5,999 research outputs found
Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements
This paper addresses the problem of distributed coding of images whose
correlation is driven by the motion of objects or positioning of the vision
sensors. It concentrates on the problem where images are encoded with
compressed linear measurements. We propose a geometry-based correlation model
in order to describe the common information in pairs of images. We assume that
the constitutive components of natural images can be captured by visual
features that undergo local transformations (e.g., translation) in different
images. We first identify prominent visual features by computing a sparse
approximation of a reference image with a dictionary of geometric basis
functions. We then pose a regularized optimization problem to estimate the
corresponding features in correlated images given by quantized linear
measurements. The estimated features have to comply with the compressed
information and to represent consistent transformation between images. The
correlation model is given by the relative geometric transformations between
corresponding features. We then propose an efficient joint decoding algorithm
that estimates the compressed images such that they stay consistent with both
the quantized measurements and the correlation model. Experimental results show
that the proposed algorithm effectively estimates the correlation between
images in multi-view datasets. In addition, the proposed algorithm provides
effective decoding performance that compares advantageously to independent
coding solutions as well as state-of-the-art distributed coding schemes based
on disparity learning
One-bit compressive sensing with norm estimation
Consider the recovery of an unknown signal from quantized linear
measurements. In the one-bit compressive sensing setting, one typically assumes
that is sparse, and that the measurements are of the form
. Since such
measurements give no information on the norm of , recovery methods from
such measurements typically assume that . We show that if one
allows more generally for quantized affine measurements of the form
, and if the vectors
are random, an appropriate choice of the affine shifts allows
norm recovery to be easily incorporated into existing methods for one-bit
compressive sensing. Additionally, we show that for arbitrary fixed in
the annulus , one may estimate the norm up to additive error from
such binary measurements through a single evaluation of the inverse Gaussian
error function. Finally, all of our recovery guarantees can be made universal
over sparse vectors, in the sense that with high probability, one set of
measurements and thresholds can successfully estimate all sparse vectors
within a Euclidean ball of known radius.Comment: 20 pages, 2 figure
Robust 1-Bit Compressed Sensing via Hinge Loss Minimization
This work theoretically studies the problem of estimating a structured
high-dimensional signal from noisy -bit Gaussian
measurements. Our recovery approach is based on a simple convex program which
uses the hinge loss function as data fidelity term. While such a risk
minimization strategy is very natural to learn binary output models, such as in
classification, its capacity to estimate a specific signal vector is largely
unexplored. A major difficulty is that the hinge loss is just piecewise linear,
so that its "curvature energy" is concentrated in a single point. This is
substantially different from other popular loss functions considered in signal
estimation, e.g., the square or logistic loss, which are at least locally
strongly convex. It is therefore somewhat unexpected that we can still prove
very similar types of recovery guarantees for the hinge loss estimator, even in
the presence of strong noise. More specifically, our non-asymptotic error
bounds show that stable and robust reconstruction of can be achieved with
the optimal oversampling rate in terms of the number of
measurements . Moreover, we permit a wide class of structural assumptions on
the ground truth signal, in the sense that can belong to an arbitrary
bounded convex set . The proofs of our main results
rely on some recent advances in statistical learning theory due to Mendelson.
In particular, we invoke an adapted version of Mendelson's small ball method
that allows us to establish a quadratic lower bound on the error of the first
order Taylor approximation of the empirical hinge loss function
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