11,124 research outputs found
Compressive Sensing with Local Geometric Features
We propose a framework for compressive sensing of images with local
distinguishable objects, such as stars, and apply it to solve a problem in
celestial navigation. Specifically, let x be an N-pixel real-valued image,
consisting of a small number of local distinguishable objects plus noise. Our
goal is to design an m-by-N measurement matrix A with m << N, such that we can
recover an approximation to x from the measurements Ax.
We construct a matrix A and recovery algorithm with the following properties:
(i) if there are k objects, the number of measurements m is O((k log N)/(log
k)), undercutting the best known bound of O(k log(N/k)) (ii) the matrix A is
very sparse, which is important for hardware implementations of compressive
sensing algorithms, and (iii) the recovery algorithm is empirically fast and
runs in time polynomial in k and log(N).
We also present a comprehensive study of the application of our algorithm to
attitude determination, or finding one's orientation in space. Spacecraft
typically use cameras to acquire an image of the sky, and then identify stars
in the image to compute their orientation. Taking pictures is very expensive
for small spacecraft, since camera sensors use a lot of power. Our algorithm
optically compresses the image before it reaches the camera's array of pixels,
reducing the number of sensors that are required
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
Masking Strategies for Image Manifolds
We consider the problem of selecting an optimal mask for an image manifold,
i.e., choosing a subset of the pixels of the image that preserves the
manifold's geometric structure present in the original data. Such masking
implements a form of compressive sensing through emerging imaging sensor
platforms for which the power expense grows with the number of pixels acquired.
Our goal is for the manifold learned from masked images to resemble its full
image counterpart as closely as possible. More precisely, we show that one can
indeed accurately learn an image manifold without having to consider a large
majority of the image pixels. In doing so, we consider two masking methods that
preserve the local and global geometric structure of the manifold,
respectively. In each case, the process of finding the optimal masking pattern
can be cast as a binary integer program, which is computationally expensive but
can be approximated by a fast greedy algorithm. Numerical experiments show that
the relevant manifold structure is preserved through the data-dependent masking
process, even for modest mask sizes
How to find real-world applications for compressive sensing
The potential of compressive sensing (CS) has spurred great interest in the
research community and is a fast growing area of research. However, research
translating CS theory into practical hardware and demonstrating clear and
significant benefits with this hardware over current, conventional imaging
techniques has been limited. This article helps researchers to find those niche
applications where the CS approach provides substantial gain over conventional
approaches by articulating lessons learned in finding one such application; sea
skimming missile detection. As a proof of concept, it is demonstrated that a
simplified CS missile detection architecture and algorithm provides comparable
results to the conventional imaging approach but using a smaller FPA. The
primary message is that all of the excitement surrounding CS is necessary and
appropriate for encouraging our creativity but we all must also take off our
"rose colored glasses" and critically judge our ideas, methods and results
relative to conventional imaging approaches.Comment: 10 page
Building profile reconstruction using TerraSAR-X data time-series and tomographic techniques
This work aims to show the potentialities of SAR Tomography (TomoSAR) techniques for the 3-D characterization (height, reflectivity, time stability) of built-up areas using data acquired by the satellite sensor TerraSAR-X. For this purpose 19 TerraSAR-X single-polarimetric multibaseline images acquired over Paris urban area have been processed applying classical nonparametric (Beamforming and Capon) and parametric (MUSIC) spectral estimation techniques
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