658 research outputs found
Compressive Signal Processing with Circulant Sensing Matrices
Compressive sensing achieves effective dimensionality reduction of signals,
under a sparsity constraint, by means of a small number of random measurements
acquired through a sensing matrix. In a signal processing system, the problem
arises of processing the random projections directly, without first
reconstructing the signal. In this paper, we show that circulant sensing
matrices allow to perform a variety of classical signal processing tasks such
as filtering, interpolation, registration, transforms, and so forth, directly
in the compressed domain and in an exact fashion, \emph{i.e.}, without relying
on estimators as proposed in the existing literature. The advantage of the
techniques presented in this paper is to enable direct
measurement-to-measurement transformations, without the need of costly recovery
procedures
Experimental and Numerical Investigations of Novel Architectures Applied to Compressive Imaging Systems
A recent breakthrough in information theory known as compressive sensing is one component of an ongoing revolution in data acquisition and processing that guides one to acquire less data yet still recover the same amount of information as traditional techniques, meaning less resources such as time, detector cost, or power are required. Starting from these basic principles, this thesis explores the application of these techniques to imaging. The first laboratory example we introduce is a simple infrared camera. Then we discuss the application of compressive sensing techniques to hyperspectral microscopy, specifically Raman microscopy, which should prove to be a powerful technique to bring the acquisition time for such microscopies down from hours to minutes. Next we explore a novel sensing architecture that uses partial circulant matrices as sensing matrices, which results in a simplified, more robust imaging system. The results of these imaging experiments lead to questions about the performance and fundamental nature of sparse signal recovery with partial circulant compressive sensing matrices. Thus, we present the results of a suite of numerical experiments that show some surprising and suggestive results that could stimulate further theoretical and applied research of partial circulant compressive sensing matrices. We conclude with a look ahead to adaptive sensing procedures that allow real-time, interactive optical signal processing to further reduce the resource demands of an imaging system
Performance analysis of compressive sensing recovery algorithms for image processing using block processing
The modern digital world comprises of transmitting media files like image, audio, and video which leads to usage of large memory storage, high data transmission rate, and a lot of sensory devices. Compressive sensing (CS) is a sampling theory that compresses the signal at the time of acquiring it. Compressive sensing samples the signal efficiently below the Nyquist rate to minimize storage and recoveries back the signal significantly minimizing the data rate and few sensors. The proposed paper proceeds with three phases. The first phase describes various measurement matrices like Gaussian matrix, circulant matrix, and special random matrices which are the basic foundation of compressive sensing technique that finds its application in various fields like wireless sensors networks (WSN), internet of things (IoT), video processing, biomedical applications, and many. Finally, the paper analyses the performance of the various reconstruction algorithms of compressive sensing like basis pursuit (BP), compressive sampling matching pursuit (CoSaMP), iteratively reweighted least square (IRLS), iterative hard thresholding (IHT), block processing-based basis pursuit (BP-BP) based onmean square error (MSE), and peak signal to noise ratio (PSNR) and then concludes with future works
GPU-Accelerated Algorithms for Compressed Signals Recovery with Application to Astronomical Imagery Deblurring
Compressive sensing promises to enable bandwidth-efficient on-board
compression of astronomical data by lifting the encoding complexity from the
source to the receiver. The signal is recovered off-line, exploiting GPUs
parallel computation capabilities to speedup the reconstruction process.
However, inherent GPU hardware constraints limit the size of the recoverable
signal and the speedup practically achievable. In this work, we design parallel
algorithms that exploit the properties of circulant matrices for efficient
GPU-accelerated sparse signals recovery. Our approach reduces the memory
requirements, allowing us to recover very large signals with limited memory. In
addition, it achieves a tenfold signal recovery speedup thanks to ad-hoc
parallelization of matrix-vector multiplications and matrix inversions.
Finally, we practically demonstrate our algorithms in a typical application of
circulant matrices: deblurring a sparse astronomical image in the compressed
domain
Compressive Pattern Matching on Multispectral Data
We introduce a new constrained minimization problem that performs template
and pattern detection on a multispectral image in a compressive sensing
context. We use an original minimization problem from Guo and Osher that uses
minimization techniques to perform template detection in a multispectral
image. We first adapt this minimization problem to work with compressive
sensing data. Then we extend it to perform pattern detection using a formal
transform called the spectralization along a pattern. That extension brings out
the problem of measurement reconstruction. We introduce shifted measurements
that allow us to reconstruct all the measurement with a small overhead and we
give an optimality constraint for simple patterns. We present numerical results
showing the performances of the original minimization problem and the
compressed ones with different measurement rates and applied on remotely sensed
data.Comment: Published in IEEE Transactions on Geoscience and Remote Sensin
Modulated Unit-Norm Tight Frames for Compressed Sensing
In this paper, we propose a compressed sensing (CS) framework that consists
of three parts: a unit-norm tight frame (UTF), a random diagonal matrix and a
column-wise orthonormal matrix. We prove that this structure satisfies the
restricted isometry property (RIP) with high probability if the number of
measurements for -sparse signals of length
and if the column-wise orthonormal matrix is bounded. Some existing structured
sensing models can be studied under this framework, which then gives tighter
bounds on the required number of measurements to satisfy the RIP. More
importantly, we propose several structured sensing models by appealing to this
unified framework, such as a general sensing model with arbitrary/determinisic
subsamplers, a fast and efficient block compressed sensing scheme, and
structured sensing matrices with deterministic phase modulations, all of which
can lead to improvements on practical applications. In particular, one of the
constructions is applied to simplify the transceiver design of CS-based channel
estimation for orthogonal frequency division multiplexing (OFDM) systems.Comment: submitted to IEEE Transactions on Signal Processin
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