475 research outputs found
Super-resolution Line Spectrum Estimation with Block Priors
We address the problem of super-resolution line spectrum estimation of an
undersampled signal with block prior information. The component frequencies of
the signal are assumed to take arbitrary continuous values in known frequency
blocks. We formulate a general semidefinite program to recover these
continuous-valued frequencies using theories of positive trigonometric
polynomials. The proposed semidefinite program achieves super-resolution
frequency recovery by taking advantage of known structures of frequency blocks.
Numerical experiments show great performance enhancements using our method.Comment: 7 pages, double colum
Stable Camera Motion Estimation Using Convex Programming
We study the inverse problem of estimating n locations (up to
global scale, translation and negation) in from noisy measurements of a
subset of the (unsigned) pairwise lines that connect them, that is, from noisy
measurements of for some pairs (i,j) (where the
signs are unknown). This problem is at the core of the structure from motion
(SfM) problem in computer vision, where the 's represent camera locations
in . The noiseless version of the problem, with exact line measurements,
has been considered previously under the general title of parallel rigidity
theory, mainly in order to characterize the conditions for unique realization
of locations. For noisy pairwise line measurements, current methods tend to
produce spurious solutions that are clustered around a few locations. This
sensitivity of the location estimates is a well-known problem in SfM,
especially for large, irregular collections of images.
In this paper we introduce a semidefinite programming (SDP) formulation,
specially tailored to overcome the clustering phenomenon. We further identify
the implications of parallel rigidity theory for the location estimation
problem to be well-posed, and prove exact (in the noiseless case) and stable
location recovery results. We also formulate an alternating direction method to
solve the resulting semidefinite program, and provide a distributed version of
our formulation for large numbers of locations. Specifically for the camera
location estimation problem, we formulate a pairwise line estimation method
based on robust camera orientation and subspace estimation. Lastly, we
demonstrate the utility of our algorithm through experiments on real images.Comment: 40 pages, 12 figures, 6 tables; notation and some unclear parts
updated, some typos correcte
Separation-Free Spectral Super-Resolution via Convex Optimization
Atomic norm methods have recently been proposed for spectral super-resolution
with flexibility in dealing with missing data and miscellaneous noises. A
notorious drawback of these convex optimization methods however is their lower
resolution in the high signal-to-noise (SNR) regime as compared to conventional
methods such as ESPRIT. In this paper, we devise a simple weighting scheme in
existing atomic norm methods and show that the resolution of the resulting
convex optimization method can be made arbitrarily high in the absence of
noise, achieving the so-called separation-free super-resolution. This is proved
by a novel, kernel-free construction of the dual certificate whose existence
guarantees exact super-resolution using the proposed method. Numerical results
corroborating our analysis are provided.Comment: 19 pages, 6 figure
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