35,401 research outputs found
What the 2008 Stock Market Crash Means for Retirement Security
Compares future retirement resources before and after the stock market decline, by gender, marital status, race/ethnicity, education, and retirement income quintile, under three scenarios: no recovery, full recovery, and partial recovery in ten years
Achievable Angles Between two Compressed Sparse Vectors Under Norm/Distance Constraints Imposed by the Restricted Isometry Property: A Plane Geometry Approach
The angle between two compressed sparse vectors subject to the norm/distance
constraints imposed by the restricted isometry property (RIP) of the sensing
matrix plays a crucial role in the studies of many compressive sensing (CS)
problems. Assuming that (i) u and v are two sparse vectors separated by an
angle thetha, and (ii) the sensing matrix Phi satisfies RIP, this paper is
aimed at analytically characterizing the achievable angles between Phi*u and
Phi*v. Motivated by geometric interpretations of RIP and with the aid of the
well-known law of cosines, we propose a plane geometry based formulation for
the study of the considered problem. It is shown that all the RIP-induced
norm/distance constraints on Phi*u and Phi*v can be jointly depicted via a
simple geometric diagram in the two-dimensional plane. This allows for a joint
analysis of all the considered algebraic constraints from a geometric
perspective. By conducting plane geometry analyses based on the constructed
diagram, closed-form formulae for the maximal and minimal achievable angles are
derived. Computer simulations confirm that the proposed solution is tighter
than an existing algebraic-based estimate derived using the polarization
identity. The obtained results are used to derive a tighter restricted isometry
constant of structured sensing matrices of a certain kind, to wit, those in the
form of a product of an orthogonal projection matrix and a random sensing
matrix. Follow-up applications to three CS problems, namely, compressed-domain
interference cancellation, RIP-based analysis of the orthogonal matching
pursuit algorithm, and the study of democratic nature of random sensing
matrices are investigated.Comment: submitted to IEEE Trans. Information Theor
Joint Reconstruction of Multi-view Compressed Images
The distributed representation of correlated multi-view images is an
important problem that arise in vision sensor networks. This paper concentrates
on the joint reconstruction problem where the distributively compressed
correlated images are jointly decoded in order to improve the reconstruction
quality of all the compressed images. We consider a scenario where the images
captured at different viewpoints are encoded independently using common coding
solutions (e.g., JPEG, H.264 intra) with a balanced rate distribution among
different cameras. A central decoder first estimates the underlying correlation
model from the independently compressed images which will be used for the joint
signal recovery. The joint reconstruction is then cast as a constrained convex
optimization problem that reconstructs total-variation (TV) smooth images that
comply with the estimated correlation model. At the same time, we add
constraints that force the reconstructed images to be consistent with their
compressed versions. We show by experiments that the proposed joint
reconstruction scheme outperforms independent reconstruction in terms of image
quality, for a given target bit rate. In addition, the decoding performance of
our proposed algorithm compares advantageously to state-of-the-art distributed
coding schemes based on disparity learning and on the DISCOVER
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