3 research outputs found
Sparsity and Incoherence in Compressive Sampling
We consider the problem of reconstructing a sparse signal from a
limited number of linear measurements. Given randomly selected samples of
, where is an orthonormal matrix, we show that minimization
recovers exactly when the number of measurements exceeds where is the number of
nonzero components in , and is the largest entry in properly
normalized: . The smaller ,
the fewer samples needed.
The result holds for ``most'' sparse signals supported on a fixed (but
arbitrary) set . Given , if the sign of for each nonzero entry on
and the observed values of are drawn at random, the signal is
recovered with overwhelming probability. Moreover, there is a sense in which
this is nearly optimal since any method succeeding with the same probability
would require just about this many samples
Compressive imaging spectrometers using coded apertures
Abstract: We describe a novel method to track targets in a large field of view. This method simultaneously images multiple, encoded sub-fields of view onto a common focal plane. Sub-field encoding enables target tracking by creating a unique connection between target characteristics in superposition space and the target's true position in real space. This is accomplished without reconstructing a conventional image of the large field of view. Potential encoding schemes include spatial shift, rotation, and magnification. We discuss each of these encoding schemes, but the main emphasis of the paper and all examples are based on one-dimensional spatial shift encoding. System performance is evaluated in terms of two criteria: average decoding time and probability of decoding error. We study these performance criteria as a function of resolution in the encoding scheme and signal-to-noise ratio. Finally, we include simulation and experimental results demonstrating our novel tracking method