Related papers: Surgery of spline-type and molecular frames
Observations made in continuous time are often irregular and contain the missing values across different channels. One approach to handle the missing data is imputing it using splines, by fitting the piecewise polynomials to the observed…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…
Recently, fusion frames and frames for operators were considered as generalizations of frames in Hilbert spaces. In this paper, we generalize some of the known results in frame theory to fusion frames related to a linear bounded operator K…
In this paper, we consider the problem of reconstructing piecewise smooth functions to high accuracy from nonuniform samples of their Fourier transform. We use the framework of nonuniform generalized sampling (NUGS) to do this, and to…
We study phaseless sampling in spline spaces generated by B-splines with arbitrary knots. For real spline spaces, we give a necessary and sufficient condition for a sequence of sampling points to admit a local phase retrieval of any…
We propose a method to efficiently compute tomographic projections of a 3D volume represented by a linear combination of shifted B-splines. To do so, we propose a ray-tracing algorithm that computes 3D line integrals with arbitrary…
We propose a supervised machine learning approach for boosting existing signal and image recovery methods and demonstrate its efficacy on example of image reconstruction in computed tomography. Our technique is based on a local nonlinear…
Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…
It is shown that Paley-Wiener functions on Riemannian manifolds of bounded geometry can be reconstructed in a stable way from some countable sets of their inner products with certain distributions of compact support. A reconstruction method…
This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as…
Diffusion models have been increasingly used as strong generative priors for solving inverse problems such as super-resolution in medical imaging. However, these approaches typically utilize a diffusion prior trained at a single scale,…
Based on Beurling's theory of balayage, we develop the theory of non-uniform sampling in the context of the theory of frames for the settings of the Short Time Fourier Transform and pseudo-differential operators. There is sufficient…
A new principle of subwavelength imaging based on frequency scanning is considered. It is shown that it is possible to reconstruct the spatial profile of an external field exciting an array (or coupled arrays) of subwavelength-sized…
Recent advancements in model checking have demonstrated significant potential across diverse applications, particularly in signal and image analysis. Medical imaging stands out as a critical domain where model checking can be effectively…
We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…
We formulate as an inverse problem the construction of sparse parametric continuous curve models that fit a sequence of contour points. Our prior is incorporated as a regularization term that encourages rotation invariance and sparsity. We…
Frame interpolation is an essential video processing technique that adjusts the temporal resolution of an image sequence. While deep learning has brought great improvements to the area of video frame interpolation, techniques that make use…
Spline functions have long been used in numerical solution of differential equations. Recently it revives as isogeometric analysis, which offers integration of finite element analysis and NURBS based CAD into a single unified process.…
We derive necessary conditions for localization of continuous frames in terms of generalized Beurling densities. As an important application we provide necessary density conditions for sampling and interpolation in a very large class of…