There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Real and Complex Analysis

The known median-based denoising methods tend to work well for restoring the images corrupted by random-valued impulse noise with low noise level but poorly for highly corrupted images. This letter proposes a new impulse detector, which is based on the differences between the current pixel and its neighbors aligned with four main directions. Then, we combine it with the weighted median filter to get a new directional weighted median (DWM) filter. Extensive simulations show that the proposed filter not only can provide better performance of suppressing impulse with high noise level but can preserve more detail features, even thin lines. As extended to restoring corrupted color images, this filter also performs very well

A New Directional Weighted Median Filter for Removal of Random-Valued Impulse Noise

Two approaches for integrating encryption with multimedia compression systems are studied in this research, i.e., selective encryption and modified entropy coders with multiple statistical models. First, we examine the limitations of selective encryption using cryptanalysis, and provide examples that use selective encryption successfully. Two rules to determine whether selective encryption is suitable for a compression system are concluded. Next, we propose another approach that turns entropy coders into encryption ciphers using multiple statistical models. Two specific encryption schemes are obtained by applying this approach to the Huffman coder and the QM coder. It is shown that security is achieved without sacrificing the compression performance and the computational speed. This modified entropy coding methodology can be applied to most modern compressed audio/video such as MPEG audio, MPEG video, and JPEG/JPEG2000 images.

Design of integrated multimedia compression and encryption systems

Topology and Geometry

A new method for impulse noise removal is presented, where a robust estimator of the variance, MAD (median of the absolute deviations from the median), is modified and used to efficiently separate noisy pixels from the image details. The algorithm is free of varying parameters, requires no previous training or optimization, and successfully removes all types of impulse noise. The pixel-wise MAD concept is straightforward, low in complexity, and achieves high filtering performance.

Advanced impulse Detection Based on pixel-wise MAD

A novel approach to provide unequal error protection (UEP) using rateless codes over erasure channels, named Expanding Window Fountain (EWF) codes, is developed and discussed. EWF codes use a windowing technique rather than a weighted (non-uniform) selection of input symbols to achieve UEP property. The windowing approach introduces additional parameters in the UEP rateless code design, making it more general and flexible than the weighted approach. Furthermore, the windowing approach provides better performance of UEP scheme, which is confirmed both theoretically and experimentally.

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Expanding window fountain codes for unequal error protection

In this letter, we propose a generalization of the progressive edge-growth (PEG) algorithm with the aim of designing LDPC code graphs with substantially improved approximated cycle extrinsic message degree (ACE) properties. The proposed realization of generalized PEG algorithm outperforms original PEG algorithm and its subsequent modification proposed by Xiao and Banihashemi.

Generalized ACE Constrained Progressive Edge-Growth LDPC Code Design

In this paper, some general properties of Shannon information measures are investigated over sets of probability distributions with restricted marginals. Certain optimization problems associated with these functionals are shown to be NP-hard, and their special cases are found to be essentially information-theoretic restatements of well-known computational problems, such as the Subset sum and the 3-Partition . The notion of minimum entropy coupling is introduced and its relevance is demonstrated in information-theoretic, computational, and statistical contexts. Finally, a family of pseudometrics (on the space of discrete probability distributions) defined by these couplings is studied, in particular their relation to the total variation distance, and a new characterization of the conditional entropy is given.

On the entropy of couplings

The construction of finite-length irregular LDPC codes with low error floors is currently an attractive research problem. In particular, for the binary erasure channel (BEC), the problem is to find the elements of selected irregular LDPC code ensembles with the size of their minimum stopping set being maximized. Due to the lack of analytical solutions to this problem, a simple but powerful heuristic design algorithm, the approximate cycle extrinsic message degree (ACE) constrained design algorithm, has recently been proposed. Building upon the ACE metric associated with a cycle in a code graph, we introduce the ACE spectrum of LDPC codes as a useful tool for evaluation of codes from selected irregular LDPC code ensembles. Using the ACE spectrum, we generalize the ACE constrained design algorithm, making it more flexible and efficient. We justify the ACE spectrum approach through examples and simulation results.

Vojin Senk

Papers

Advanced impulse Detection Based on pixel-wise MAD

Expanding window fountain codes for unequal error protection

Generalized ACE Constrained Progressive Edge-Growth LDPC Code Design

On the entropy of couplings

Transactions papers evaluation and design of irregular LDPC codes using ACE spectrum