Related papers: Adaptive algorithms in sampling recovery
Acquisition of Magnetic Resonance Imaging (MRI) scans can be accelerated by under-sampling in k-space (i.e., the Fourier domain). In this paper, we consider the problem of optimizing the sub-sampling pattern in a data-driven fashion. Since…
We consider the problem of approximating a function from $L^2$ by an element of a given $m$-dimensional space $V_m$, associated with some feature map $\boldsymbol{\varphi}$, using evaluations of the function at random points $x_1,…
We consider the problem of approximating an unknown function from point evaluations. This problem is a crucial subproblem in many modern (nonlinear) approximation schemes. When obtaining these point evaluations is costly, minimising the…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
The problem of recovering a structured signal $\mathbf{x} \in \mathbb{C}^p$ from a set of dimensionality-reduced linear measurements $\mathbf{b} = \mathbf {A}\mathbf {x}$ arises in a variety of applications, such as medical imaging,…
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…
In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of…
When attempting to recover functions from observational data, one naturally seeks to do so in an optimal manner with respect to some modeling assumption. With a focus put on the worst-case setting, this is the standard goal of Optimal…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
Models based on approximation capabilities have recently been studied in the context of Optimal Recovery. These models, however, are not compatible with overparametrization, since model- and data-consistent functions could then be…
Let us assume that $f$ is a continuous function defined on the unit ball of $\mathbb R^d$, of the form $f(x) = g (A x)$, where $A$ is a $k \times d$ matrix and $g$ is a function of $k$ variables for $k \ll d$. We are given a budget $m \in…
We study the problem of estimating the value of a known smooth function $f$ at an unknown point $\boldsymbol{\mu} \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of…
Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received…
Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a…
Relief algorithm is a feature selection algorithm used in binary classification proposed by Kira and Rendell, and its computational complexity remarkable increases with both the scale of samples and the number of features. In order to…
We develop a sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at $L$ using only $L^2$ samples. We obtain the optimal number of samples given by the…
We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on…
Selection of perefect parameters for low-pass filters can sometimes be an expensive problem with no analytical solution or differentiability of cost function. In this paper, we introduce a new PSO-inspired algorithm, that incorporates the…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…