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Gabor transform is one of the performed tools for time-frequency signal analysis. The principal aim of this paper is to generalize the Gabor Fourier transform to the quaternion linear canonical transform. Actually, this transform gives us…
The concept of measurement in classical scattering is interpreted as an overlap of a particle packet with some area in phase space that describes the detector. Considering that usually we record the passage of particles at some point in…
This work proposes a green learning (GL) approach to restore medical images. Without loss of generality, we use low-dose computed tomography (LDCT) images as examples. LDCT images are susceptible to noise and artifacts, where the imaging…
The class of regular transformations has several equivalent characterizations such as functional MSO transductions, deterministic two-way transducers, streaming string transducers, as well as regular transducer expressions (RTE). For…
Canonical correlation analysis (CCA) is a powerful technique for discovering whether or not hidden sources are commonly present in two (or more) datasets. Its well-appreciated merits include dimensionality reduction, clustering,…
Link prediction tasks focus on predicting possible future connections. Most existing researches measure the likelihood of links by different similarity scores on node pairs and predict links between nodes. However, the similarity-based…
Linear time invariant (LTI) systems are widely used for modeling system dynamics in science and engineering problems. Harmonic oscillation of LTI systems are widely used for modeling and analyses of periodic physical phenomenon. This study…
Accurate camera-LiDAR calibration is a prerequisite for robust multi-modal perception in robotics. Recent target-less approaches based on deep point correspondences achieve remarkable performance for extrinsic calibration but assume…
The design of the optimal inverse discrete cosine transform (IDCT) to compensate the quantization error is proposed for effective lossy image compression in this work. The forward and inverse DCTs are designed in pair in current image/video…
In numerical simulations of classical and quantum lattice systems, 2d corner transfer matrices (CTMs) and 3d corner tensors (CTs) are a useful tool to compute approximate contractions of infinite-size tensor networks. In this paper we show…
We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
To excel in signal processing or control systems, a deep understanding of transforms is essential. But what exactly is this mathematical tool, and how does it function? In this article, we will explore the fundamentals of transforms, their…
This paper studies the recovery of a joint piece-wise linear trend from a time series using L1 regularization approach, called L1 trend filtering (Kim, Koh and Boyd, 2009). We provide some sufficient conditions under which a L1 trend filter…
Linear time-translation-invariant (LTI) models offer simple, yet powerful, abstractions of complex classical dynamical systems. Quantum versions of such models have so far relied on assumptions of Markovianity or an internal state-space…
Optoacoustic imaging technologies require fast and accurate signal pre-processing algorithms to enable widespread deployment in clinical and home-care settings. However, they still rely on the Discrete Fourier Transform (DFT) as the default…
Randomized controlled trials (RCTs) are widely regarded as the gold standard for causal inference in biomedical research. For instance, when estimating the average treatment effect on the treated (ATT), a doubly robust estimation procedure…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
This work proposes a new image analysis tool called Label Consistent Transform Learning (LCTL). Transform learning is a recent unsupervised representation learning approach; we add supervision by incorporating a label consistency…
Transformers are very powerful tools for a variety of tasks across domains, from text generation to image captioning. However, transformers require substantial amounts of training data, which is often a challenge in biomedical settings,…