Since speckle is multiplicative in nature, the constituent image regions…
We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the denoising problem directly on the hyperbolic space, we exploit…