The maximum correntropy criterion (MCC) has received increasing attention in signal processing and machine learning due to its robustness against outliers (or impulsive noises). Some gradient based adaptive filtering algorithms under MCC have been developed and available for practical use. The fixed-point algorithms under MCC are, however, seldom studied. In particular, too little attention has been paid to the convergence issue of the fixed-point MCC algorithms. In this letter, we will study this problem and give a sufficient condition to guarantee the convergence of a fixed-point MCC algorithm.
Fractal image compression (FIC) is an image coding technology based on the local similarity of image structure. It is widely used in many fields such as image retrieval, image denoising, image authentication, and encryption. FIC, however, suffers from the high computational complexity in encoding. Although many schemes are published to speed up encoding, they do not easily satisfy the encoding time or the reconstructed image quality requirements. In this paper, a new FIC scheme is proposed based on the fact that the affine similarity between two blocks in FIC is equivalent to the absolute value of Pearson's correlation coefficient (APCC) between them. First, all blocks in the range and domain pools are chosen and classified using an APCC-based block classification method to increase the matching probability. Second, by sorting the domain blocks with respect to APCCs between these domain blocks and a preset block in each class, the matching domain block for a range block can be searched in the selected domain set in which these APCCs are closer to APCC between the range block and the preset block. Experimental results show that the proposed scheme can significantly speed up the encoding process in FIC while preserving the reconstructed image quality well.
Entropy has been widely employed as a measure of variability for problems, such as machine learning and signal processing. In this paper, we provide some new insights into the behaviors of entropy as a measure of multivariate variability. The relationships between multivariate entropy (joint or total marginal) and traditional measures of multivariate variability, such as total dispersion and generalized variance, are investigated. It is shown that for the jointly Gaussian case, the joint entropy (or entropy power) is equivalent to the generalized variance, while total marginal entropy is equivalent to the geometric mean of the marginal variances and total marginal entropy power is equivalent to the total dispersion. The smoothed multivariate entropy (joint or total marginal) and the kernel density estimation (KDE)-based entropy estimator (with finite samples) are also studied, which, under certain conditions, will be approximately equivalent to the total dispersion (or a total dispersion estimator), regardless of the data distribution.
Over the past decade, the simultaneous recording of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) data has garnered growing interest because it may provide an avenue towards combining the strengths of both imaging modalities. Given their pronounced differences in temporal and spatial statistics, the combination of EEG and fMRI data is however methodologically challenging. Here, we propose a novel screening approach that relies on a Cross Multivariate Correlation Coefficient (xMCC) framework. This approach accomplishes three tasks:(1) It provides a measure for testing multivariate correlation and multivariate uncorrelation of the two modalities; (2) it provides criterion for the selection of EEG features; (3) it performs a screening of relevant EEG information by grouping the EEG channels into clusters to improve efficiency and to reduce computational load when searching for the best predictors of the BOLD signal. The present report applies this approach to a data set with concurrent recordings of steady-state-visual evoked potentials (ssVEPs) and fMRI, recorded while observers viewed phase-reversing Gabor patches. We test the hypothesis that fluctuations in visuo-cortical mass potentials systematically covary with BOLD fluctuations not only in visual cortical, but also in anterior temporal and prefrontal areas. Results supported the hypothesis and showed that the xMCC-based analysis provides straightforward identification of neurophysiological plausible brain regions with EEG-fMRI covariance. Furthermore xMCC converged with other extant methods for EEG-fMRI analysis.
As a structure-based image compression technology, fractal image compression (FIC) has been applied not only in image coding but also in many important image processing algorithms. However, two main bottlenecks restrained the develop and application of FIC for a long time. First, the encoding phase of FIC is time-consuming. Second, the quality of the reconstructed images for some images which have low structure-similarity is usually unacceptable. Based on the absolute value of Pearson’s correlation coefficient (APCC), we had proposed an accelerating method to significantly speed up the encoding of FIC. In this paper, we make use of the sparse searching strategy to greatly improve the quality of the reconstructed images in FIC. We call it the sparse fractal image compression (SFIC). Furthermore, we combine both the APCC-based accelerating method and the sparse searching strategy to propose the fast sparse fractal image compression (FSFIC), which can effectively improve the two main bottlenecks of FIC. The experimental results show that the proposed algorithm greatly improves both the efficiency and effectiveness of FIC.
Since Jacquin proposed original fractal image compression technique in 1990, fractal coding method has been developed into various schemes. Traditionally, fractal coding uses mean square error (MSE) to evaluate similarity of image blocks, but the similarity evaluated by MSE usually differs from human visual system (HVS). Compared with MSE, structural similarity (SSIM) is an image measure index which is more appropriate for the HVS. This paper proposes a new fractal coding scheme which uses structural similarity to measure the similarity between image blocks and compute these blocks' coefficients. The experiment results show that the proposed method generates higher quality images for the HVS than MSE scheme.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.