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LABELED SAMPLING CONSENSUS: A NOVEL ALGORITHM FOR ROBUSTLY FITTING MULTIPLE STRUCTURES USING COMPRESSED SAMPLING
Title
LABELED SAMPLING CONSENSUS: A NOVEL ALGORITHM FOR ROBUSTLY FITTING MULTIPLE STRUCTURES USING COMPRESSED SAMPLING.
Creator
Messina, Carl, Foroosh, Hassan, University of Central Florida
Abstract / Description
The ability to robustly fit structures in datasets that contain outliers is a very important task in Image Processing, Pattern Recognition and Computer Vision. Random Sampling Consensus or RANSAC is a very popular method for this task, due to its ability to handle over 50% outliers. The problem with RANSAC is that it is only capable of finding a single structure. Therefore, if a dataset contains multiple structures, they must be found sequentially by finding the best fit, removing the points,...
Show moreThe ability to robustly fit structures in datasets that contain outliers is a very important task in Image Processing, Pattern Recognition and Computer Vision. Random Sampling Consensus or RANSAC is a very popular method for this task, due to its ability to handle over 50% outliers. The problem with RANSAC is that it is only capable of finding a single structure. Therefore, if a dataset contains multiple structures, they must be found sequentially by finding the best fit, removing the points, and repeating the process. However, removing incorrect points from the dataset could prove disastrous. This thesis offers a novel approach to sampling consensus that extends its ability to discover multiple structures in a single iteration through the dataset. The process introduced is an unsupervised method, requiring no previous knowledge to the distribution of the input data. It uniquely assigns labels to different instances of similar structures. The algorithm is thus called Labeled Sampling Consensus or L-SAC. These unique instances will tend to cluster around one another allowing the individual structures to be extracted using simple clustering techniques. Since divisions instead of modes are analyzed, only a single instance of a structure need be recovered. This ability of L-SAC allows a novel sampling procedure to be presented "compressing" the required samples needed compared to traditional sampling schemes while ensuring all structures have been found. L-SAC is a flexible framework that can be applied to many problem domains.
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Date Issued
2011
Identifier
CFE0003893, ucf:48727
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0003893
Compressive Sensing and Recovery of Structured Sparse Signals
Title
Compressive Sensing and Recovery of Structured Sparse Signals.
Creator
Shahrasbi, Behzad, Rahnavard, Nazanin, Vosoughi, Azadeh, Wei, Lei, Atia, George, Pensky, Marianna, University of Central Florida
Abstract / Description
In the recent years, numerous disciplines including telecommunications, medical imaging, computational biology, and neuroscience benefited from increasing applications of high dimensional datasets. This calls for efficient ways of data capturing and data processing. Compressive sensing (CS), which is introduced as an efficient sampling (data capturing) method, is addressing this need. It is well-known that the signals, which belong to an ambient high-dimensional space, have much smaller...
Show moreIn the recent years, numerous disciplines including telecommunications, medical imaging, computational biology, and neuroscience benefited from increasing applications of high dimensional datasets. This calls for efficient ways of data capturing and data processing. Compressive sensing (CS), which is introduced as an efficient sampling (data capturing) method, is addressing this need. It is well-known that the signals, which belong to an ambient high-dimensional space, have much smaller dimensionality in an appropriate domain. CS taps into this principle and dramatically reduces the number of samples that is required to be captured to avoid any distortion in the information content of the data. This reduction in the required number of samples enables many new applications that were previously infeasible using classical sampling techniques.Most CS-based approaches take advantage of the inherent low-dimensionality in many datasets. They try to determine a sparse representation of the data, in an appropriately chosen basis using only a few significant elements. These approaches make no extra assumptions regarding possible relationships among the significant elements of that basis. In this dissertation, different ways of incorporating the knowledge about such relationships are integrated into the data sampling and the processing schemes.We first consider the recovery of temporally correlated sparse signals and show that using the time correlation model. The recovery performance can be significantly improved. Next, we modify the sampling process of sparse signals to incorporate the signal structure in a more efficient way. In the image processing application, we show that exploiting the structure information in both signal sampling and signal recovery improves the efficiency of the algorithm. In addition, we show that region-of-interest information can be included in the CS sampling and recovery steps to provide a much better quality for the region-of-interest area compared the rest of the image or video. In spectrum sensing applications, CS can dramatically improve the sensing efficiency by facilitating the coordination among spectrum sensors. A cluster-based spectrum sensing with coordination among spectrum sensors is proposed for geographically disperse cognitive radio networks. Further, CS has been exploited in this problem for simultaneous sensing and localization. Having access to this information dramatically facilitates the implementation of advanced communication technologies as required by 5G communication networks.
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Date Issued
2015
Identifier
CFE0006392, ucf:51509
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0006392
Spatial and Temporal Compressive Sensing for Vibration-based Monitoring: Fundamental Studies with Beam Vibrations
Title
Spatial and Temporal Compressive Sensing for Vibration-based Monitoring: Fundamental Studies with Beam Vibrations.
Creator
Ganesan, Vaahini, Das, Tuhin, Kauffman, Jeffrey L., Raghavan, Seetha, University of Central Florida
Abstract / Description
Vibration data from mechanical systems carry important information that is useful for characterization and diagnosis. Standard approaches rely on continually streaming data at a fixed sampling frequency. For applications involving continuous monitoring, such as Structural Health Monitoring (SHM), such approaches result in high data volume and require powering sensors for prolonged duration. Furthermore, adequate spatial resolution, typically involves instrumenting structures with a large...
Show moreVibration data from mechanical systems carry important information that is useful for characterization and diagnosis. Standard approaches rely on continually streaming data at a fixed sampling frequency. For applications involving continuous monitoring, such as Structural Health Monitoring (SHM), such approaches result in high data volume and require powering sensors for prolonged duration. Furthermore, adequate spatial resolution, typically involves instrumenting structures with a large array of sensors. This research shows that applying Compressive Sensing (CS) can significantly reduce both the volume of data and number of sensors in vibration monitoring applications. Random sampling and the inherent sparsity of vibration signals in the frequency domain enables this reduction. Additionally, by exploiting the sparsity of mode shapes, CS can also enable efficient spatial reconstruction using fewer spatially distributed sensors than a traditional approach. CS can thereby reduce the cost and power requirement of sensing as well as streamline data storage and processing in monitoring applications. In well-instrumented structures, CS can enable continuous monitoring in case of sensor or computational failures. The scope of this research was to establish CS as a viable method for SHM with application to beam vibrations. Finite element based simulations demonstrated CS-based frequency recovery from free vibration response of simply supported, fixed-fixed and cantilever beams. Specifically, CS was used to detect shift in natural frequencies of vibration due to structural change using considerably less data than required by traditional sampling. Experimental results using a cantilever beam provided further insight into this approach. In the experimental study, impulse response of the beam was used to recover natural frequencies of vibration with CS. It was shown that CS could discern changes in natural frequencies under modified beam parameters. When the basis functions were modified to accommodate the effect of damping, the performance of CS-based recovery further improved. Effect of noise in CS-based frequency recovery was also studied. In addition to incorporating damping, formulating noise-handling as a part of the CS algorithm for beam vibrations facilitated detecting shift in frequencies from even fewer samples. In the spatial domain, CS was primarily developed to focus on image processing applications, where the signals and basis functions are very different from those required for mechanical beam vibrations. Therefore, it mandated reformulation of the CS problem that would handle related challenges and enable the reconstruction of spatial beam response using very few sensor data. Specifically, this research addresses CS-based reconstruction of deflection shape of beams with fixed boundary conditions. Presence of a fixed end makes hyperbolic terms indispensable in the basis, which in turn causes numerical inconsistencies. Two approaches are discussed to mitigate this problem. The first approach is to restrict the hyperbolic terms in the basis to lower frequencies to ensure well conditioning. The second, a more systematic approach, is to generate an augmented basis function that will combine harmonic and hyperbolic terms. At higher frequencies, the combined hyperbolic terms will limit each other's magnitude, thus ensuring boundedness. This research thus lays the foundation for formulating the CS problem for the field of mechanical vibrations. It presents fundamental studies and discusses open-ended challenges while implementing CS to this field that will pave way for further research.
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Date Issued
2017
Identifier
CFE0007120, ucf:51954
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0007120