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Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
The ability to accurately measure the shapes of faint objects in images taken with the Advanced Camera for Surveys(ACS) on the Hubble Space Telescope (HST) depends upon detailed knowledge of the Point Spread Function (PSF). We show that…
We consider the problem of robustly recovering a $k$-sparse coefficient vector from the Fourier series that it generates, restricted to the interval $[- \Omega, \Omega]$. The difficulty of this problem is linked to the superresolution…
Investigations of the point spread functions (PSFs) and flux calibrations for stacking analysis have been performed with the far-infrared (wavelengths range of 60 to 140 um all-sky maps taken by the Far-Infrared Surveyor (FIS) onboard the…
In positron emission tomography (PET) imaging, statistical iterative reconstruction (IR) techniques appear particularly promising since they can provide accurate system model. The system model matrix which describes the relationship between…
Faint red galaxies in the Sloan Digital Sky Survey show a puzzling clustering pattern in previous measurements. In the two-point correlation function (2PCF), they appear to be strongly clustered on small-scales, indicating a tendency to…
Thermal infrared (TIR) target tracking methods often adopt the correlation filter (CF) framework due to its computational efficiency. However, the low resolution of TIR images, along with tracking interference, significantly limits the…
Interferometers (e.g. ALMA and NOEMA) allow us to obtain the detailed brightness distribution of astronomical sources in 3 dimensions (R.A., Dec., frequency). However, the spatial correlation of the noise makes it difficult to evaluate the…
One way of imaging X-ray emission from solar flares is to measure Fourier components of the spatial X-ray source distribution. We present a new Compressed Sensing-based algorithm named VIS_CS, which reconstructs the spatial distribution…
The desire for wide-field of view, large fractional bandwidth, high sensitivity, high spectral and temporal resolution has driven radio interferometry to the point of big data revolution where the data is represented in at least three…
Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…
In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at $p$ locations and $n$ time points with the possibility that $p>n$. While principal component analysis…
Synthetic aperture sonar (SAS) image resolution is constrained by waveform bandwidth and array geometry. Specifically, the waveform bandwidth determines a point spread function (PSF) that blurs the locations of point scatterers in the…
This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency. The obtained steerable principal components are…
An undersampled point spread function may interact with the microstructure of a solid-state detector such that the total flux detected can depend sensitively on where the PSF center falls within a pixel. Such intra-pixel sensitivity…
Slow feature analysis (SFA) is a method for extracting slowly varying features from a quickly varying multidimensional signal. An open source Matlab-implementation sfa-tk makes SFA easily useable. We show here that under certain…
We propose to measure the weak cosmic shear using the spatial derivatives of the galaxy surface brightness field. The measurement should be carried out in Fourier space, in which the point spread function (PSF) can be transformed to a…
A compressive sensing (CS) reconstruction method for polynomial phase signals is proposed in this paper. It relies on the Polynomial Fourier transform, which is used to establish a relationship between the observation and sparsity domain.…
Faraday tomography offers crucial information on the magnetized astronomical objects, such as quasars, galaxies, or galaxy clusters, by observing its magnetoionic media. The observed linear polarization spectrum is inverse Fourier…
This paper presents a new Bayesian collaborative sparse regression method for linear unmixing of hyperspectral images. Our contribution is twofold; first, we propose a new Bayesian model for structured sparse regression in which the…