Related papers: Diffusion Tensor Regularization with Metric Double…
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,…
Denosing diffusion model, as a generative model, has received a lot of attention in the field of image generation recently, thanks to its powerful generation capability. However, diffusion models have not yet received sufficient research in…
The image deblurring problem consists of reconstructing images from blur and noise contaminated available data. In this AMS Notices article, we provide an overview of some well known numerical linear algebra techniques that are use for…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
Dimensional regularization is incompatible with the standard covariant projection methods that are used to calculate the short-distance coefficients in inclusive heavy quarkonium production and annihilation rates. A new method is developed…
Photon-counting computed tomography (PCCT) has emerged as a promising imaging technique, enabling spectral imaging and material decomposition (MD). However, images typically suffer from a low signal-to-noise ratio (SNR) due to constraints…
Magnetic Resonance Imaging (MRI), including diffusion MRI (dMRI), serves as a ``microscope'' for anatomical structures and routinely mitigates the influence of low signal-to-noise ratio scans by compromising temporal or spatial resolution.…
From the optimization point of view, a difficulty with parallel MRI with simultaneous coil sensitivity estimation is the multiplicative nature of the non-linear forward operator: the image being reconstructed and the coil sensitivities…
Fractional Tikhonov regularization methods have been recently proposed to reduce the oversmoothing property of the Tikhonov regularization in standard form, in order to preserve the details of the approximated solution. Their regularization…
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…
The bilateral filter is a useful nonlinear filter which without smoothing edges, it does spatial averaging. In the literature, the effectiveness of this method for image denoising is shown. In this paper, an extension of this method is…
Convolutional neural networks (CNNs) often perform well, but their stability is poorly understood. To address this problem, we consider the simple prototypical problem of signal denoising, where classical approaches such as nonlinear…
In this paper, we propose a variational approach for video denoising, based on a total directional variation (TDV) regulariser proposed in Parisotto et al. (2018), for image denoising and interpolation. In the TDV regulariser, the…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
We propose regularization schemes for deformable registration and efficient algorithms for their numerical approximation. We treat image registration as a variational optimal control problem. The deformation map is parametrized by its…
Denoising diffusion models have recently shown impressive results in generative tasks. By learning powerful priors from huge collections of training images, such models are able to gradually modify complete noise to a clean natural image…
Diffusion models have attained remarkable success in the domains of image generation and editing. It is widely recognized that employing larger inversion and denoising steps in diffusion model leads to improved image reconstruction quality.…
The existence of a global minimizer for a variational problem arising in registration of diffusion tensor images is proved, which ensures that there is a regular spatial transformation for the registration of diffusion tensor images.
Ultrasound image reconstruction can be approximately cast as a linear inverse problem that has traditionally been solved with penalized optimization using the $l_1$ or $l_2$ norm, or wavelet-based terms. However, such regularization…