Related papers: Signal Recovery Using Splines

This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold of images based on the metamorphosis model defines shortest…

Modular design is a key challenge for enabling large-scale reuse of hardware modules. Unlike software, however, hardware designs correspond to physical circuits and inherit constraints from them. Timing constraints -- which cycle a signal…

This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…

Single-Pixel Imaging (SPI) enables the reconstruction of objects using a single detector through sequential illuminations with structured light patterns. The choice of illumination patterns is critical, particularly in highly undersampled…

The Piecewise Polynomial Interpolation (PPI) function approach is aimed at solving nonlinear programming problems with disjoint feasible regions. In such problems, disjointedness is generally associated with prohibited operating zones,…

This paper is concerned with the inverse problem of reconstructing a small object from far field measurements. The inverse problem is severally ill-posed because of the diffraction limit and low signal to noise ratio. We propose a novel…

Polynomial interpolation is an important component of many computational problems. In several of these computational problems, failure to preserve positivity when using polynomials to approximate or map data values between meshes can lead…

This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…

Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…

Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…

Recovering a source signal from indirect measurements often requires estimating latent parameters, such as wireless channel states or MRI coil sensitivities, that cannot be directly observed. Here, we introduce Physics-Embedded Inverse…

A new type of an optical interferometer is discussed the phase difference between the interfering beams in which is substantially wavelength dependent. It is shown that the function measured with this device is an integral transform of the…

Semialgebraic splines are functions that are piecewise polynomial with respect to a cell decomposition into sets defined by polynomial inequalities. We study bivariate semialgebraic splines, formulating spaces of semialgebraic splines in…

We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each…

It was recently shown that the phase retrieval imaging of a sample can be modeled as a simple convolution process. Sometimes, such a convolution depends on physical parameters of the sample which are difficult to estimate a priori. In this…

In diffraction imaging, one is tasked with reconstructing a signal from its power spectrum. To resolve the ambiguity in this inverse problem, one might invoke prior knowledge about the signal, but phase retrieval algorithms in this vein…

Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…

Single-pixel imaging (SPI) is significant for applications constrained by transmission bandwidth or lighting band, where 3D SPI can be further realized through capturing signals carrying depth. Sampling strategy and reconstruction algorithm…

Spin-echo instruments are typically used to measure diffusive processes and the dynamics and motion in samples on ps and ns timescales. A key aspect of the spin-echo technique is to determine the polarisation of a particle beam. We present…

Polarimetric imaging is one of the most effective techniques for high-contrast imaging and characterization of circumstellar environments. These environments can be characterized through direct-imaging polarimetry at near-infrared…