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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…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
Regularization is used in many different areas of optimization when solutions are sought which not only minimize a given function, but also possess a certain degree of regularity. Popular applications are image denoising, sparse regression…
In this paper we are concerned with a sequence of univariate random variables with piecewise polynomial means and independent sub-Gaussian noise. The underlying polynomials are allowed to be of arbitrary but fixed degrees. All the other…
Sampling and quantization are standard practices in signal and image processing, but a theoretical understanding of their impact is incomplete. We consider discrete image registration when the underlying function is a one-dimensional…
Regularization plays a pivotal role when facing the challenge of solving ill-posed inverse problems, where the number of observations is smaller than the ambient dimension of the object to be estimated. A line of recent work has studied…
Given $n$ samples of a function $f\colon D\to\mathbb C$ in random points drawn with respect to a measure $\varrho_S$ we develop theoretical analysis of the $L_2(D, \varrho_T)$-approximation error. For a parituclar choice of $\varrho_S$…
This paper studies the convergence of a spatial semidiscretization of a three-dimensional stochastic Allen-Cahn equation with multiplicative noise. For non-smooth initial data, the regularity of the mild solution is investigated, and an…
We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…
Recent medical imaging studies have given rise to distinct but inter-related datasets corresponding to multiple experimental tasks or longitudinal visits. Standard scalar-on-image regression models that fit each dataset separately are not…
A discrete frame for $L^2({\mathbb R}^d)$ is a countable sequence $\{e_j\}_{j\in J}$ in $L^2({\mathbb R}^d)$ together with real constants $0<A\leq B< \infty$ such that $$ A\|f\|_2^2 \leq \sum_{j\in J}|\langle f,e_j \rangle |^2 \leq…
Medical image segmentation plays a crucial role in clinical workflows, but domain shift often leads to performance degradation when models are applied to unseen clinical domains. This challenge arises due to variations in imaging…
We study approximation and statistical learning properties of deep ReLU networks under structural assumptions that mitigate the curse of dimensionality. We prove minimax-optimal uniform approximation rates for $s$-H\"older smooth functions…
Semantic segmentation consists of predicting a semantic label for each image pixel. While existing deep learning approaches achieve high accuracy, they often overlook the ordinal relationships between classes, which can provide critical…
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding…
A fast and exact algorithm is developed for the spin +-2 spherical harmonics transforms on equi-angular pixelizations on the sphere. It is based on the Driscoll and Healy fast scalar spherical harmonics transform. The theoretical exactness…
We construct an adaptive asymptotically optimal in the classical norm of the space L(2) of square integrable functions non - parametrical multidimensional time defined signal regaining (adaptive filtration, noise canceller) on the…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
Most detection algorithms in spatial modulation (SM) are formulated as linear regression via the regularized least-squares (RLS) method. In this method, the transmit signal is estimated by minimizing the residual sum of squares penalized…