1,947 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
Analysis of Basis Pursuit Via Capacity Sets
Finding the sparsest solution for an under-determined linear system
of equations is of interest in many applications. This problem is
known to be NP-hard. Recent work studied conditions on the support size of
that allow its recovery using L1-minimization, via the Basis Pursuit
algorithm. These conditions are often relying on a scalar property of
called the mutual-coherence. In this work we introduce an alternative set of
features of an arbitrarily given , called the "capacity sets". We show how
those could be used to analyze the performance of the basis pursuit, leading to
improved bounds and predictions of performance. Both theoretical and numerical
methods are presented, all using the capacity values, and shown to lead to
improved assessments of the basis pursuit success in finding the sparest
solution of
A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
Demixing problems in many areas such as hyperspectral imaging and
differential optical absorption spectroscopy (DOAS) often require finding
sparse nonnegative linear combinations of dictionary elements that match
observed data. We show how aspects of these problems, such as misalignment of
DOAS references and uncertainty in hyperspectral endmembers, can be modeled by
expanding the dictionary with grouped elements and imposing a structured
sparsity assumption that the combinations within each group should be sparse or
even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain
good solutions using convex or greedy methods, such as non-negative least
squares (NNLS) or orthogonal matching pursuit. We use penalties related to the
Hoyer measure, which is the ratio of the and norms, as sparsity
penalties to be added to the objective in NNLS-type models. For solving the
resulting nonconvex models, we propose a scaled gradient projection algorithm
that requires solving a sequence of strongly convex quadratic programs. We
discuss its close connections to convex splitting methods and difference of
convex programming. We also present promising numerical results for example
DOAS analysis and hyperspectral demixing problems.Comment: 38 pages, 14 figure
Image registration with sparse approximations in parametric dictionaries
We examine in this paper the problem of image registration from the new
perspective where images are given by sparse approximations in parametric
dictionaries of geometric functions. We propose a registration algorithm that
looks for an estimate of the global transformation between sparse images by
examining the set of relative geometrical transformations between the
respective features. We propose a theoretical analysis of our registration
algorithm and we derive performance guarantees based on two novel important
properties of redundant dictionaries, namely the robust linear independence and
the transformation inconsistency. We propose several illustrations and insights
about the importance of these dictionary properties and show that common
properties such as coherence or restricted isometry property fail to provide
sufficient information in registration problems. We finally show with
illustrative experiments on simple visual objects and handwritten digits images
that our algorithm outperforms baseline competitor methods in terms of
transformation-invariant distance computation and classification
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