35 research outputs found
The spectra of random abelian G-circulant matrices
This paper studies the asymptotic behavior of eigenvalues of random abelian
G-circulant matrices, that is, matrices whose structure is related to a finite
abelian group G in a way that naturally generalizes the relationship between
circulant matrices and cyclic groups. It is shown that, under mild conditions,
when the size of the group G goes to infinity, the spectral measures of such
random matrices approach a deterministic limit. Depending on some aspects of
the structure of the groups, whether the matrices are constrained to be
Hermitian, and a few details of the distributions of the matrix entries, the
limit measure is either a (complex or real) Gaussian distribution or a mixture
of two Gaussian distributions
Short-Wave Infrared Compressive Imaging of Single Photons
We present a short-wave infrared (SWIR) single photon camera based on a single superconducting nanowire single photon detector (SNSPD) and compressive imaging. We show SWIR single photon imaging at a megapixel resolution with a low signal-to-background ratio around 0.6, show SWIR video acquisition at 20 frames per second and 64x64 pixel video resolution, and demonstrate sub-nanosecond resolution time-of-flight imaging. All scenes were sampled by detecting only a small number of photons for each compressive sampling matrix. In principle, our technique can be used for imaging faint objects in the mid-IR regime
Frequency-modulated continuous-wave LiDAR compressive depth-mapping
We present an inexpensive architecture for converting a frequency-modulated
continuous-wave LiDAR system into a compressive-sensing based depth-mapping
camera. Instead of raster scanning to obtain depth-maps, compressive sensing is
used to significantly reduce the number of measurements. Ideally, our approach
requires two difference detectors. % but can operate with only one at the cost
of doubling the number of measurments. Due to the large flux entering the
detectors, the signal amplification from heterodyne detection, and the effects
of background subtraction from compressive sensing, the system can obtain
higher signal-to-noise ratios over detector-array based schemes while scanning
a scene faster than is possible through raster-scanning. %Moreover, we show how
a single total-variation minimization and two fast least-squares minimizations,
instead of a single complex nonlinear minimization, can efficiently recover
high-resolution depth-maps with minimal computational overhead. Moreover, by
efficiently storing only data points from measurements of an
pixel scene, we can easily extract depths by solving only two linear equations
with efficient convex-optimization methods
Compressive Pattern Matching on Multispectral Data
We introduce a new constrained minimization problem that performs template
and pattern detection on a multispectral image in a compressive sensing
context. We use an original minimization problem from Guo and Osher that uses
minimization techniques to perform template detection in a multispectral
image. We first adapt this minimization problem to work with compressive
sensing data. Then we extend it to perform pattern detection using a formal
transform called the spectralization along a pattern. That extension brings out
the problem of measurement reconstruction. We introduce shifted measurements
that allow us to reconstruct all the measurement with a small overhead and we
give an optimality constraint for simple patterns. We present numerical results
showing the performances of the original minimization problem and the
compressed ones with different measurement rates and applied on remotely sensed
data.Comment: Published in IEEE Transactions on Geoscience and Remote Sensin