6,039 research outputs found
High-Dimensional Matched Subspace Detection When Data are Missing
We consider the problem of deciding whether a highly incomplete signal lies
within a given subspace. This problem, Matched Subspace Detection, is a
classical, well-studied problem when the signal is completely observed. High-
dimensional testing problems in which it may be prohibitive or impossible to
obtain a complete observation motivate this work. The signal is represented as
a vector in R^n, but we only observe m << n of its elements. We show that
reliable detection is possible, under mild incoherence conditions, as long as m
is slightly greater than the dimension of the subspace in question
Simultaneous Multicolor Detection of Faint Galaxies in the Hubble Deep Field
We present a novel way to detect objects when multiband images are available.
Typically, object detection is performed in one of the available bands or on a
somewhat arbitrarily co-added image. Our technique provides an almost optimal
way to use all the color information available. We build up a composite image
of the N passbands where each pixel value corresponds to the probability that
the given pixel is just sky. By knowing the probability distribution of sky
pixels (a chi-square distribution with N degrees of freedom), the data can be
used to derive the distribution of pixels dominated by object flux. From the
two distributions an optimal segmentation threshold can be determined. Clipping
the probability image at this threshold yields a mask, where pixels unlikely to
be sky are tagged. After using a standard connected-pixel criterion, the
regions of this mask define the detected objects. Applying this technique to
the Hubble Deep Field data, we find that we can extend the detection limit of
the data below that possible using linearly co-added images. We also discuss
possible ways of enhancing object detection probabilities for certain well
defined classes of objects by using various optimized linear combinations of
the pixel fluxes (optimal subspace filtering).Comment: 8 pages, 5 figures (4 postscript, 1 JPEG). To be published in A
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