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Applications of Sparse Representation in Image Processing
, M.Sc. Thesis Sharif University of Technology ; Babaie Zadeh, Massoud (Supervisor)
Abstract
The sparse decomposition problem or nding sparse solutions of underdetermined linear systems of equations is one of the fundamental issues in signal processing and statistics. In recent years, this issue has been of great interest to researches in various elds of signal processing and accordingly found to be greatly benecial in those elds. This thesis aims at the investigation of the applications of the sparse decomposition problem in image processing. Among dierent applications such as compression, reconstruction, separation and image denoising, this thesis mainly focuses on the last one. One of the methods of image denoising which is closely tied to the sparse decomposition, is the method...
New dictionary learning methods for two-dimensional signals
, Article 28th European Signal Processing Conference, EUSIPCO 2020, 24 August 2020 through 28 August 2020 ; Volume 2021-January , 2021 , Pages 2021-2025 ; 22195491 (ISSN); 9789082797053 (ISBN) ; Parsa, J ; Babaie Zadeh, M ; Jutten, C ; Sharif University of Technology
European Signal Processing Conference, EUSIPCO
2021
Abstract
By growing the size of signals in one-dimensional dictionary learning for sparse representation, memory consumption and complex computations restrict the learning procedure. In applications of sparse representation and dictionary learning in two-dimensional signals (e.g. in image processing), if one opts to convert two-dimensional signals to one-dimensional ones, and use the existing one-dimensional dictionary learning and sparse representation techniques, too huge signals and dictionaries will be encountered. Two-dimensional dictionary learning has been proposed to avoid this problem. In this paper, we propose two algorithms for two-dimensional dictionary learning. According to our...
Two-Dimensional Dictionary Learning and its Application in Image Denoising
, M.Sc. Thesis Sharif University of Technology ; Babaiezadeh, Masoud (Supervisor)
Abstract
Sparse representation and consequently, dictionary learning have been two of the great importance topics in signal processing problems for the last two decades. In sparse representation, each signal has to be represented as a linear combination of some basic signals, which are called atoms, and their collection is called a dictionary. To put it in other words, if complete dictionaries such as Fourier or Wavelet dictionaries are used for the representation of signals, the representation will be unique, but not sparse. On the other hand, if overcomplete dictionaries are used, we will confront with too many representations, and the goal of sparse representation is to find the sparsest one. ...
Sparse decomposition of two dimensional signals
, Article 2009 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2009, Taipei, 19 April 2009 through 24 April 2009 ; 2009 , Pages 3157-3160 ; 15206149 (ISSN); 9781424423545 (ISBN) ; Babaie Zadeh, M ; Jutten, C ; Institute of Electrical and Electronics Engineers; Signal Processing Society ; Sharif University of Technology
2009
Abstract
In this paper, we consider sparse decomposition (SD) of two-dimensional (2D) signals on overcomplete dictionaries with separable atoms. Although, this problem can be solved by converting it to the SD of one-dimensional (1D) signals, this approach requires a tremendous amount of memory and computational cost. Moreover, the uniqueness constraint obtained by this approach is too restricted. Then in the paper, we present an algorithm to be used directly for sparse decomposition of 2D signals on dictionaries with separable atoms. Moreover, we will state another uniqueness constraint for this class of decomposition. Our algorithm is obtained by modifying the Smoothed L0 (SL0) algorithm, and hence...