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In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
Recent developments in image acquisition literature have miniaturized the confocal laser endomicroscopes to improve usability and flexibility of the apparatus in actual clinical settings. However, miniaturized devices collect less light and…
In this paper, we present a novel deep learning-based approach for still image super-resolution, that unlike the mainstream models does not rely solely on the input low resolution image for high quality upsampling, and takes advantage of a…
We propose an extended primal-dual algorithm framework for solving a general nonconvex optimization model. This work is motivated by image reconstruction problems in a class of nonlinear imaging, where the forward operator can be formulated…
We present a simple and effective image super-resolution algorithm that imposes an image formation constraint on the deep neural networks via pixel substitution. The proposed algorithm first uses a deep neural network to estimate…
We present a new approach to the numerical upscaling for elliptic problems with rough diffusion coefficient at high contrast. It is based on the localizable orthogonal decomposition of $H^1$ into the image and the kernel of some novel…
Image super-resolution using self-optimizing mask via fractional-order gradient interpolation and reconstruction aims to recover detailed information from low-resolution images and reconstruct them into high-resolution images. Due to the…
This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive…
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a "modular black box polynomial", e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers.…
Interpolation based image zooming methods provide a high execution speed and low computational complexity. However, the quality of the zoomed images is unsatisfactory in many cases. The main challenge of super- resolution methods is to…
Image Fusion is the process in which core information from a set of component images is merged to form a single image, which is more informative and complete than the component input images in quality and appearance. This paper presents a…
The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…
Due to strong learning abilities of convolutional neural networks (CNNs), they have become mainstream methods for image super-resolution. However, there are big differences of different deep learning methods with different types. There is…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
In this work we apply commonly known methods of non-adaptive interpolation (nearest pixel, bilinear, B-spline, bicubic, Hermite spline) and sampling (point sampling, supersampling, mip-map pre-filtering, rip-map pre-filtering and FAST) to…
This paper concerns with nonuniform sampling and interpolation methods combined with variational models for the solution of a generalized image inpainting problem and the restoration of digital signals. In particular, we discuss the problem…
Constructing a propagation map from a set of scattered measurements finds important applications in many areas, such as localization, spectrum monitoring and management. Classical interpolation-type methods have poor performance in regions…
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating…