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Over-complete Dictionary Learning for Sparse Representation
, M.Sc. Thesis Sharif University of Technology ; Babaie-Zadeh, Massoud (Supervisor)
Abstract
Sparse representation has been an important problem in recent decade. The main idea in this problem is that natural signals have information contents much lower than their ambient dimensions and as such, they can be represented by using only a few atoms. For example, if the dimension of signal is n, the purpose in sparse representation is to achieve the representation of signal in terms of s atom (s ≪ n). In sparse coding, the dictionary depends on the used signal. In some of the problem, dictionary is specified and sparse representation is obtained by this dictionary. In this case, because the dictionary is known, maybe sparse representation is not suitable for this signal. For this reason,...
Erratum: ISI sparse channel estimation based on SL0 and its application in ML sequence-by-sequence equalization (Signal Processing (2012) 92 (1875-1885))
, Article Signal Processing ; Vol. 94, issue. 1 , 2014 , p. 703- ; 01651684 ; Ghalehjegh, S. H ; Babaie-Zadeh, M ; Jutten, C ; Sharif University of Technology
2014
Abstract
[No abstract available]
Corrigendum to "ISI sparse channel estimation based on SL0 and its application in ML sequence-by-sequence equalization" [Signal Processing 92 (2012) 1875-1885] (DOI:10.1016/j.sigpro.2011.09.035)
, Article Signal Processing ; 2013 ; 01651684 (ISSN) ; Hamidi Ghalehjegh, S ; Babaie Zadeh, M ; Jutten, C ; Sharif University of Technology
2013
Abstract
In this paper, which is an extended version of our work at LVA/ICA 2010 [1], the problem of Inter Symbol Interface (ISI) Sparse channel estimation and equalization will be investigated. We firstly propose an adaptive method based on the idea of Least Mean Square (LMS) algorithm and the concept of smoothed l0 (SL0) norm presented in [2] for estimation of sparse ISI channels. Afterwards, a new non-adaptive fast channel estimation method based on SL0 sparse signal representation is proposed. ISI channel estimation will have a direct effect on the performance of the ISI equalizer at the receiver. So, in this paper we investigate this effect in the case of optimal Maximum Likelihood...
Adaptive and non-adaptive ISI sparse channel estimation based on SL0 and its application in ML sequence-by-sequence equalization
, Article Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 27 September 2010 through 30 September 2010 ; Volume 6365 LNCS , September , 2010 , Pages 579-587 ; 03029743 (ISSN) ; 9783642159947 (ISBN) ; Hamidi Ghalehjegh, S ; Babaie Zadeh, M ; Jutten, C ; Sharif University of Technology
2010
Abstract
In this paper, we firstly propose an adaptive method based on the idea of Least Mean Square (LMS) algorithm and the concept of smoothed l 0 (SL0) norm presented in [1] for estimation of sparse Inter Symbol Interface (ISI) channels which will appear in wireless and acoustic underwater transmissions. Afterwards, a new non-adaptive fast channel estimation method based on SL0 sparse signal representation is proposed. ISI channel estimation will have a direct effect on the performance of the ISI equalizer at the receiver. So, in this paper we investigate this effect in the case of optimal Maximum Likelihood Sequence-by-sequence Equalizer (MLSE) [2]. In order to implement this equalizer, we...
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...
Sparse signal recovery using iterative proximal projection
, Article IEEE Transactions on Signal Processing ; Volume 66, Issue 4 , 2018 , Pages 879-894 ; 1053587X (ISSN) ; Sadeghi, M ; Babaie Zadeh, M ; Chatterjee, S ; Skoglund, M ; Jutten, C ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018
Abstract
This paper is concerned with designing efficient algorithms for recovering sparse signals from noisy underdetermined measurements. More precisely, we consider minimization of a nonsmooth and nonconvex sparsity promoting function subject to an error constraint. To solve this problem, we use an alternating minimization penalty method, which ends up with an iterative proximal-projection approach. Furthermore, inspired by accelerated gradient schemes for solving convex problems, we equip the obtained algorithm with a so-called extrapolation step to boost its performance. Additionally, we prove its convergence to a critical point. Our extensive simulations on synthetic as well as real data verify...
Application of Blind Source Separation in Information Hiding
, M.Sc. Thesis Sharif University of Technology ; Babaie Zadeh, Massoud (Supervisor)
Abstract
This thesis proposes new algorithms for digital watermarking that are based on Independent Component Analysis (ICA) technique. First, we will show that ICA allows the maximization of the information content and minimization of the induced distortion by decomposing the covertext (in this thesis the image) into statistically independent components. In fact, for a broad class of attacks and fixed capacity values, one can show that distortion is minimized when the message is embedded in statistically independent components. Information theoretical analysis also shows that the information hiding capacity of statistically independent components is maximal. Then we will propose a new wavelet...
On the error of estimating the sparsest solution of underdetermined linear systems
, Article IEEE Transactions on Information Theory ; Volume 57, Issue 12 , December , 2011 , Pages 7840-7855 ; 00189448 (ISSN) ; Jutten, C ; Mohimani, H ; Sharif University of Technology
2011
Abstract
Let A be an n × m matrix with m > n, and suppose that the underdetermined linear system As = x admits a sparse solution ∥s 0∥o < 1/2spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now that we have somehow a solution ŝ as an estimation of s0, and suppose that ŝ is only "approximately sparse", that is, many of its components are very small and nearly zero, but not mathematically equal to zero. Is such a solution necessarily close to the true sparsest solution? More generally, is it possible to construct an upper bound on the estimation error ∥ŝ - s 0∥2 without knowing s0? The answer is positive, and in this paper, we construct such a bound based on...
A geometric approach for separating post non-linear mixtures
, Article European Signal Processing Conference, 3 September 2002 through 6 September 2002 ; Volume 2015-March , September , 2015 ; 22195491 (ISSN) ; Jutten, C ; Nayebi, K ; Sharif University of Technology
European Signal Processing Conference, EUSIPCO
2015
Abstract
A geometric method for separating PNL mixtures, for the case of 2 sources and 2 sensors, has been presented. The main idea is to find compensating nonlinearities to transform the scatter plot of observations to a parallelogram. It then results in a linear mixture which can be separated by any linear source separation algorithm. An indirect result of the paper is another separability proof of PNL mixtures of bounded sources for 2 sources and 2 sensors
Sparse ICA via cluster-wise PCA
, Article Neurocomputing ; Volume 69, Issue 13-15 , 2006 , Pages 1458-1466 ; 09252312 (ISSN) ; Jutten, C ; Mansour, A ; Sharif University of Technology
2006
Abstract
In this paper, it is shown that independent component analysis (ICA) of sparse signals (sparse ICA) can be seen as a cluster-wise principal component analysis (PCA). Consequently, Sparse ICA may be done by a combination of a clustering algorithm and PCA. For the clustering part, we use, in this paper, an algorithm inspired from K-means. The final algorithm is easy to implement for any number of sources. Experimental results points out the good performance of the method, whose the main restriction is to request an exponential growing of the sample number as the number of sources increases. © 2006 Elsevier B.V. All rights reserved
A geometric approach for separating post non-linear mixtures
, Article 11th European Signal Processing Conference, EUSIPCO 2002, 3 September 2002 through 6 September 2002 ; Volume 2002-March , 2002 ; 22195491 (ISSN) ; Jutten, C ; Nayebi, K ; Sharif University of Technology
European Signal Processing Conference, EUSIPCO
2002
Abstract
A geometric method for separating PNL mixtures, for the case of 2 sources and 2 sensors, has been presented. The main idea is to find compensating nonlinearities to transform the scatter plot of observations to a parallelogram. It then results in a linear mixture which can be separated by any linear source separation algorithm. An indirect result of the paper is another separability proof of PNL mixtures of bounded sources for 2 sources and 2 sensors. © 2002 EUSIPCO
Using multivariate score functions in source separation: Application to post non-linear mixtures
, Article Scientia Iranica ; Volume 9, Issue 4 , 2002 , Pages 409-418 ; 10263098 (ISSN) ; Jutten, C ; Nayebi, K ; Sharif University of Technology
Sharif University of Technology
2002
Abstract
In this paper, Joint Score Function (JSF) and Marginal Score Function (MSF) are first defined. It is then pointed out that their difference (SFD) can be treated as the stochastic gradient of mutual information and, hence, can be used in minimizing the mutual information with gradient-based methods. An estimator for SFD is then presented, based on nonlinear regression by means of spline smoothing. It is shown that SFD can be used to obtain a new non parametric algorithm for source separation in Post Non-Linear (PNL) mixtures. The method is very general and can be extended to convolutive mixtures, which is currently being studied
ICA by Mutual Information minimization: An approach for avoiding local minima
, Article 13th European Signal Processing Conference, EUSIPCO 2005, Antalya, 4 September 2005 through 8 September 2005 ; 2005 , Pages 253-256 ; 1604238216 (ISBN); 9781604238211 (ISBN) ; Bahmani, B ; Jutten, C ; Sharif University of Technology
2005
Abstract
Using Mutual Information (MI) minimization is very common in Blind Source Separation (BSS). However, it is known that gradient descent approaches may trap in local minima of MI in constrained models. In this paper, it is proposed that this problem may be solved using a 'poor' estimation of the derivative of MI
Differential of the Mutual Information
, Article IEEE Signal Processing Letters ; Volume 11, Issue 1 , 2004 , Pages 48-51 ; 10709908 (ISSN) ; Jutten, C ; Nayebi, K ; Sharif University of Technology
2004
Abstract
In this letter, we compute the variation of the mutual information, resulting from a small variation in its argument. Although the result can be applied in many problems, we consider only one example: the result is used for deriving a new method for blind source separation in linear mixtures. The experimental results emphasize the performance of the resulting algorithm
A Minimization-Projection (MP) approach for blind separating convolutive mixtures
, Article Proceedings - IEEE International Conference on Acoustics, Speech, and Signal Processing, Montreal, Que, 17 May 2004 through 21 May 2004 ; Volume 5 , 2004 , Pages V-533-V-536 ; 15206149 (ISSN) ; Jutten, C ; Nayebi, K ; Sharif University of Technology
2004
Abstract
In this paper, a new algorithm for blind source separation in convolutive mixtures, based on minimizing the mutual information of the outputs, is proposed. This minimization is done using a recently proposed Minimization-Projection (MP) approach for minimizing mutual information in a parametric model. Since the minimization step of the MP approach is proved to have no local minimum, it is expected that this new algorithm has good convergence behaviours
Separating convolutive mixtures by mutual information minimization
, Article 6th International Work-Conference on Artificial and Natural Neural Networks, IWANN 2001, Granada, 13 June 2001 through 15 June 2001 ; Volume 2085 LNCS, Issue PART 2 , 2001 , Pages 834-842 ; 03029743 (ISSN); 9783540422372 (ISBN) ; Jutten, C ; Nayebi, K ; Sharif University of Technology
Springer Verlag
2001
Abstract
Blind Source Separation (BSS) is a basic problem in signal processing. In this paper, we present a new method for separating convolutive mixtures based on the minimization of the output mutual information. We also introduce the concept of joint score function, and derive its relationship with marginal score function and independence. The new approach for minimizing the mutual information is very efficient, although limited by multivariate distribution estimations. © Springer-Verlag Berlin Heidelberg 2001
A proper transform for satisfying benford's law and its application to double JPEG image forensics
, Article 2012 IEEE International Symposium on Signal Processing and Information Technology, ISSPIT 2012, 12 December 2012 through 15 December 2012 ; 2012 , Pages 240-244 ; 9781467356060 (ISBN) ; Razzazi, F ; Behrad, A ; Ahmadi, A ; Babaie-Zadeh, M ; Sharif University of Technology
2012
Abstract
This paper presents a new transform domain to evaluate the goodness of fit of natural image data to the common Benford's Law. The evaluation is made by three statistical fitness criteria including Pearson's chi-square test statistic, normalized cross correlation and a distance measure based on symmetrized Kullback-Leibler divergence. It is shown that the serial combination of variance filtering and block 2-D discrete cosine transform reveals the best goodness of fit for the first significant digit. We also show that the proposed transform domain brings reasonable fit for the second, third and fourth significant digits. As an application, the proposed transform domain is utilized to detect...
A novel forensic image analysis tool for discovering double JPEG compression clues
, Article Multimedia Tools and Applications ; Volume 76, Issue 6 , 2017 , Pages 7749-7783 ; 13807501 (ISSN) ; Razzazi, F ; Behrad, A ; Ahmadi, A ; Babaie Zadeh, M ; Sharif University of Technology
Springer New York LLC
2017
Abstract
This paper presents a novel technique to discover double JPEG compression traces. Existing detectors only operate in a scenario that the image under investigation is explicitly available in JPEG format. Consequently, if quantization information of JPEG files is unknown, their performance dramatically degrades. Our method addresses both forensic scenarios which results in a fresh perceptual detection pipeline. We suggest a dimensionality reduction algorithm to visualize behaviors of a big database including various single and double compressed images. Based on intuitions of visualization, three bottom-up, top-down and combined top-down/bottom-up learning strategies are proposed. Our tool...
Quantization-unaware double JPEG compression detection
, Article Journal of Mathematical Imaging and Vision ; Volume 54, Issue 3 , 2016 , Pages 269-286 ; 09249907 (ISSN) ; Razzazi, F ; Behrad, A ; Ahmadi, A ; Babaie Zadeh, M ; Sharif University of Technology
Springer New York LLC
2016
Abstract
The current double JPEG compression detection techniques identify whether or not an JPEG image file has undergone the compression twice, by knowing its embedded quantization table. This paper addresses another forensic scenario in which the quantization table of a JPEG file is not explicitly or reliably known, which may compel the forensic analyst to blindly reveal the recompression clues. To do this, we first statistically analyze the theory behind quantized alternating current (AC) modes in JPEG compression and show that the number of quantized AC modes required to detect double compression is a function of both the image’s block texture and the compression’s quality level in a fresh...
A novel forensic image analysis tool for discovering double JPEG compression clues
, Article Multimedia Tools and Applications ; Volume 76, Issue 6 , 2017 , Pages 7749-7783 ; 13807501 (ISSN) ; Razzazi, F ; Behrad, A ; Ahmadi, A ; Babaie Zadeh, M ; Sharif University of Technology
2017
Abstract
This paper presents a novel technique to discover double JPEG compression traces. Existing detectors only operate in a scenario that the image under investigation is explicitly available in JPEG format. Consequently, if quantization information of JPEG files is unknown, their performance dramatically degrades. Our method addresses both forensic scenarios which results in a fresh perceptual detection pipeline. We suggest a dimensionality reduction algorithm to visualize behaviors of a big database including various single and double compressed images. Based on intuitions of visualization, three bottom-up, top-down and combined top-down/bottom-up learning strategies are proposed. Our tool...