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#### A correlation measure based on vector-valued Lp norms

, Article 2019 IEEE International Symposium on Information Theory, ISIT 2019, 7 July 2019 through 12 July 2019 ; Volume 2019-July , 2019 , Pages 1132-1136 ; 21578095 (ISSN); 9781538692912 (ISBN) ; Beigi, S ; Gohari, A ; Yassaee, M. H ; Aref, M. R ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019

Abstract

In this paper, a new measure of correlation is introduced. This measure depends on a parameter α, and is defined in terms of vector-valued Lp norms. The measure is within a constant of the exponential of α-Rényi mutual information, and reduces to the trace norm (total variation distance) for α = 1. We provide some properties and applications of this measure of correlation. In particular, we establish a bound on the secrecy exponent of the wiretap channel (under the total variation metric) in terms of the α-Rényi mutual information according to Csiszár's proposal. © 2019 IEEE

#### Existence and continuity of differential entropy for a class of distributions

, Article IEEE Communications Letters ; Volume 21, Issue 7 , 2017 , Pages 1469-1472 ; 10897798 (ISSN) ; Gohari, A ; Amini, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2017

Abstract

In this letter, we identify a class of absolutely continuous probability distributions, and show that the differential entropy is uniformly convergent over this space under the metric of total variation distance. One of the advantages of this class is that the requirements could be readily verified for a given distribution. © 1997-2012 IEEE

#### Living near the edge: A lower-bound on the phase transition of total variation minimization

, Article IEEE Transactions on Information Theory ; Volume 66, Issue 5 , 2020 , Pages 3261-3267 ; Haddadi, F ; Amini, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020

Abstract

This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to success as the number of measurements increases. In fact, in large dimensions, TV minimization succeeds in recovering the gradient-sparse signal with high probability when the number of measurements exceeds a certain threshold; otherwise, it fails almost certainly. Obtaining a closed-form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet. In this work, we derive a tight lower-bound on...

#### Coordination via a relay

, Article IEEE International Symposium on Information Theory - Proceedings ; 2012 , Pages 3048-3052 ; 9781467325790 (ISBN) ; Yassaee, M. H ; Gohari, A ; Aref, M. R ; Sharif University of Technology
IEEE
2012

Abstract

In this paper, we study the problem of coordinating two nodes which can only exchange information via a relay at limited rates. The nodes are allowed to do a two-round interactive two-way communication with the relay, after which they should be able to generate i.i.d. copies of two random variables with a given joint distribution within a vanishing total variation distance. We prove inner and outer bounds on the coordination capacity region for this problem. Our inner bound is proved using the technique of "output statistics of random binning" that has recently been developed by Yassaee, et al

#### Weak solutions to Vlasov-McKean equations under Lyapunov-type conditions

, Article Stochastics and Dynamics ; Volume 19, Issue 6 , 2019 ; 02194937 (ISSN) ; Stannat, W ; Sharif University of Technology
World Scientific Publishing Co. Pte Ltd
2019

Abstract

We present a Lyapunov-type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature, most results concerning existence and uniqueness are obtained under regularity assumptions of the coefficients with respect to the Wasserstein distance. Some existence and uniqueness results for irregular coefficients have been obtained by considering the total variation distance. Here, we extend this approach to the control of the solution in some weighted total variation distance, that allows us now to derive a rather general weak uniqueness result, merely assuming measurability and certain integrability on the drift...

#### A robust FCM algorithm for image segmentation based on spatial information and total variation

, Article 9th Iranian Conference on Machine Vision and Image Processing, 18 November 2015 through 19 November 2015 ; Volume 2016-February , 2015 , Pages 180-184 ; 21666776 (ISSN) ; 9781467385398 (ISBN) ; Mohebbi Kalkhoran, H. M ; Fatemizadeh, E ; Sharif University of Technology
IEEE Computer Society

Abstract

Image segmentation with clustering approach is widely used in biomedical application. Fuzzy c-means (FCM) clustering is able to preserve the information between tissues in image, but not taking spatial information into account, makes segmentation results of the standard FCM sensitive to noise. To overcome the above shortcoming, a modified FCM algorithm for MRI brain image segmentation is presented in this paper. The algorithm is realized by incorporating the spatial neighborhood information into the standard FCM algorithm and modifying the membership weighting of each cluster by smoothing it by Total Variation (TV) denoising. The proposed algorithm is evaluated with accuracy index in...

#### Shapes from Pixels

, Article IEEE Transactions on Image Processing ; Volume 25, Issue 3 , 2016 , Pages 1193-1206 ; 10577149 (ISSN) ; Amini, A ; Baboulaz, L ; Vetterli, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2016

Abstract

Continuous-domain visual signals are usually captured as discrete (digital) images. This operation is not invertible in general, in the sense that the continuous-domain signal cannot be exactly reconstructed based on the discrete image, unless it satisfies certain constraints (e.g., bandlimitedness). In this paper, we study the problem of recovering shape images with smooth boundaries from a set of samples. Thus, the reconstructed image is constrained to regenerate the same samples (consistency), as well as forming a shape (bilevel) image. We initially formulate the reconstruction technique by minimizing the shape perimeter over the set of consistent binary shapes. Next, we relax the...

#### Sample complexity of total variation minimization

, Article IEEE Signal Processing Letters ; Volume 25, Issue 8 , 2018 , Pages 1151-1155 ; 10709908 (ISSN) ; Haddadi, F ; Amini, A ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2018

Abstract

This letter considers the use of total variation (TV) minimization in the recovery of a given gradient sparse vector from Gaussian linear measurements. It has been shown in recent studies that there exists a sharp phase transition behavior in TV minimization for the number of measurements necessary to recover the signal in asymptotic regimes. The phase-transition curve specifies the boundary of success and failure of TV minimization for large number of measurements. It is a challenging task to obtain a theoretical bound that reflects this curve. In this letter, we present a novel upper bound that suitably approximates this curve and is asymptotically sharp. Numerical results show that our...

#### Total Variation Regularization In Medical Imaging

, M.Sc. Thesis Sharif University of Technology ; Fotouhi Firouzabad, Morteza (Supervisor)
Abstract

In this thesis, we study image restoration problems, which can be modeled as inverse problems. Our main focus is on inverse problems with Poisson noise; which are useful in many problems like positron emission tomography, fluorescence microscopy, and astronomy imaging. As a popular method in the literature, we use statistic modeling of inverse problem with Poisson noise, in the MAP-estimation framework. Then we introduce a semi-implicit minimization method, FB-EM-TV, that involves two alternate steps, including an EM step and a weighted ROF problem. Then we study well-posedness, existence and stability of the solution. This method can be interpreted as a forward-backward splitting strategy,...

#### A robust image registration method based on total variation regularization under complex illumination changes

, Article Computer Methods and Programs in Biomedicine ; Volume 134 , 2016 , Pages 89-107 ; 01692607 (ISSN) ; Manzuri, M. T ; Yousefpour, R ; Sharif University of Technology
Elsevier Ireland Ltd
2016

Abstract

Background and objective Image registration is one of the fundamental and essential tasks for medical imaging and remote sensing applications. One of the most common challenges in this area is the presence of complex spatially varying intensity distortion in the images. The widely used similarity metrics, such as MI (Mutual Information), CC (Correlation Coefficient), SSD (Sum of Square Difference), SAD (Sum of Absolute Difference) and CR (Correlation Ratio), are not robust against this kind of distortion because stationarity assumption and the pixel-wise independence cannot be obeyed and captured by these metrics. Methods In this paper, we propose a new intensity-based method for...

#### On Mixing Time for Some Markov Chain Monte Carlo

, M.Sc. Thesis Sharif University of Technology ; Alishahi, Kasra (Supervisor)
Abstract

Markov chains are memoryless stochastic processes that undergoes transitions from one state to another state on a state space having the property that, given the present,the future is conditionally independent of the past. Under general conditions, the markov chain has a stationary distribution and the probability distribution of the markov chain, independent of the staring state, converges to it’s stationary distribution.

We use this fact to construct markov chain monte carlo, which are a class of algorithms for sampling from probability distributions based on constructing a markov chain that has the desired distribution as its stationary distribution. The state of a chain after a large...

We use this fact to construct markov chain monte carlo, which are a class of algorithms for sampling from probability distributions based on constructing a markov chain that has the desired distribution as its stationary distribution. The state of a chain after a large...

#### Image Registration Using a Total Variation Based Similarity Metric

, Ph.D. Dissertation Sharif University of Technology ; Manzouri Shelmani, Mohammad Taghi (Supervisor)
Abstract

Image registration is one of the fundamental and essential tasks for medical imaging and remote sensing applications. One of the most common challenges in this area is the presence of complex spatially varying intensity distortion in the images. The widely used similarity metrics, such as MI (Mutual Information), CC (Correlation Coefficient), SSD (Sum of Square Difference), SAD (Sum of Absolute Difference) and CR (Correlation Ratio), are not robust against this kind of distortion; because stationarity assumption and the pixel-wise independence cannot be obeyed and captured by these metrics. In this research, we proposed a new intensity-based method for simultaneous image registration and...

#### Playing games with bounded entropy

, Article IEEE International Symposium on Information Theory - Proceedings, 25 June 2017 through 30 June 2017 ; 2017 , Pages 1460-1464 ; 21578095 (ISSN) ; 9781509040964 (ISBN) ; Gohari, A ; Sharif University of Technology
Abstract

We study a two-player zero-sum game in which one of the players is restricted to mixed strategies with limited randomness. More precisely, we consider the maximum payoff that the maximizer (Alice) can secure with limited randomness h. This problem finds an operational interpretation in the context of repeated games with non-ideal sources of randomness. The computational aspects of this problem has not received much attention in the game theory literature. We begin by observing the equivalence of this problem with entropy minimization problems in other scientific contexts. Next, we provide two explicit lower bounds on the entropy-payoff tradeoff curve. To do this, we provide and utilize new...

#### On the error in phase transition computations for compressed sensing

, Article IEEE Transactions on Information Theory ; Volume 65, Issue 10 , 2019 , Pages 6620-6632 ; 00189448 (ISSN) ; Haddadi, F ; Amini, A ; Lotz, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2019

Abstract

Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and it has become standard to replace it with an upper-bound. To ensure that this technique is suitable, [1] has introduced an upper-bound on the gap between the statistical dimension and its approximation. In this work, we first show that the error bound in [1] in some low-dimensional models such as total variation and ell _{1} analysis minimization becomes poorly large. Next, we develop a new error bound which significantly improves the estimation gap...

#### State masking over a two-state compound channel

, Article IEEE Transactions on Information Theory ; Volume 67, Issue 9 , 2021 , Pages 5651-5673 ; 00189448 (ISSN) ; Yassaee, M. H ; Tan, V. Y. F ; Ahmadipour, M ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2021

Abstract

We consider the fundamental limits of reliable communication over a two-state compound channel when the state of the channel needs to be masked. Our model is closely related to an area of study known as covert communication, a setting in which the transmitter wishes to communicate to legitimate receiver(s) while ensuring that the communication is not detected by an adversary. Our main contribution is the establishment of upper and lower bounds on the throughput-key length region when the constraint that quantifies how much the states are masked is defined to be the total variation distance between the channel output distributions of the two states. When length of the key is sufficiently...

#### Modified Computed Tomographic Imaging Systems with Improved Reconstructed Image Quality

, M.Sc. Thesis Sharif University of Technology ; Kavehvash, Zahra (Supervisor)
Abstract

Computerized tomography (CT) imaging is a powerful tool among the existing bio-imaging techniques for capturing bio-images. In a CT scan procedure, linear sensors receive x-ray radiations, passed through the patient’s body and the reconstruction algorithms provide the required image for physicians from the captured data. In spite of its great advantages, due to the use of x-ray radiations and its ionization effect, it will raise the risk of cancer in long times. Therefore, to take benefit from several advantages of CT such as low-cost and high speed, solving this problem is aimed by many physicians and scientists. A new compressed sensing-based algorithm in order to reduce the number of...

#### A spatially-variant deconvolution method based on total variation for optical coherence tomography images

, Article Progress in Biomedical Optics and Imaging - Proceedings of SPIE, 12 February 2017 through 14 February 2017 ; Volume 10137 , 2017 ; 16057422 (ISSN) ; 9781510607194 (ISBN) ; Adabi, S ; Fatemizadeh, E ; Xu, Q ; Sadeghi, H ; Daveluy, S ; Nasiriavanaki, M ; Gimi, B ; Krol, A ; Sharif University of Technology
Abstract

Optical Coherence Tomography (OCT) has a great potential to elicit clinically useful information from tissues due to its high axial and transversal resolution. In practice, an OCT setup cannot reach to its theoretical resolution due to imperfections of its components, which make its images blurry. The blurriness is different alongside regions of image; thus, they cannot be modeled by a unique point spread function (PSF). In this paper, we investigate the use of solid phantoms to estimate the PSF of each sub-region of imaging system. We then utilize Lucy-Richardson, Hybr and total variation (TV) based iterative deconvolution methods for mitigating occurred spatially variant blurriness. It is...

#### Reconstruction of binary shapes from blurred images via hankel-structured low-rank matrix recovery

, Article IEEE Transactions on Image Processing ; Volume 29 , 2020 , Pages 2452-2462 ; Amini, A ; Daei, S ; Sharif University of Technology
Institute of Electrical and Electronics Engineers Inc
2020

Abstract

With the dominance of digital imaging systems, we are often dealing with discrete-domain samples of an analog image. Due to physical limitations, all imaging devices apply a blurring kernel on the input image before taking samples to form the output pixels. In this paper, we focus on the reconstruction of binary shape images from few blurred samples. This problem has applications in medical imaging, shape processing, and image segmentation. Our method relies on representing the analog shape image in a discrete grid much finer than the sampling grid. We formulate the problem as the recovery of a rank $r$ matrix that is formed by a Hankel structure on the pixels. We further propose efficient...

#### A Deconvolution Method Based on Total Variation Using Spatially Variant PSF Estimation for OCT Image Quality Enhancement

, M.Sc. Thesis Sharif University of Technology ; Fatemizadeh, Emad (Supervisor) ; Nasiri Avanaki, Mohammad Reza (Co-Advisor)
Abstract

Optical Coherence Tomography (OCT) has a great potential to elicit clinically useful information from tissues due to its high axial and transversal resolution. In practice, an OCT setup cannot reach to its theoretical resolution due to imperfections of its components, which make its images blurry. The blurriness is different alongside regions of image, thus they cannot be modeled by a unique point spread function (PSF). In this paper, we investigate the use of solid phantoms to estimate the PSF of each sub-region of imaging system. We then utilize Lucy-Richardson, steepest descent (SD) and total variation (TV) based iterative deconvolution methods for mitigating occurred spatially variant...