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1 
Applications of NonTraditional Measurements for Computational ImagingTreeaporn, Vicha, Treeaporn, Vicha January 2017 (has links)
Imaging systems play an important role in many diverse applications. Requirements for these applications, however, can lead to complex or suboptimal designs. Traditionally, imaging systems are designed to yield a visually pleasing representation, or "pretty picture", of the scene or object. Often this is because a human operator is viewing the acquired image to perform a specific task. With digital computers increasingly being used for automation, a large number of algorithms have been designed to accept as input a pretty picture. This isomorphic representation however is neither necessary nor optimal for tasks such as data compression, transmission, pattern recognition or classification. This disconnect between optical measurement and post processing for the final system outcome has motivated an interest in computational imaging (CI). In a CI system the optical subsystem and postprocessing subsystem is jointly designed to optimize system performance for a specific task. In these hybrid imagers, the measured image may no longer be a pretty picture but rather an intermediate nontraditional measurement. In this work, applications of nontraditional measurements are considered for computational imaging. Two systems for an image reconstruction task are studied and one system for a detection task is investigated. First, a CI system to extend the field of view is analyzed and an experimental prototype demonstrated. This prototype validates the simulation study and is designed to yield a 3x field of view improvement relative to a conventional imager. Second, a CI system to acquire timevarying natural scenes, i.e. video, is developed. A candidate system using 8x8x16 spatiotemporal blocks yields about 292x compression compared to a conventional imager. Candidate electrooptical architectures, including chargedomain processing, to implement this approach are also discussed. Lastly, a CI system with xray pencil beam illumination is investigated for a detection task where system performance is quantified using an informationtheoretic metric.

2 
Compressive sensing using lp optimizationPant, Jeevan Kumar 26 April 2012 (has links)
Three problems in compressive sensing, namely, recovery of sparse signals from noisefree measurements, recovery of sparse signals from noisy measurements, and recovery of so called blocksparse signals from noisy measurements, are investigated.
In Chapter 2, the reconstruction of sparse signals from noisefree measurements is investigated and three algorithms are developed. The first and second algorithms minimize the approximate L0 and Lp pseudonorms, respectively, in the null space of the measurement matrix using a sequential quasiNewton algorithm. An efficient line search based on Banach's fixedpoint theorem is developed and applied in the second algorithm. The third algorithm minimizes the approximate Lp pseudonorm in the null space by using a sequential conjugategradient (CG) algorithm. Simulation results are presented which demonstrate that the proposed algorithms yield improved signal reconstruction performance relative to that of the iterative reweighted (IR), smoothed L0 (SL0), and L1minimization based algorithms. They also require a reduced amount of computations relative to the IR and L1minimization based algorithms. The Lpminimization based algorithms require less computation than the SL0 algorithm.
In Chapter 3, the reconstruction of sparse signals and images from noisy measurements is investigated. First, two algorithms for the reconstruction of signals are developed by minimizing an Lppseudonorm regularized squared error as the objective function using the sequential optimization procedure developed in Chapter 2. The first algorithm minimizes the objective function by taking steps along descent directions that are computed in the null space of the measurement matrix and its complement space. The second algorithm minimizes the objective function in the time domain by using a CG algorithm. Second, the well known total variation (TV) norm has been extended to a nonconvex version called the TVp pseudonorm and an algorithm for the reconstruction of images is developed that involves minimizing a TVppseudonorm regularized squared error using a sequential FletcherReeves' CG algorithm. Simulation results are presented which demonstrate that the first two algorithms yield improved signal reconstruction performance relative to the IR, SL0, and L1minimization based algorithms and require a reduced amount of computation relative to the IR and L1minimization based algorithms. The TVpminimization based algorithm yields improved image reconstruction performance and a reduced amount of computation relative to Romberg's algorithm.
In Chapter 4, the reconstruction of socalled blocksparse signals is investigated. The L2/1 norm is extended to a nonconvex version, called the L2/p pseudonorm, and an algorithm based on the minimization of an L2/ppseudonorm regularized squared error is developed. The minimization is carried out using a sequential FletcherReeves' CG algorithm and the line search described in Chapter 2. A reweighting technique for the reduction of amount of computation and a method to use prior information about the locations of nonzero blocks for the improvement in signal reconstruction performance are also proposed. Simulation results are presented which demonstrate that the proposed algorithm yields improved reconstruction performance and requires a reduced amount of computation relative to the L2/1minimization based, block orthogonal matching pursuit, IR, and L1minimization based algorithms. / Graduate

3 
Stochastic Modelling of a Collection of Correlated Sparse Signals and its Recovery via Belief Propagation MethodsLee, Jefferson 14 December 2011 (has links)
The field of compressive sensing deals with the recovery of a sparse signal from a small
set of measurements or linear projections of the signal. In this thesis, we introduce a
stochastic framework that allows a collection of correlated sparse signals to be recovered
by exploiting both intra and inter signal correlation. Our approach differs from others by not assuming that the collection of sparse signals have a common support or a common
component; in some cases, this assumption does not hold true. Imagine a simplified
cognitive radio problem, where users can send a single tone (sinewave) in a finite number
of frequencies; it is desired to find the used frequencies over a large area (creation of a radio map). This is a sparse problem; however, as we move spatially, the occuppied
frequencies change, thus voiding the assumption of a common support/component.
Our solution to multi sparse signal recovery addresses this problem, where signals
that are close geographically are highly correlated and their support gradually changes as the distance between signals grow. Our approach consists of the creation of a probabilistic model that accounts for inter and intra signal correlation and then using belief propagation to calculate the posterior distribution of the signals and perform recovery.

4 
Stochastic Modelling of a Collection of Correlated Sparse Signals and its Recovery via Belief Propagation MethodsLee, Jefferson 14 December 2011 (has links)
The field of compressive sensing deals with the recovery of a sparse signal from a small
set of measurements or linear projections of the signal. In this thesis, we introduce a
stochastic framework that allows a collection of correlated sparse signals to be recovered
by exploiting both intra and inter signal correlation. Our approach differs from others by not assuming that the collection of sparse signals have a common support or a common
component; in some cases, this assumption does not hold true. Imagine a simplified
cognitive radio problem, where users can send a single tone (sinewave) in a finite number
of frequencies; it is desired to find the used frequencies over a large area (creation of a radio map). This is a sparse problem; however, as we move spatially, the occuppied
frequencies change, thus voiding the assumption of a common support/component.
Our solution to multi sparse signal recovery addresses this problem, where signals
that are close geographically are highly correlated and their support gradually changes as the distance between signals grow. Our approach consists of the creation of a probabilistic model that accounts for inter and intra signal correlation and then using belief propagation to calculate the posterior distribution of the signals and perform recovery.

5 
Calibration of High Dimensional Compressive Sensing Systems: A Case Study in Compressive Hyperspectral ImagingPoon, Phillip, Dunlop, Matthew 10 1900 (has links)
ITC/USA 2013 Conference Proceedings / The FortyNinth Annual International Telemetering Conference and Technical Exhibition / October 2124, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / Compressive Sensing (CS) is a set of techniques that can faithfully acquire a signal from sub Nyquist measurements, provided the class of signals have certain broadlyapplicable properties. Reconstruction (or exploitation) of the signal from these subNyquist measurements requires a forward model  knowledge of how the system maps signals to measurements. In highdimensional CS systems, determination of this forward model via direct measurement of the system response to the complete set of impulse functions is impractical. In this paper, we will discuss the development of a parameterized forward model for the Adaptive, FeatureSpecific Spectral Imaging Classifier (AFSSIC), an experimental compressive spectral image classifier. This parameterized forward model drastically reduces the number of calibration measurements.

6 
Quantifying the Gains of Compressive Sensing for Telemetering ApplicationsDavis, Philip 10 1900 (has links)
ITC/USA 2011 Conference Proceedings / The FortySeventh Annual International Telemetering Conference and Technical Exhibition / October 2427, 2011 / Bally's Las Vegas, Las Vegas, Nevada / In this paper we study a new streaming Compressive Sensing (CS) technique that aims to replace high speed Analog to Digital Converters (ADC) for certain classes of signals and reduce the artifacts that arise from block processing when conventional CS is applied to continuous signals. We compare the performance of both streaming and block processing methods on several types of signals and quantify the signal reconstruction quality when packet loss is applied to the transmitted sampled data.

7 
Compressive Sensing for Feedback Reduction in Wireless Multiuser NetworksElkhalil, Khalil 05 1900 (has links)
User/relay selection is a simple technique that achieves spatial diversity in multiuser networks. However, for user/relay selection algorithms to make a selection decision, channel state information (CSI) from all cooperating users/relays is usually required at a central node. This requirement poses two important challenges. Firstly, CSI acquisition generates a great deal of feedback overhead (airtime) that could result in significant transmission delays. Secondly, the fedback channel information is usually corrupted by additive noise. This could lead to transmission outages if the central node selects the set of cooperating relays based on inaccurate feedback information.
Motivated by the aforementioned challenges, we propose a limited feedback user/relay selection scheme that is based on the theory of compressed sensing. Firstly, we introduce a limited feedback relay selection algorithm for a multicast relay network. The proposed algorithm exploits the theory of compressive sensing to first obtain the identity of the “strong” relays with limited feedback airtime. Following that, the CSI of the selected relays is estimated using minimum mean square error estimation without any additional feedback. To minimize the effect of noise on the fedback CSI, we introduce a backoff strategy that optimally backsoff on the noisy received CSI.
In the second part of the thesis, we propose a feedback reduction scheme for fullduplex relayaided multiuser networks. The proposed scheme permits the base station (BS) to obtain channel state information (CSI) from a subset of strong users under substantially reduced feedback overhead. More specifically, we cast the problem of user identification and CSI estimation as a block sparse signal recovery problem in compressive sensing (CS). Using existing CS block recovery algorithms, we first obtain the identity of the strong users and then estimate their CSI using the best linear unbiased estimator (BLUE). Moreover, we derive the error covariance matrix of the postdetection noise to be used in the backoff strategy. In addition to this, we provide exact closed form expressions for the average maximum equivalent SNR at the destination user.
The last part of the thesis treats the problem of user selection in a network MIMO setting. We propose a distributed user selection strategy that is based on a well known technique called semiorthogonal user selection when the zeroforcing beamforming (ZFBF) is adopted. Usually this technique requires perfect channel state information at the transmitter (CSIT) which might not be available or need large feedback overhead. Instead, we propose a distributed user selection technique where no communication between base stations is needed. In order to reduce the feedback overhead, each user set a timer that is inversely proportional to his channel quality indicator (CQI). This technique will allow only the user with the highest CQI to feedback provided that the transmission time is shorter than the difference between his timer and the second strongest user timer, otherwise a collision will occur. In the case of collision, we propose another feedback strategy that is based on the theory of compressive sensing, where collision is allowed and each user encode its feedback using Gaussian codewords and feedback the combination at the same time with other users. We prove that the problem can be formulated as a block sparse recovery problem and that this approach is agnostic on the transmission time, thus it could be a good alternative to the timer approach when collision is dominant. Simulation results show that the proposed CSbased selection algorithms yield a rate performance that is close to the ones achieved when perfect CSI is available while consuming a small amount of feedback.

8 
From Theory to Practice: Randomly Sampled Arrays for Passive RadarElgayar, Saad M. January 2017 (has links)
No description available.

9 
On Invertibility of the Radon Transform and Compressive SensingAndersson, Joel January 2014 (has links)
This thesis contains three articles. The first two concern inversion andlocal injectivity of the weighted Radon transform in the plane. The thirdpaper concerns two of the key results from compressive sensing.In Paper A we prove an identity involving three singular double integrals.This is then used to prove an inversion formula for the weighted Radon transform,allowing all weight functions that have been considered previously.Paper B is devoted to stability estimates of the standard and weightedlocal Radon transform. The estimates will hold for functions that satisfy an apriori bound. When weights are involved they must solve a certain differentialequation and fulfill some regularity assumptions.In Paper C we present some new constant bounds. Firstly we presenta version of the theorem of uniform recovery of random sampling matrices,where explicit constants have not been presented before. Secondly we improvethe condition when the socalled restricted isometry property implies the nullspace property. / <p>QC 20140228</p>

10 
A compressive sensing approach to solving nonogramsLopez, Oscar Fabian 12 December 2013 (has links)
A nonogram is a logic puzzle where one shades certain cells of a 2D grid to reveal a hidden image. One uses the sequences of numbers on the left and the top of the grid to figure out how many and which cells to shade. We propose a new technique to solve a nonogram using compressive sensing. Our method avoids (1) partial fillins, (2) heuristics, and (3) overcomplication, and only requires that we solve a binary integer programming problem. / text

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