Cosmic Ray Rejection by Linear Filtering of Single Images

We present a convolution-based algorithm for finding cosmic rays in single well-sampled astronomical images. The spatial filter used is the point spread function (approximated by a Gaussian) minus a scaled delta function, and cosmic rays are identified by thresholding the filtered image. This filter searches for features with significant power at spatial frequencies too high for legitimate objects. Noise properties of the filtered image are readily calculated, which allows us to compute the probability of rejecting a pixel not contaminated by a cosmic ray (the false alarm probability). We demonstrate that the false alarm probability for a pixel containing object flux will never exceed the corresponding probability for a blank sky pixel, provided we choose the convolution kernel appropriately. This allows confident rejection of cosmic rays superposed on real objects. Identification of multiple-pixel cosmic ray hits can be enhanced by running the algorithm iteratively, replacing flagged pixels with the background level at each iteration.Comment: Accepted for publication in PASP (May 2000 issue). An iraf script implementing the algorithm is available from the author, or from http://sol.stsci.edu/~rhoads/ . 16 pages including 3 figures. Uses AASTeX aaspp4 styl

Latitude: A Model for Mixed Linear-Tropical Matrix Factorization

Nonnegative matrix factorization (NMF) is one of the most frequently-used matrix factorization models in data analysis. A significant reason to the popularity of NMF is its interpretability and the `parts of whole' interpretation of its components. Recently, max-times, or subtropical, matrix factorization (SMF) has been introduced as an alternative model with equally interpretable `winner takes it all' interpretation. In this paper we propose a new mixed linear--tropical model, and a new algorithm, called Latitude, that combines NMF and SMF, being able to smoothly alternate between the two. In our model, the data is modeled using the latent factors and latent parameters that control whether the factors are interpreted as NMF or SMF features, or their mixtures. We present an algorithm for our novel matrix factorization. Our experiments show that our algorithm improves over both baselines, and can yield interpretable results that reveal more of the latent structure than either NMF or SMF alone.Comment: 14 pages, 6 figures. To appear in 2018 SIAM International Conference on Data Mining (SDM '18). For the source code, see https://people.mpi-inf.mpg.de/~pmiettin/linear-tropical

Max-Plus Algebraic Statistical Leverage Scores

The statistical leverage scores of a matrix A ∈ Rn×d record the degree of alignment between col(A) and the coordinate axes in Rn. These scores are used in random sampling algorithms for solving certain numerical linear algebra problems. In this paper we present a max-plus algebraic analogue of statistical leverage scores. We show that max-plus statistical leverage scores can be used to calculate the exact asymptotic behavior of the conventional statistical leverage scores of a generic radial basis function network (RBFN) matrix. We also show how max-plus statistical leverage scores can provide a novel way to approximate the conventional statistical leverage scores of a fixed, nonparametrized matrix

Max-plus linear inverse problems:2-norm regression and system identification of max-plus linear dynamical systems with Gaussian noise

In this paper we present new theory and algorithms for 2-norm regression over the max-plus semiring. As an application we also show how max-plus 2-norm regression can be used in system identification of max-plus linear dynamical systems with Gaussian noise. We also introduce and provide methods for solving a max-plus linear inverse problem with regularization, which can be used when the the original problem is not well posed.Comment: arXiv admin note: substantial text overlap with arXiv:1712.0349

As goes the seminary : how seminaries are intentionally producing spiritually alive pastors

https://place.asburyseminary.edu/ecommonsatsdissertations/1232/thumbnail.jp

Blighting of field and garden peas, chiefly due to seed infection; Powdery mildew of the pea

Caption title.Mode of access: Internet