Image denoising is an indispensable process of manifold high level tasks in image processing and computer vision. However, the traditional low-rank minimization-based methods suffer from a biased problem since only the noisy observation is used to estimate the underlying clean matrix. To overcome this issue, a new low-rank minimization-based method, called nuclear norm minus Frobenius norm rank residual minimization (NFRRM), is proposed for image denoising. The propose method transforms the ill-posed image denoising problem to rank residual minimization problems through excavating the nonlocal self-similarity prior. The proposed NFRRM model can perform an accurate estimation to the underlying clean matrix through treating each rank residual component flexibly. More importantly, the global optimum of the proposed NFRRM model can be obtained in closed-form. Extensive experiments demonstrate that the proposed NFRRM method outperforms many state-of-the-art image denoising methods.

In this paper, we propose a highly accurate method for estimating the quality of images compressed using fractal image compression. Using an iterated function system, fractal image compression compresses images by exploiting their self-similarity, thereby achieving high levels of performance; however, we cannot always use fractal image compression as a standard compression technique because some compressed images are of low quality. Generally, sufficient time is required for encoding and decoding an image before it can be determined whether the compressed image is of low quality or not. Therefore, in our previous study, we proposed a method to estimate the quality of images compressed using fractal image compression. Our previous method estimated the quality using image features of a given image without actually encoding and decoding the image, thereby providing an estimate rather quickly; however, estimation accuracy was not entirely sufficient. Therefore, in this paper, we extend our previously proposed method for improving estimation accuracy. Our improved method adopts a new image feature, namely lacunarity. Results of simulation showed that the proposed method achieves higher levels of accuracy than those of our previous method.

This paper presents a single image super-resolution (SR) algorithm based on self-similarity using non-local-mean (NLM) metric. In order to accurately find the best self-example even under noisy environment, NLM weight is employed as a self-similarity metric. Also, a pixel-wise soft-switching is presented to overcome an inherent drawback of conventional self-example-based SR that it seldom works for texture areas. For the pixel-wise soft-switching, an edge-oriented saliency map is generated for each input image. Here, we derived the saliency map which can be robust against noises by using a specific training. The proposed algorithm works as follows: First, auxiliary images for an input low-resolution (LR) image are generated. Second, self-examples for each LR patch are found from the auxiliary images on a block basis, and the best match in terms of self-similarity is found as the best self-example. Third, a preliminary high-resolution (HR) image is synthesized using all the self-examples. Next, an edge map and a saliency map are generated from the input LR image, and pixel-wise weights for soft-switching of the next step are computed from those maps. Finally, a super-resolved HR image is produced by soft-switching between the preliminary HR image for edges and a linearly interpolated image for non-edges. Experimental results show that the proposed algorithm outperforms state-of-the-art SR algorithms qualitatively and quantitatively.

In the self-similarity super resolution (SR) approach, similar examples are searched across down-scales in the image pyramid, and the computations of searching similar examples are very heavy. This makes it difficult to work in a real-time way under common software implementation. Therefore, the search process should be further accelerated at an algorithm level. Cauchy-Schwarz inequality has been used previously for fast vector quantization (VQ) encoding. The candidate patches in the search region of SR are analogous to the code-words in the VQ, and Cauchy-Schwarz inequality is exploited to exclude implausible candidate patches early. Consequently, significant acceleration of the similar patch search process is achieved. The proposed method can easily make an optimal trade-off between running speed and visual quality by appropriately configuring the bypass-threshold.

In this letter, we present a fast image/video super resolution framework using edge and nonlocal constraint. The proposed method has three steps. First, we improve the initial estimation using content-adaptive bilateral filtering to strengthen edge. Second, the high resolution image is estimated by using classical back projection method. Third, we use joint content-adaptive nonlocal means filtering to get the final result, and self-similarity structures are obtained by the low resolution image. Furthermore, content-adaptive filtering and fast self-similarity search strategy can effectively reduce computation complexity. The experimental results show the proposed method has good performance with low complexity and can be used for real-time environment.

Temporal Self-Similarity Matrix (SSM) based action recognition is one of the important approaches of single-person oriented action analysis in computer vision. In this study, we propose a new kind of SSM and a fast computation method. The computation method does not require time-consuming pre-processing to find bounding boxes of the human body, instead it processes difference images to obtain action patterns which can be done very quickly. The proposed SSM is experimentally confirmed to have high power/capacity to achieve a better classification performance than four typical kinds of SSMs.

Menger's sponge (MS) is a kind of three-dimensional fractal structure. To analyze non-resonant electromagnetic properties of MS composed of isotropic paraelectric material, a novel, high-speed computation method employing simple recursion equations in terms of scattering amplitudes for two MS's with adjacent stage numbers, which are the parameters describing structural differences of MS's, is formulated. Within the scope of non-resonant electromagnetic phenomena, scattering patterns, forward and backward scattering amplitudes, and total cross sections of MS are investigated as a function of stage number and incident plane waves, and behaviors typical to fractal structures are extracted from the numerical results of the above equations. In addition, scattering properties at infinite stage number are discussed.

Numerous studies have shown that scaling exponents of internet traffic change over time or scaling ranges. In order to analyze long-range dependent traffic with changing scaling exponents over time scales, we propose a multi-scale traffic model that incorporates the notion of a piecewise self-similar process, a process with spectral changes on its scaling behavior. We can obtain a performance curve smoothened over the range of queue length corresponding to time scales with different scaling exponents by adopting multiple self-similar processes piecewise into different spectra of time scale. The analytical method for the multiscale fractional Brownian motion is discussed as a model for this approach. A comparison of the analytical and simulation results, using traffic data obtained from backbone networks, shows that our model provides a good approximation for Gaussian traffic.

Recent studies of high quality, high resolution traffic measurements have revealed that network traffic appears to be statistically self similar. Contrary to the common belief, aggregating self-similar traffic streams can actually intensify rather than diminish burstiness. Thus, traffic prediction plays an important role in network management. In this paper, Least Mean Kurtosis (LMK), which uses the negated kurtosis of the error signal as the cost function, is proposed to predict the self similar traffic. Simulation results show that the prediction performance is improved greatly over the Least Mean Square (LMS) algorithm.

An efficient void filling (VF) algorithm is proposed for wavelength division multiplexing (WDM) optical packet switches (OPSes) handling variable-packet-length self-similar traffic. The computation complexity of the proposed algorithm is extremely low. We further compare the switching performance of the proposed algorithm with that of the conventional one. We demonstrate that the proposed algorithm offers significantly lower computation complexity with adequate performance.

The problem of aggregating different stochastic process into a unique one that must be characterized based on the statistical knowledge of its components is a key point in the modeling of many complex phenomena such as the merging of traffic flows at network nodes. Depending on the physical intuition on the interaction between the processes, many different aggregation policies can be devised, from averaging to taking the maximum in each time slot. We here address flows averaging and maximum since they are very common modeling options. Then we give a set of axioms defining a general aggregation operator and, based on some advanced results of functional analysis, we investigate how the decay of correlation of the original processes affect the decay of correlation (and thus the self-similar features) of the aggregated process.

Multilayered filters with a dielectric distribution along their thickness forming a one-dimensional quasi-fractal structure are theoretically analyzed, focusing on exposing their resonant properties in order to understand a dielectric Menger's sponge resonator [4],[5]. "Quasi-fractal" refers to the triadic Cantor set with finite generation. First, a novel calculation method that has the ability to deal with filters with fine fractal structures is derived. This method takes advantage of Clifford algebra based on the theory of thin-film optics. The method is then applied to classify resonant modes and, especially, to investigate quality factors for them in terms of the following design parameters: a dielectric constant, a loss tangent, and a stage number. The latter determines fractal structure. Finally, behavior of the filters with perfect fractal structure is considered. A crucial finding is that the high quality factor of the modes is not due to the complete self-similarity, but rather to the breaking of such a fractal symmetry.

Most of the proposed self-similar traffic models are asymptotic in nature. Hence, they are less effective in queueing-based performance evaluation when the buffer sizes are small. In this paper, we propose a short range dependent (SRD) process modelling by a generalized variance-based Markovian fitting to provide effective queueing-based performance measures when buffer sizes are small. The proposed method is to match the variance of the exact second-order self-similar processes. The fitting procedure determines the related parameters in an exact and straightforward way. The resultant traffic model essentially consists of a superposition of several two-state Markov-modulated Poisson processes (MMPPs) with distinct modulating parameters. We present how well the resultant MMPP could emulate the variance of original self-similar traffic in the range of the specified time scale, and could provide more accurate bounds for the queueing-based performance measures, namely tail probability, mean waiting time and loss probability. Numerical results show that both the second-order statistics and queueing-based performance measures when buffer capacity is small are more accurate than that of the variance-based fitting where the modulating parameters of each superposed two-state MMPP are equal. We then investigate the relationship between time scale and the number of superposed two-state MMPPs. We found that when the performance measures pertaining to larger time scales are not better than that of smaller ones, we need to increase the number of superposed two-state MMPPs to maintain the accurate and reliable queueing-based performance measures. We then conclude from the extensive numerical examples that an exact second-order self-similar traffic can be well represented by the proposed model.

In this paper, we investigate packet loss and system dimensioning of feedback (FB) type wavelength division multiplexing (WDM) optical routers under asynchronous and variable packet length self-similar traffic. We first study the packet loss performance for two different types of WDM optical routers under asynchronous and variable packet length self-similar traffic. Based on simulation results, we demonstrate that a 1616 FB type WDM optical router employing more than 4 re-circulated ports without using void filling (VF) algorithm has better performance. We then present the system dimensioning issues of FB type WDM optical routers, by showing the performance of FB type WDM optical routers as a function of the number of re-circulated ports, buffer depth, re-circulation limit, basic delay unit in the fiber delay line optical buffers and traffic characteristics. The sensitivity of the mutual effects of the above parameters on packet loss is investigated in details. Based on our results, we conclude that the FB type WDM optical routers must be dimensioned with the appropriate number of re-circulated ports, re-circulation limits, buffer depth, and optimal basic delay unit in the fiber delay line optical buffers under relevant traffic characteristics to achieve high switching performance.

We study the statistical multiplexing performance of self-similar traffic. We consider that input streams have different QoS (Quality of Service) requirements such as loss and delay jitter. By applying the FBM (fractal Brownian motion) model, we present methods of estimating the effective bandwidth of aggregated traffic. We performed simulations to evaluate the QoS performances and the bandwidths required to satisfy them. The comparison between the estimation and the simulation confirms that the estimation could give rough data of the effective bandwidth. Finally, we analyze the bandwidth gain with priority multiplexing against non-prioritized multiplexing and suggest how to get better performance with the right configuration of QoS parameters.

This paper describes an analysis of IP-network traffic in terms of the time variation of self-similarity. To get a comprehensive view in analyzing the degree of long-range dependence (LRD) of IP-network traffic, this paper used a self-organizing map, which provides a way to map high-dimensional data onto a low-dimensional domain. Also, in the LRD-based analysis, this paper employed detrended fluctuation analysis (DFA), which is applicable to the analysis of long-range power-law correlations or LRD in non-stationary time-series signals. In applying this method to traffic analysis, this paper performed two kinds of traffic measurement: one based on IP-network traffic flowing into NTT Musashino R&D center (Tokyo, Japan) from the Internet and the other based on IP-network traffic flowing through at an interface point between an access provider (Tokyo, Japan) and the Internet. Based on sequential measurements of IP-network traffic, this paper derived corresponding values for the LRD-related parameter α of measured traffic. As a result, we found that the characteristic of self-similarity seen in the measured traffic fluctuated over time, with different time variation patterns for two measurement locations. In training the self-organizing map, this paper used three parameters: two α values for different plot ranges, and Shannon-based entropy, which reflects the degree of concentration of measured time-series data. We visually confirmed that the traffic data could be projected onto the map in accordance with the traffic properties, resulting in a combined depiction of the effects of the degree of LRD and network utilization rates. The proposed method can deal with multi-dimensional parameters, projecting its results onto a two-dimensional space in which the projected data positions give us an effective depiction of network conditions at different times.

Measuring and modeling network traffic is of key importance for the traffic engineering of IP networks, due to the growing diversity of multimedia applications and the need to efficiently support QoS differentiation in the network. Several recent measurements have shown that Internet traffic may incorporate long-range dependence and self-similar characteristics, which can have significant impact on network performance. Self-similar traffic shows variability over many time scales, and this behavior must be taken into account for accurate prediction of network performance. In this paper, we propose a new parameter fitting procedure for a superposition of Markov Modulated Poisson Processes (MMPPs), which is able to capture self-similarity over a range of time scales. The fitting procedure matches the complete distribution of the arrival process at each time scale of interest. We evaluate the procedure by comparing the Hurst parameter, the probability mass function at each time scale, and the queuing behavior (as assessed by the loss probability and average waiting time), corresponding to measured traffic traces and to traces synthesized according to the proposed model. We consider three measured traffic traces, all exhibiting self-similar behavior: the well-known pOct Bellcore trace, a trace of aggregated IP WAN traffic, and a trace corresponding to the popular file sharing application Kazaa. Our results show that the proposed fitting procedure is able to match closely the distribution over the time scales present in data, leading to an accurate prediction of the queuing behavior.

This letter presents a significant property of the mapping parameters that play a central role to represent a given signal in Fractal Interpolation Functions (FIF). Thanks to our theoretical analysis, it is derived that the mapping parameters required to represent a given signal are also applicable to represent the upsampled signal of a given one. Furthermore, the upsampled signal obtained by using the property represents the self-affine property more distinctly than the given signal. Experiments show the validity and usefulness of the significant property.

This paper proposes an idea for modeling aggregated TCP/IP traffic arriving at a bottleneck link by focusing on its scaling behavior. Here, the aggregated TCP/IP traffic means the IP packet traffic from many TCP connections sharing the bottleneck link. The model is constructed based on the outcomes of our previous works investigating how the TCP/IP networking mechanism affects the self-similar scaling behavior of the aggregated TCP/IP traffic in a LAN/WAN environment. The proposed traffic model has been examined from the perspective of application to network performance estimation. The examinations have shown that it models the scaling behavior and queueing behavior of actual traffic, though it neglects the interaction among TCP connections that compete with each other for the single bottleneck link bandwidth.

This paper discusses self-similarity in cell dwell time of a mobile terminal, the discovery of which was described in our previous paper, and its effects on teletraffic of mobile communication networks. We have evaluated various teletraffic statistics, such as cell dwell time and channel occupancy time, of a mobile terminal based on measurements of motion for various types of vehicles. Those results show that cell dwell time follows a long-tailed log-normal distribution rather than the exponential distribution that has been used for modeling. Here, we first elaborate on self-similarity in cell dwell time of various vehicles. We then evaluate self-similarity in channel occupancy time. For future mobile multimedia communication systems employing a micro-cell configuration, it is anticipated that data communication will be the main form of communication and that call holding time will be long. For such cases, we have shown that channel occupancy time will be greatly affected by the cell dwell time of the mobile terminal, and that self-similarity, a characteristic that is not seen in conventional systems, will consequently appear. We have also found that hand-off frequently fails as self-similarity in cell dwell time of a mobile terminal becomes stronger.