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We introduce Contrastive Multivariate Singular Spectrum Analysis, a novel unsupervised method for dimensionality reduction and signal decomposition of time series data. By utilizing an appropriate background dataset, the method transforms a…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
This paper presents a general framework for modeling dependence in multivariate time series. Its fundamental approach relies on decomposing each signal in a system into various frequency components and then studying the dependence…
We introduce an efficient method for the reconstruction of the correlation between a compressively measured image and a phase-only filter. The proposed method is based on two properties of phase-only filtering: such filtering is a unitary…
In this paper we tackle the problem of stereo image compression, and leverage the fact that the two images have overlapping fields of view to further compress the representations. Our approach leverages state-of-the-art single-image…
The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…
Visual object tracking is a challenging computer vision task with numerous real-world applications. Here we propose a simple but efficient Spectral Filter Tracking (SFT)method. To characterize rotational and translation invariance of…
Spectrogram-based representations have grown to dominate the feature space for deep learning audio analysis systems, and are often adopted for speech analysis also. Initially, the primary motivator for spectrogram-based representations was…
Trend filtering---first introduced into the astronomical literature in Paper I of this series---is a state-of-the-art statistical tool for denoising one-dimensional signals that possess varying degrees of smoothness. In this work, we…
The decomposition of a stochastic time series into three component series representing a dual signal - namely, the mean and dispersion - while isolating noise is presented. The decomposition is performed by applying machine learning…
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…
Due to limited size and imperfect of the optical components in a spectrometer, aberration has inevitably been brought into two-dimensional multi-fiber spectrum image in LAMOST, which leads to obvious spacial variation of the point spread…
Complex, multivariable systems are often analyzed by grouping their constituent units into components, sometimes referred to as latent features, which afford physical or biological interpretation. However, a priori many different types of…
Data compression is a method of improving the efficiency of transmission and storage of images. Dithering, as a method of data compression, can be used to convert an 8-bit gray level image into a 1-bit / binary image. Undithering is the…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…
We demonstrate spectroscopy of incoherent light with sub-diffraction resolution. In a proof-of-principle experiment we analyze the spectrum of a pair of incoherent point-like sources whose separation is below the diffraction limit. The two…
Hyperspectral unmixing aims at identifying a set of elementary spectra and the corresponding mixture coefficients for each pixel of an image. As the elementary spectra correspond to the reflectance spectra of real materials, they are often…
It is challenging to remove rain-steaks from a single rainy image because the rain steaks are spatially varying in the rainy image. Although the CNN based methods have reported promising performance recently, there are still some defects,…
In comparing the behavior of an energy spectrum to the predictions of random matrix theory one must transform the spectrum such that the averaged level spacing is constant, a procedure known as unfolding. Once energy spectrums belong to an…
This study explores the relationship between hypergraph automorphisms and the spectral properties of matrices associated with hypergraphs. For an automorphism $f$, an \( f \)-compatible matrices capture aspects of the symmetry, represented…