Kernel-Based MMSE Multimedia Signal Reconstruction and Its Application to Spatial Error Concealment

In this paper, a minimum mean square error-optimized mixture-based estimator is used for packet video error concealment. At the same time as on-line computational complexity is reduced, performance in peak signal-to-noise ratio (PSNR) is increased in comparison with a Gaussian mixture-based estimator that obtains its parameters through probability density estimation by means of the expectation maximization algorithm. Moreover, our method increases performance in PSNR compared to several other previous error concealment algorithms.

In kernel density estimation methods, an approximation of the data probability density function is achieved by locating a kernel function at each data location. The smoothness of the functional approximation and the modelling ability are controlled by the kernel bandwidth. In this paper we propose a Bayesian estimation method for finding the kernel bandwidth. The distribution corresponding to the bandwidth is estimated from distributions characterizing the second order statistics estimates calculated from local neighbourhoods. The proposed bandwidth estimation method is applied in three different kernel density estimation based approaches: scale space, mean shift and quantum clustering. The third method is a novel pattern recognition approach using the principles of quantum mechanics.

Wavelet-Based Identification of Linear Discrete-Time Systems

Numerous facets of scientific research implicitly or explicitly call for the estimation of probability densities. Histograms and kernel density estimates (KDEs) are two commonly used techniques for estimating such information, with the KDE generally providing a higher fidelity representation of the probability density function (PDF). Both methods require specification of either a bin width or a kernel bandwidth. While techniques exist for choosing the kernel bandwidth optimally and objectively, they are computationally intensive, since they require repeated calculation of the KDE. A solution for objectively and optimally choosing both the kernel shape and width has recently been developed by Bernacchia and Pigolotti (2011). While this solution theoretically applies to multidimensional KDEs, it has not been clear how to practically do so.A method for practically extending the Bernacchia–Pigolotti KDE to multidimensions is introduced. This multidimensional extension is combined with a recently-developed computational improvement to their method that makes it computationally efficient: a 2D KDE on 105 samples only takes 1 s on a modern workstation. This fast and objective KDE method, called the fastKDE method, retains the excellent statistical convergence properties that have been demonstrated for univariate samples. The fastKDE method exhibits statistical accuracy that is comparable to state-of-the-science KDE methods publicly available in R, and it produces kernel density estimates several orders of magnitude faster. The fastKDE method does an excellent job of encoding covariance information for bivariate samples. This property allows for direct calculation of conditional PDFs with fastKDE. It is demonstrated how this capability might be leveraged for detecting non-trivial relationships between quantities in physical systems, such as transitional behavior.

Speckle noise, a granular noise, occurs in synthetic aperture radar (SAR) data due to the interference of reflected signals with several scatterers in a resolution cell. One of the simplest techniques to suppress speckle noise from polarimetric SAR data is to use local statistics. The Lee filter employs sample mean and variance of pixels of data degraded by speckle noise, which can be multiplicative, additive, or a mixture of both, in a searching window. The refined Lee method utilizes directional windows with local minimum mean square error (LMMSE), which ensures superior maintenance of spatial resolution and features. The Lee-Sigma filter is constructed on the basis of the two-sigma probability, which effectively suppresses the speckle noise. However, insufficiencies were observed in the generation of a biased evaluation, blurring of edges, and suppression of point targets. To eliminate these insufficiencies, the improved Lee-Sigma filter was developed, which employs the minimum mean square error estimate as a priori mean. Thus, an excellent maintenance of point targets and subtle details is displayed. In this study, the Lee, refined Lee, Lee-Sigma, and improved Lee-Sigma filters were evaluated using full polarimetric data. The evaluated results indicated that the improved Lee-Sigma filter performed better than other local statistics filters.

Since conventional cross-validation bandwidth selection methods don't work for the case where the data considered are dependent time series, alternative bandwidth selection methods are needed. In recent years, Bayesian based global bandwidth selection methods have been proposed. Our experience shows that the use of a global bandwidth is however less suitable than using a localized bandwidth in kernel density estimation in the case where the data are dependent time series as discussed in an empirical application of this paper. Nonetheless, a difficult issue is how we can consistently estimate a localized bandwidth. In this paper, we propose a semiparametric estimation method, for which we establish an asymptotic theory for the proposed semiparametric estimator. A by-product of this bandwidth estimate is a new sampling-based likelihood approach to hyperparameter estimation. Monte Carlo simulation studies show that the proposed hyperparameter estimation method works very well, and that the proposed bandwidth estimator outperforms its competitors. Applications of the new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate, as well as the S&P 500 daily return under conditional heteroscedasticity, demonstrate the effectiveness and competitiveness of the proposed semiparametric localized bandwidth.

Visible light communication (VLC) has been proposed as a promising way for next generation wireless communication networks to mitigate the scarcity of the radio frequency (RF) spectrum, and has consequently attracted much attention. This paper introduces a single-input single-output (SISO) VLC system under the joint effects of statistical random channel and signal-dependent shot noise (SDSN). Moreover, it estimates the channel of the considered system using maximum likelihood (ML), least square (LS), linear minimum mean square error (LMMSE), maximum posteriori probability (MAP) and minimum mean square error (MMSE) estimators. Furthermore, a Bayesian Cramér-Rao lower bound (BCRLB) is derived for the proposed system and it is compared to the mean square error (MSE) of the proposed estimators. The problem of unknown SDSN factor, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\zeta ^{2}$</tex-math></inline-formula> , at the receiver side is discussed and two solutions are investigated. The receiver of a VLC system under SDSN and random channel gain <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$h$</tex-math></inline-formula> is designed and its BER is studied. Finally, Monte Carlo simulation results of the proposed estimators, which show the dramatic effect of the SDSN on the considered system, are provided. In particular, the presence of noise variance, as well as the SDSN factor, causes an increase in the MSE of the system, while increasing the power reinforces the system performance.

This paper investigates the placement of training symbols within the data packets of a wireless system in which transmissions are subject to asynchronous interference. The minimum mean square error of the training-based channel estimator is expressed as a function of the Fisher information of the received signal. It is shown that the placement that minimizes the minimum mean square error should be searched for within a set containing half as many elements as the number of training symbols in the packet. Furthermore, a lower bound on the minimum mean square error is derived and analyzed. It is shown that this bound is tight when the power of the interference is high. The placement of the training symbols in two clusters of equal or quasiequal length at the two edges of the data packet minimizes the lower bound for all values of the parameters and, thus, gives the solution of the problem for high values of the interference power. The influence of the training symbols placement on the data transmission performance is also investigated.

In spatial error concealment (SEC), methods like bilinear interpolation (BI) and directional interpolation (DI) are commonly used to estimate the missing pixel values resulting from losses occurring in video streams. Despite being able to preserve spatial smoothness, BI produces a blurring effect and is unable to preserve structural information. DI produces spurious edges in regions with no strong edges, resulting in visible artefacts. In this paper, we propose a SEC algorithm that addresses the above drawbacks by formulating a weighted sum of candidate macroblocks produced from DI and BI, with weights derived adaptively through local information. We demonstrate that the proposed algorithm offers visual improvements over both DI based algorithms and the SEC algorithm based on BI in the H.264/AVC reference software JM 12.0. Most importantly, this unique approach preserves edge information and spatial smoothness in the error concealed macroblock due to the integration of both BI and DI.

Particle density estimation with grid-projected and boundary-corrected adaptive kernels

Error concealment at a decoder is an efficient method to reduce the degradation of visual quality caused by channel errors. In this paper, we propose a novel spatio-temporal error concealment algorithm based on the spatial-temporal fading (STF) scheme which has been recently introduced. Although STF achieves good performance for the error concealment, several drawbacks including blurring still remain in the concealed blocks. To alleviate these drawbacks, in the proposed method, hybrid approaches with adaptive weights are proposed. First, the boundary matching algorithm and the decoder motion vector estimation which are well-known temporal error concealment methods are adaptively combined to compensate for the defect of each other. Then, an edge preserved method is utilized to reduce the blurring effects caused by the bilinear interpolation for spatial error concealment. Finally, two concealed results obtained by the hybrid spatial and temporal error concealment are pixel-wisely blended with adaptive weights. Experimental results exhibit that the proposed method outperforms conventional methods including STF in terms of the PSNR performance as well as subjective visual quality, and the computational complexity of the proposed method is similar to that of STF.

Error concealment is of great importance for block-based video systems, such as DVB or video streaming services. In this paper, we propose a novel scalable spatial error concealment algorithm that aims at obtaining high quality reconstructions with reduced computational burden. The proposed technique exploits the excellent reconstructing abilities of the kernel-based minimum mean square error K-MMSE estimator. We propose to decompose this approach into a set of hierarchically stacked layers. The first layer performs the basic reconstruction that the subsequent layers can eventually refine. In addition, we design a layer management mechanism, based on profiles, that dynamically adapts the use of higher layers to the visual complexity of the area being reconstructed. The proposed technique outperforms other state-of-the-art algorithms and produces high quality reconstructions, equivalent to K-MMSE, while requiring around one tenth of its computational time.

In time division-synchronous code division multiple access systems, the channel estimation for multiple subscribers requires the computation of very complicated algorithms through short training sequences. This situation causes mismodeling of the actual channels and introduces significant errors in the detected data of multiple users. This paper presents a novel channel estimation method with low complexity, which relies on reducing the rank order of the total channel matrix H. We exploit the rank deficient of H to reduce the number of parameters that characterizes this matrix. The adopted reduced rank technique is based on singular value decomposition algorithm. Equations for reduced rank-joint channel estimation (JCE) are derived and compared against traditional full rank-joint channel estimators: least square (LS) or Steiner, enhanced LS, and minimum mean square error algorithms. Simulation results of the normalized mean square error for the above mentioned estimators showed the superiority of reduced rank estimators. Multi-user joint data detectors based linear equalizers are used to suppress inter-symbol interference and mitigate intra-cell multiple access interference. The detectors: zero forcing block linear equalizer and minimum mean square error block linear equalizer algorithms are considered in this paper to recover the data. The results of bit error rate simulation have shown that reduced rank-JCE based detectors have an improvement by 5 dB lower than other traditional full rank-JCE based detectors.

We generalize the multiuser (CDMA spread spectrum) communication systems to the fading environments. We first extend Verdu's (1986) conventional optimum receiver to Rayleigh-fading environments and then evaluate its performance. Having no knowledge of the received power at the receiving end, we therefore need an estimator to efficiently estimate the received signal strength of each user in fading environments. A linear minimum mean square error (LMMSE) unbiased estimator is proposed to attain this goal. By using the minimum mean square error (MMSE) Bayesian estimation, we further propose the LMMSE bit estimator for efficient demodulation. Its performance is close to the optimum multiuser receiver but with a much simpler polynomial complexity. To further reduce the complexity, we extend the LMMSE estimator to the sequential LMMSE estimator. In sequential estimation, we do not need to implement the matched filter banks and to perform the matrix inversion when estimating. In addition, it converges after approximately 2k iterations, where k is the number of users. With this fast convergence property and the simple structure, the sequential LMMSE estimator provides an attractive alternative to the implementation of a multiuser system.

In present days, there has been a race among the communication systems in different schemes and generations. Gradually the transmission rate of data is increasing tremendously and breaking the previous generation's record. Now people are thinking of transmitting data beyond imagination. Using multiple antennas both at transmitter and receiver side, MIMO wireless technology efficiently provides very high spectral efficiency, boost the data transmission rate, enhance link reliability and improve system coverage. While transmitting data over mobile radio channels at high bit rates, the impulse response of the channel can be extended over a lot of symbol periods, leading fading and Inter-symbol interference (lSI). Equalizers are used to minimize Fading and interference effects. The analysis of the paper is studying the performance of Minimum mean square error method in terms of BER for MIMO (2×2) and (3×3) wireless channels. Binary Phase Shift Keying (BPSK) modulation technique was used in Rayleigh flat fading channel. Simulating in MATLAB results show that Minimum mean square error (MMSE) receivers is good for noise free channel and is successful in removing ISI. Successive interference method with optimal ordering outperforms the MMSE however a few problems arise because of iterative nature of the algorithm.