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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  

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  

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... 

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  

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... 

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... 

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... 

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... 

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... 

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... 

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... 

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... 

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... 

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...