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Tensors, or multidimensional arrays, are data structures that can naturally represent visual data of multiple dimensions. Inherently able to efficiently capture structured, latent semantic spaces and high-order interactions, tensors have a…
Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…
Scattering in complex media scrambles light, thus obscuring images and limiting applications from astronomy to microscopy. Existing computational and wavefront-shaping methods treat scattering as a linear optical-wave inversion problem that…
We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Low-rank tensors appear to be prosperous in many applications. However, the sets of bounded-rank tensors are non-smooth and non-convex algebraic varieties, rendering the low-rank optimization problems to be challenging. To this end, we…
Complicated mathematical equations involving products of tensors with permutation symmetries, frequently encountered in fields such as general relativity and quantum chemistry (e.g., equations in high-order coupled cluster theories),…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with…
Bounds consistency is usually enforced on continuous constraints by first decomposing them into binary and ternary primitives. This decomposition has long been shown to drastically slow down the computation of solutions. To tackle this,…
Image deblurring is a challenging problem in imaging due to its highly ill-posed nature. Deep learning models have shown great success in tackling this problem but the quest for the best image quality has brought their computational…
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…
We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work, We…
We describe the construction of a spherical wavelet analysis through the inverse stereographic projection of the Euclidean planar wavelet framework, introduced originally by Antoine and Vandergheynst and developed further by Wiaux et al.…
Synthetic dimensions based on particles' internal degrees of freedom, such as frequency, spatial modes and arrival time, have attracted significant attention. They offer ideal large-scale lattices to simulate nontrivial topological…
While learning based compression techniques for images have outperformed traditional methods, they have not been widely adopted in machine learning pipelines. This is largely due to lack of standardization and lack of retention of salient…
The core of many approaches for the resolution of variational inverse problems arising in signal and image processing consists of promoting the sought solution to have a sparse representation in a well-suited space. A crucial task in this…
A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the…
This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of a wavelet representation. We reinterpret the acquisition procedure of a…