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In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…
We develop a new, efficient, and accurate method to simulate frequency-domain borehole electromagnetic (EM) measurements acquired in the presence of three-dimensional (3D) variations of the anisotropic subsurface conductivity. The method is…
Vector Fitting is a popular method of constructing rational approximants designed to fit given frequency response measurements. The original method, which we refer to as VF, is based on a least-squares fit to the measurements by a rational…
We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1, \dots, x_N)$, where $x_i \in \mathbb{R}^d$, and $f$ is invariant under permutations of its $N$…
We present a deep neural network-enabled method to accelerate near-field (NF) antenna measurement. We develop a Near-field Super-resolution Network (NFS-Net) to reconstruct significantly undersampled near-field data as high-resolution data,…
Trigonometric polynomials are widely used for the approximation of a smooth function $f$ from a set of nonuniformly spaced samples $\{f(x_j)\}_{j=0}^{N-1}$. If the samples are perturbed by noise, controlling the smoothness of the…
Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…
When search methods are being designed it is very important to know which parameters have the greatest influence on the behaviour and performance of the algorithm. To this end, algorithm parameters are commonly calibrated by means of either…
Due to the computational complexity of 3D medical image segmentation, training with downsampled images is a common remedy for out-of-memory errors in deep learning. Nevertheless, as standard spatial convolution is sensitive to variations in…
Ultrasound-based elasticity imaging is a non-invasive technique for estimating tissue stiffness fields from displacement fields obtained by comparing ultrasound signals before and after compression. While recent deep learning approaches…
In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
Learning approximations to smooth target functions of many variables from finite sets of pointwise samples is an important task in scientific computing and its many applications in computational science and engineering. Despite well over…
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of…
Deeper and wider Convolutional Neural Networks (CNNs) achieve superior performance but bring expensive computation cost. Accelerating such over-parameterized neural network has received increased attention. A typical pruning algorithm is a…
In this paper, we study efficient beam coverage design for multi-antenna systems in both far-field and near-field cases. To reduce the computational complexity of existing sampling-based optimization methods, we propose a new low-complexity…
Tensor decomposition of convolutional and fully-connected layers is an effective way to reduce parameters and FLOP in neural networks. Due to memory and power consumption limitations of mobile or embedded devices, the quantization step is…
Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its…
Fourier extension is an approximation method that alleviates the periodicity requirements of Fourier series and avoids the Gibbs phenomenon when approximating functions. We describe a similar extension approach using regular wavelet bases…
Fourier Neural Operators are deep learning models that learn mappings between function spaces and can be used to learn and solve partial differential equations (PDEs), in some cases significantly faster than traditional PDE solvers. Within…