Related papers: New Risk Bounds for 2D Total Variation Denoising
Speckle noise suppression is a challenging and crucial pre-processing stage for higher-level image analysis. In this work, a new attempt has been made using telegraph total variation equation and fuzzy set theory for speckle noise…
We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys…
We consider the problem of estimating a multivariate function $f_0$ of bounded variation (BV), from noisy observations $y_i = f_0(x_i) + z_i$ made at random design points $x_i \in \mathbb{R}^d$, $i=1,\ldots,n$. We study an estimator that…
Video transformers have recently emerged as an effective alternative to convolutional networks for action classification. However, most prior video transformers adopt either global space-time attention or hand-defined strategies to compare…
A novel numerical method for the estimation of large time-varying parameter (TVP) models is proposed. The updating and smoothing estimates of the TVP model are derived within the context of generalised linear least squares and through…
Denoising is omnipresent in image processing. It is usually addressed with algorithms relying on a set of hyperparameters that control the quality of the recovered image. Manual tuning of those parameters can be a daunting task, which calls…
Over the last decades, the total variation (TV) evolved to one of the most broadly-used regularisation functionals for inverse problems, in particular for imaging applications. When first introduced as a regulariser, higher-order…
Motivated in part by models arising from mathematical descriptions of Bose-Einstein condensation, we consider total variation minimization problems in which the total variation is weighted by a function that may degenerate near the domain…
In representation learning and non-linear dimension reduction, there is a huge interest to learn the 'disentangled' latent variables, where each sub-coordinate almost uniquely controls a facet of the observed data. While many regularization…
Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we…
In a tie-breaker design (TBD), subjects with high values of a running variable are given some (usually desirable) treatment, subjects with low values are not, and subjects in the middle are randomized. TBDs are intermediate between…
Neural network approaches have been demonstrated to work quite well to solve partial differential equations in practice. In this context approaches like physics-informed neural networks and the Deep Ritz method have become popular. In this…
We study the problem of approximation of 2D set of points. Such type of problems always occur in physical experiments, econometrics, data analysis and other areas. The often problems of outliers or spikes usually make researchers to apply…
Discrete diffusion models have recently shown great promise for modeling complex discrete data, with masked diffusion models (MDMs) offering a compelling trade-off between quality and generation speed. MDMs denoise by progressively…
Image denoising is the first step in many biomedical image analysis pipelines and Deep Learning (DL) based methods are currently best performing. A new category of DL methods such as Noise2Void or Noise2Self can be used fully unsupervised,…
This paper presents a data-driven framework for learning optimal second-order total variation diminishing (TVD) flux limiters via differentiable simulations. In our fully differentiable finite volume solvers, the limiter functions are…
Today, Convolutional Neural Networks (CNNs) are the leading method for image denoising. They are traditionally trained on pairs of images, which are often hard to obtain for practical applications. This motivates self-supervised training…
The concept of learning to optimize involves utilizing a trainable optimization strategy rather than relying on manually defined full gradient estimations such as ADAM. We present a framework that jointly trains the full gradient estimator…
The ultimate goal for foundation models is realizing task-agnostic, i.e., supporting out-of-the-box usage without task-specific fine-tuning. Although breakthroughs have been made in natural language processing and image representation…
In this thesis, we offer a thorough investigation of different regularisation terms used in variational imaging problems, together with detailed optimisation processes of these problems. We begin by studying smooth problems and partially…