25,026 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
Two are better than one: Fundamental parameters of frame coherence
This paper investigates two parameters that measure the coherence of a frame:
worst-case and average coherence. We first use worst-case and average coherence
to derive near-optimal probabilistic guarantees on both sparse signal detection
and reconstruction in the presence of noise. Next, we provide a catalog of
nearly tight frames with small worst-case and average coherence. Later, we find
a new lower bound on worst-case coherence; we compare it to the Welch bound and
use it to interpret recently reported signal reconstruction results. Finally,
we give an algorithm that transforms frames in a way that decreases average
coherence without changing the spectral norm or worst-case coherence
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