Compressive Sensing for 3D Data Processing Tasks: Applications, Models and Algorithms

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dc.contributor.advisorZhang, Yinen_US
dc.creatorLi, Chengboen_US
dc.date.accessioned2013-03-08T00:35:48Zen_US
dc.date.available2013-03-08T00:35:48Zen_US
dc.date.issued2012en_US
dc.description.abstractCompressive sensing (CS) is a novel sampling methodology representing a paradigm shift from conventional data acquisition schemes. The theory of compressive sensing ensures that under suitable conditions compressible signals or images can be reconstructed from far fewer samples or measurements than what are required by the Nyquist rate. So far in the literature, most works on CS concentrate on one-dimensional or two-dimensional data. However, besides involving far more data, three-dimensional (3D) data processing does have particularities that require the development of new techniques in order to make successful transitions from theoretical feasibilities to practical capacities. This thesis studies several issues arising from the applications of the CS methodology to some 3D image processing tasks. Two specific applications are hyperspectral imaging and video compression where 3D images are either directly unmixed or recovered as a whole from CS samples. The main issues include CS decoding models, preprocessing techniques and reconstruction algorithms, as well as CS encoding matrices in the case of video compression. Our investigation involves three major parts. (1) Total variation (TV) regularization plays a central role in the decoding models studied in this thesis. To solve such models, we propose an efficient scheme to implement the classic augmented Lagrangian multiplier method and study its convergence properties. The resulting Matlab package TVAL3 is used to solve several models. Computational results show that, thanks to its low per-iteration complexity, the proposed algorithm is capable of handling realistic 3D image processing tasks. (2) Hyperspectral image processing typically demands heavy computational resources due to an enormous amount of data involved. We investigate low-complexity procedures to unmix, sometimes blindly, CS compressed hyperspectral data to directly obtain material signatures and their abundance fractions, bypassing the high-complexity task of reconstructing the image cube itself. (3) To overcome the "cliff effect" suffered by current video coding schemes, we explore a compressive video sampling framework to improve scalability with respect to channel capacities. We propose and study a novel multi-resolution CS encoding matrix, and a decoding model with a TV-DCT regularization function. Extensive numerical results are presented, obtained from experiments that use not only synthetic data, but also real data measured by hardware. The results establish feasibility and robustness, to various extent, of the proposed 3D data processing schemes, models and algorithms. There still remain many challenges to be further resolved in each area, but hopefully the progress made in this thesis will represent a useful first step towards meeting these challenges in the future.en_US
dc.format.extent166 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoTHESIS MATH.SCI. 2012 LIen_US
dc.identifier.citationLi, Chengbo. "Compressive Sensing for 3D Data Processing Tasks: Applications, Models and Algorithms." (2012) Diss., Rice University. <a href="https://hdl.handle.net/1911/70314">https://hdl.handle.net/1911/70314</a>.en_US
dc.identifier.digitalLiCen_US
dc.identifier.urihttps://hdl.handle.net/1911/70314en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectApplied sciencesen_US
dc.subjectCompressive sensingen_US
dc.subjectData processingen_US
dc.subjectHyperspectral imagingen_US
dc.subjectConvex optimizationen_US
dc.subjectScalable video codingen_US
dc.subjectTotal variation regularizationen_US
dc.subjectApplied mathematicsen_US
dc.subjectElectrical engineeringen_US
dc.titleCompressive Sensing for 3D Data Processing Tasks: Applications, Models and Algorithmsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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