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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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|
|Depositing User:||Marko Filipović|
|Date Deposited:||11 May 2015 07:22|
|Last Modified:||11 May 2015 07:22|
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