Related papers: Constant rank factorizations of smooth maps
Low rank tensor decompositions are a powerful tool for learning generative models, and uniqueness results give them a significant advantage over matrix decomposition methods. However, tensors pose significant algorithmic challenges and…
Modern autonomous vehicles and robots utilize versatile sensors for localization and mapping. The fidelity of these maps is paramount, as an accurate environmental representation is a prerequisite for stable and precise localization. Factor…
Separation of variables (SoV) is a special property of integrable models which ensures that the wavefunction has a very simple factorised form in a specially designed basis. Even though the factorisation of the wavefunction was recently…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…
Forward-looking sonar can capture high resolution images of underwater scenes, but their interpretation is complex. Generic object detection in such images has not been solved, specially in cases of small and unknown objects. In comparison,…
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very…
One way to recognise an object is to study how the echo has been shaped during the interaction with the target. Wideband sonar allows the study of the energy distribution for a large range of frequencies. The frequency distribution contains…
Synthetic aperture sonar (SAS) requires precise time-of-flight measurements of the transmitted/received waveform to produce well-focused imagery. It is not uncommon for errors in these measurements to be present resulting in image…
The main purpose of this paper is to introduce a new category, which we call a resonance category, whose combinatorics reflect that of canonical stratifications of $n$-fold symmetric smash products. The study of the stratifications can then…
One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…
Object classification in synthetic aperture sonar (SAS) imagery is usually a data starved and class imbalanced problem. There are few objects of interest present among much benign seafloor. Despite these problems, current classification…
Singing techniques are used for expressive vocal performances by employing temporal fluctuations of the timbre, the pitch, and other components of the voice. Their classification is a challenging task, because of mainly two factors: 1) the…
Synthetic aperture sonar (SAS) requires precise positional and environmental information to produce well-focused output during the image reconstruction step. However, errors in these measurements are commonly present resulting in defocused…
Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to…
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…
Place recognition using SOund Navigation and Ranging (SONAR) images is an important task for simultaneous localization and mapping(SLAM) in underwater environments. This paper proposes a robust and efficient imaging SONAR based place…
Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…
We consider the problem of synthetic aperture radar (SAR) imaging and motion estimation of complex scenes. By complex we mean scenes with multiple targets, stationary and in motion. We use the usual setup with one moving antenna emitting…
In the recent decade, electronic technology gets advanced day by day the methodologies too should update. For the purpose of ranging various methods such Radio Detection and Ranging (RADAR), Light Detection and Ranging (LIDAR) and Sonic…