Abstract-We introduce a definition of the notion of compressibility for infinite deterministic and i.i.d. random sequences which is based on the asymptotic behavior of truncated subsequences. For this purpose, we use asymptotic results regarding the distribution of order statistics for heavy-tail distributions and their link with -stable laws for . In many cases, our proposed definition of compressibility coincides with intuition. In particular, we prove that heavy-tail (polynomial decaying) distributions fulfill the requirements of compressibility. On the other hand, exponential decaying distributions like Laplace and Gaussian do not. The results are such that two compressible distributions can be compared with each other in terms of their degree of compressibility.
Abstract-In this paper, a new scaling-based image-adaptive watermarking system has been presented, which exploits human visual model for adapting the watermark data to local properties of the host image. Its improved robustness is due to embedding in the low-frequency wavelet coefficients and optimal control of its strength factor from HVS point of view. Maximum-likelihood (ML) decoder is used aided by the channel side information. The performance of the proposed scheme is analytically calculated and verified by simulation. Experimental results confirm the imperceptibility of the proposed method and its higher robustness against attacks compared to alternative watermarking methods in the literature.Index Terms-Human visual system (HVS), maximum-likelihood decoder, scaling-based image watermarking, wavelet transform.
In this paper, an improved multiplicative image watermarking system is presented. Since human visual system is less sensitive to the image edges, watermarking is applied in the contourlet domain, which represents image edges sparsely. In the presented scheme, watermark data is embedded in directional subband with the highest energy. By modeling the contourlet coefficients with General Gaussian Distribution (GGD), the distribution of watermarked noisy coefficients is analytically calculated. The tradeoff between the transparency and robustness of the watermark data is solved in a novel fashion. At the receiver, based on the Maximum Likelihood (ML) decision rule, an optimal detector by the aid of channel side information is proposed. In the next step, a blind extension of the suggested algorithm is presented using the patchwork idea. Experimental results confirm the superiority of the proposed method against common attacks, such as Additive White Gaussian Noise (AWGN), JPEG compression, and rotation attacks, in comparison with the recently proposed techniques.
Asymptomatic circulating emboli can be detected by Doppler ultrasound. Embolic Doppler ultrasound signals are short duration transient like signals. The wavelet transform is an ideal method for analysis and detection of such signals by optimizing time-frequency resolution. We propose a detection system based on the discrete wavelet transform (DWT) and study some parameters, which might be useful for describing embolic signals (ES). We used a fast DWT algorithm based on the Daubechies eighth-order wavelet filters with eight scales. In order to evaluate feasibility of the DWT of ES, two independent data sets, each comprising of short segments containing an ES (N = 100), artifact (N = 100) or Doppler speckle (DS) (N = 100), were used. After applying the DWT to the data, several parameters were evaluated. The threshold values used for both data sets were optimized using the first data set. While the DWT coefficients resulting from artifacts dominantly appear at the higher scales (five, six, seven, and eight), the DWT coefficients at the lower scales (one, two, three, and four) are mainly dominated by ES and DS. The DWT is able to filter out most of the artifacts inherently during the transform process. For the first data set, 98 out of 100 ES were detected as ES. For the second data set, 95 out of 100 ES were detected as ES when the same threshold values were used. The algorithm was also tested with a third data set comprising 202 normal ES; 198 signals were detected as ES.
In communication systems, efficient use of the spectrum is an indispensable concern. Recently the use of compressed sensing for the purpose of estimating orthogonal frequency division multiplexing (OFDM) sparse multipath channels has been proposed to decrease the transmitted overhead in form of the pilot subcarriers which are essential for channel estimation. In this article, we investigate the problem of deterministic pilot allocation in OFDM systems. The method is based on minimizing the coherence of the submatrix of the unitary discrete fourier transform (DFT) matrix associated with the pilot subcarriers. Unlike the usual case of equidistant pilot subcarriers, we show that non-uniform patterns based on cyclic difference sets are optimal. In cases where there are no difference sets, we perform a greedy method for finding a suboptimal solution. We also investigate the performance of the recovery methods such as orthogonal matching pursuit (OMP) and iterative method with adaptive thresholding (IMAT) for estimation of the channel taps.
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