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Many computer vision and image processing applications rely on local features. It is well-known that motion blur decreases the performance of traditional feature detectors and descriptors. We propose an inertial-based deblurring method for…
This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The ``wavelet transform'' maps each $f(x)$ to its coefficients with respect to…
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…
In the process of performing image super-resolution processing, the processing of complex localized information can have a significant impact on the quality of the image generated. Fractal features can capture the rich details of both micro…
We present an algorithm which produces a decomposition of a regular cellular complex with a discrete Morse function analogous to the Morse-Smale decomposition of a smooth manifold with respect to a smooth Morse function. The advantage of…
A rapid transformation is derived between spherical harmonic expansions and their analogues in a bivariate Fourier series. The change of basis is described in two steps: firstly, expansions in normalized associated Legendre functions of all…
By using the most sensitive two-point correlation functions introduced to date, we reconstruct the microstructures of two-phase random media with heretofore unattained accuracy. Such media arise in a host of contexts, including porous and…
Deconvolution is essential for radio interferometric imaging to produce scientific quality data because of finite sampling in the Fourier plane. Most deconvolution algorithms are based on CLEAN which uses a grid of image pixels, or clean…
Automatic magnetic resonance (MR) image processing pipelines are widely used to study people with multiple sclerosis (PwMS), encompassing tasks such as lesion segmentation and brain parcellation. However, the presence of lesion often…
Harmonic decomposition of surfaces, such as spherical and spheroidal harmonics, is used to analyze morphology, reconstruct, and generate surface inclusions of particulate microstructures. However, obtaining high-quality meshes of…
The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency support of the trigonometric polynomial is known. We suggest a construction based on…
We analyze the method for calculation of properties of non-relativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
A new approach is proposed for reconstruction of images from Radon projections. Based on Fourier expansions in orthogonal polynomials of two and three variables, instead of Fourier transforms, the approach provides a new algorithm for the…
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…
In radar systems, high resolution in the Doppler dimension is important for detecting slow-moving targets as it allows for more distinct separation between these targets and clutter, or stationary objects. However, achieving sufficient…
Ultrasound is widely used in medical diagnostics allowing for accessible and powerful imaging but suffers from resolution limitations due to diffraction and the finite aperture of the imaging system, which restricts diagnostic use. The…
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…
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…
Far-field characterization of small objects is severely constrained by the diffraction limit. Existing tools achieving sub-diffraction resolution often utilize point-by-point image reconstruction via scanning or labelling. Here, we present…