2,857 research outputs found
A fast and accurate basis pursuit denoising algorithm with application to super-resolving tomographic SAR
regularization is used for finding sparse solutions to an
underdetermined linear system. As sparse signals are widely expected in remote
sensing, this type of regularization scheme and its extensions have been widely
employed in many remote sensing problems, such as image fusion, target
detection, image super-resolution, and others and have led to promising
results. However, solving such sparse reconstruction problems is
computationally expensive and has limitations in its practical use. In this
paper, we proposed a novel efficient algorithm for solving the complex-valued
regularized least squares problem. Taking the high-dimensional
tomographic synthetic aperture radar (TomoSAR) as a practical example, we
carried out extensive experiments, both with simulation data and real data, to
demonstrate that the proposed approach can retain the accuracy of second order
methods while dramatically speeding up the processing by one or two orders.
Although we have chosen TomoSAR as the example, the proposed method can be
generally applied to any spectral estimation problems.Comment: 11 pages, IEEE Transactions on Geoscience and Remote Sensin
Non-convex optimization for 3D point source localization using a rotating point spread function
We consider the high-resolution imaging problem of 3D point source image
recovery from 2D data using a method based on point spread function (PSF)
engineering. The method involves a new technique, recently proposed by
S.~Prasad, based on the use of a rotating PSF with a single lobe to obtain
depth from defocus. The amount of rotation of the PSF encodes the depth
position of the point source. Applications include high-resolution single
molecule localization microscopy as well as the problem addressed in this paper
on localization of space debris using a space-based telescope. The localization
problem is discretized on a cubical lattice where the coordinates of nonzero
entries represent the 3D locations and the values of these entries the fluxes
of the point sources. Finding the locations and fluxes of the point sources is
a large-scale sparse 3D inverse problem. A new nonconvex regularization method
with a data-fitting term based on Kullback-Leibler (KL) divergence is proposed
for 3D localization for the Poisson noise model. In addition, we propose a new
scheme of estimation of the source fluxes from the KL data-fitting term.
Numerical experiments illustrate the efficiency and stability of the algorithms
that are trained on a random subset of image data before being applied to other
images. Our 3D localization algorithms can be readily applied to other kinds of
depth-encoding PSFs as well.Comment: 28 page
Blind Two-Dimensional Super-Resolution and Its Performance Guarantee
In this work, we study the problem of identifying the parameters of a linear
system from its response to multiple unknown input waveforms. We assume that
the system response, which is the only given information, is a scaled
superposition of time-delayed and frequency-shifted versions of the unknown
waveforms. Such kind of problem is severely ill-posed and does not yield a
unique solution without introducing further constraints. To fully characterize
the linear system, we assume that the unknown waveforms lie in a common known
low-dimensional subspace that satisfies certain randomness and concentration
properties. Then, we develop a blind two-dimensional (2D) super-resolution
framework that applies to a large number of applications such as radar imaging,
image restoration, and indoor source localization. In this framework, we show
that under a minimum separation condition between the time-frequency shifts,
all the unknowns that characterize the linear system can be recovered precisely
and with very high probability provided that a lower bound on the total number
of the observed samples is satisfied. The proposed framework is based on 2D
atomic norm minimization problem which is shown to be reformulated and solved
efficiently via semidefinite programming. Simulation results that confirm the
theoretical findings of the paper are provided
- …