923 research outputs found
Compressive Source Separation: Theory and Methods for Hyperspectral Imaging
With the development of numbers of high resolution data acquisition systems
and the global requirement to lower the energy consumption, the development of
efficient sensing techniques becomes critical. Recently, Compressed Sampling
(CS) techniques, which exploit the sparsity of signals, have allowed to
reconstruct signal and images with less measurements than the traditional
Nyquist sensing approach. However, multichannel signals like Hyperspectral
images (HSI) have additional structures, like inter-channel correlations, that
are not taken into account in the classical CS scheme. In this paper we exploit
the linear mixture of sources model, that is the assumption that the
multichannel signal is composed of a linear combination of sources, each of
them having its own spectral signature, and propose new sampling schemes
exploiting this model to considerably decrease the number of measurements
needed for the acquisition and source separation. Moreover, we give theoretical
lower bounds on the number of measurements required to perform reconstruction
of both the multichannel signal and its sources. We also proposed optimization
algorithms and extensive experimentation on our target application which is
HSI, and show that our approach recovers HSI with far less measurements and
computational effort than traditional CS approaches.Comment: 32 page
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
Block-Sparse Recovery via Convex Optimization
Given a dictionary that consists of multiple blocks and a signal that lives
in the range space of only a few blocks, we study the problem of finding a
block-sparse representation of the signal, i.e., a representation that uses the
minimum number of blocks. Motivated by signal/image processing and computer
vision applications, such as face recognition, we consider the block-sparse
recovery problem in the case where the number of atoms in each block is
arbitrary, possibly much larger than the dimension of the underlying subspace.
To find a block-sparse representation of a signal, we propose two classes of
non-convex optimization programs, which aim to minimize the number of nonzero
coefficient blocks and the number of nonzero reconstructed vectors from the
blocks, respectively. Since both classes of problems are NP-hard, we propose
convex relaxations and derive conditions under which each class of the convex
programs is equivalent to the original non-convex formulation. Our conditions
depend on the notions of mutual and cumulative subspace coherence of a
dictionary, which are natural generalizations of existing notions of mutual and
cumulative coherence. We evaluate the performance of the proposed convex
programs through simulations as well as real experiments on face recognition.
We show that treating the face recognition problem as a block-sparse recovery
problem improves the state-of-the-art results by 10% with only 25% of the
training data.Comment: IEEE Transactions on Signal Processin
Sampling in the Analysis Transform Domain
Many signal and image processing applications have benefited remarkably from
the fact that the underlying signals reside in a low dimensional subspace. One
of the main models for such a low dimensionality is the sparsity one. Within
this framework there are two main options for the sparse modeling: the
synthesis and the analysis ones, where the first is considered the standard
paradigm for which much more research has been dedicated. In it the signals are
assumed to have a sparse representation under a given dictionary. On the other
hand, in the analysis approach the sparsity is measured in the coefficients of
the signal after applying a certain transformation, the analysis dictionary, on
it. Though several algorithms with some theory have been developed for this
framework, they are outnumbered by the ones proposed for the synthesis
methodology.
Given that the analysis dictionary is either a frame or the two dimensional
finite difference operator, we propose a new sampling scheme for signals from
the analysis model that allows to recover them from their samples using any
existing algorithm from the synthesis model. The advantage of this new sampling
strategy is that it makes the existing synthesis methods with their theory also
available for signals from the analysis framework.Comment: 13 Pages, 2 figure
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