Sparse representations of signals for information recovery from incomplete data

Filipović, Marko (2013) Sparse representations of signals for information recovery from incomplete data. Doctoral thesis, Sveučilište u Zagrebu, Prirodoslovno-matematički fakultet.

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Abstract

Mathematical modeling of inverse problems in imaging, such as inpainting, deblurring and denoising, results in ill-posed, i.e. underdetermined linearsystems. Sparseness constraintis used often to regularize these problems.That is because many classes of discrete signals (e.g. naturalimages), when expressed as vectors in a high-dimensional space, are sparse in some predefined basis or a frame(fixed or learned). An efficient approach to basis / frame learning is formulated using the independent component analysis (ICA)and biologically inspired linear model of sparse coding. In the learned basis, the inverse problem of data recovery and removal of impulsive noise is reduced to solving sparseness constrained underdetermined linear system of equations. The same situation occurs in bioinformatics data analysis when novel type of linear mixture model with a reference sample is employed for feature extraction. Extracted features can be used for disease prediction and biomarker identification.

Item Type:	Thesis (Doctoral thesis)
Uncontrolled Keywords:	Independent component analysis; Source separation; Sparsity; Sparse component analysis; Sparse representation; Sparse signal reconstruction; Underdetermined linear system; Dictionary learning; K-SVD; Incomplete data; Missing data; Image inpainting; Salt-and-pepper noise; Nonlinear filtering; Feature extraction; Linear mixture model; Bioinformatics
Subjects:	NATURAL SCIENCES > Mathematics > Applied Mathematics and Mathematical Modeling TECHNICAL SCIENCES > Computing > Data Processing
Divisions:	Division of Laser and Atomic Research and Development
Projects:	Project title Project leader Project code Project type Spektralne dekompozicije - numericke metode i primjene [160961] Zlatko Drmač 037-0372783-2750 MZOS Analiza višespektralih podataka [217905] Ivica Kopriva 098-0982903-2558 MZOS
Depositing User:	Marko Filipović
Date Deposited:	11 May 2015 07:22
URI:	http://fulir.irb.hr/id/eprint/1915

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