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Vibrational sum frequency generation (SFG) spectroscopy is a powerful technique for investigating molecular structures, orientations, and dynamics at surfaces. However, its spatial resolution is fundamentally restricted to the micrometer…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
This paper presents novel adaptive space-time reduced-rank interference suppression least squares algorithms based on joint iterative optimization of parameter vectors. The proposed space-time reduced-rank scheme consists of a joint…
This note presents a theoretical discussion of two structure tensor constructions: one proposed by Bigun and Granlund 1987, and the other by Granlund and Knutsson 1995. At first glance, these approaches may appear quite different--the…
Tensor completion and robust principal component analysis have been widely used in machine learning while the key problem relies on the minimization of a tensor rank that is very challenging. A common way to tackle this difficulty is to…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
In this paper, we consider recovering $n$ dimensional signals from $m$ binary measurements corrupted by noises and sign flips under the assumption that the target signals have low generative intrinsic dimension, i.e., the target signals can…
Many regularization schemes for high-dimensional regression have been put forward. Most require the choice of a tuning parameter, using model selection criteria or cross-validation schemes. We show that a simple non-negative or…
We introduce the tensor numerical method for solving optimal control problems that are constrained by fractional 2D and 3D elliptic operators with variable coefficients. We solve the governing equation for the control function which…
Tensor train decomposition is one of the most powerful approaches for processing high-dimensional data. For low-rank tensor train decomposition of large tensors, the alternating least squares (ALS) algorithm is widely used by updating each…
Similarity analysis using neural networks has emerged as a powerful technique for understanding and categorizing complex patterns in various domains. By leveraging the latent representations learned by neural networks, data objects such as…
The paper presents a new model for single channel images low-level interpretation. The image is decomposed into a graph which captures a complete set of structural features. The description allows to accurately identify every edge location…
The reduced-rank method exploits the distortion-variance tradeoff to yield superior solutions for classic problems in statistical signal processing such as parameter estimation and filtering. The central idea is to reduce the variance of…
Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…
Gabor wavelet is an essential tool for image analysis and computer vision tasks. Local structure tensors with multiple scales are widely used in local feature extraction. Our research indicates that the current corner detection method based…
DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…
Constrained least squares problems arise in many applications. Their memory and computation costs are expensive in practice involving high-dimensional input data. We employ the so-called "sketching" strategy to project the least squares…
The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a…
The tensor-train (TT) decomposition expresses a tensor in a data-sparse format used in molecular simulations, high-order correlation functions, and optimization. In this paper, we propose four parallelizable algorithms that compute the TT…
Atmospheric turbulence causes fluctuations in the local refractive index of air that accumulatively disturb a wave's phase and amplitude distribution as it propagates. This impairs the effective range of laser weapons as well as the…