In this paper, we consider the problem of spectrum sensing by using multiple antenna in cognitive radios when the noise and the primary user signal are assumed as independent complex zero-mean Gaussian random signals. The optimal multiple antenna spectrum sensing detector needs to know the channel gains, noise variance, and primary user signal variance. In practice some or all of these parameters may be unknown, so we derive the generalized likelihood ratio (GLR) detectors under these circumstances. The proposed GLR detector, in which all the parameters are unknown, is a blind and invariant detector with a low computational complexity. We also analytically compute the missed detection and false alarm probabilities for the proposed GLR detectors. The simulation results provide the available traded-off in using multiple antenna techniques for spectrum sensing and illustrates the robustness of the proposed GLR detectors compared to the traditional energy detector when there is some uncertainty in the given noise variance.

It is demonstrated that the distribution of speech samples is well described by Laplacian distribution (LD). The widely known speech distributions, i.e., LD, Gaussian distribution (GD), generalized GD, and gamma distribution, are tested as four hypotheses, and it is proved that speech samples during voice activity intervals are Laplacian random variables. A decorrelation transformation is then applied to speech samples to approximate their multivariate distribution. To do this, speech is decomposed using an adaptive Karhunen-Loeve transform or a discrete cosine transform. Then, the distributions of speech components in decorrelated domains are investigated. Experimental evaluations prove that the statistics of speech signals are like a multivariate LD. All marginal distributions of speech are accurately described by LD in decorrelated domains. While the energies of speech components are time-varying, their distribution shape remains Laplacian.

An adaptive Karhunen-Loeve transform (KLT) tracking-based algorithm is proposed for enhancement of speech degraded by colored additive interference. This algorithm decomposes noisy speech into its components along the axes of a KLT-based vector space of clean speech. It is observed that the noise energy is disparately distributed along each eigenvector. These energies are obtained from noise samples gathered from silence intervals between speech samples. To obtain these silence intervals, we proposed an efficient voice activity detector based on outputs of the principle component eigenfilter; the greatest eigenvalue of speech KLT. Enhancement is performed by modifying each KLT component due to its noise and clean speech energies. The objective is to minimize the produced distortion when residual noise power is limited to a specific level. At the end, the inverse KLT is performed and an estimation of the clean signal is synthesized. Our listening tests indicated that 71% of our subjects preferred the enhanced speech by the above method over former methods of enhancement of speech degraded by computer generated white Gaussian noise. Our method was preferred by 80% of our subjects when we processed real samples of noisy speech gathered from various environments.

We consider an ad hoc wireless network consisting of d source-destination pairs communicating, in a pairwise manner, via R relaying nodes. The relay nodes wish to cooperate, through a decentralized beamforming algorithm, in order to establish all the communication links from each source to its respective destination. Our communication strategy consists of two steps. In the first step, all sources transmit their signals simultaneously. As a result, each relay receives a noisy faded mixture of all source signals. In the second step, each relay transmits an amplitude- and phase-adjusted version of its received signal. That is each relay multiply its received signal by a complex coefficient and retransmits the so-obtained signal. Our goal is to obtain these complex coefficients (beamforming weights) through minimization of the total relay transmit power while the signal-to-interference-plus-noise ratio (SINR) at the destinations are guaranteed to be above certain predefined thresholds. Although such a power minimization problem is not convex, we use semidefinite relaxation to turn this problem into a semidefinite programming (SDP) problem. Therefore, we can efficiently solve the SDP problem using interior point methods. Our numerical examples reveal that for high network data rates, our space division multiplexing scheme requires significantly less total relay transmit power compared to other orthogonal multiplexing schemes, such as time-division multiple access schemes.

Speckle noise is an inherent nature of ultrasound images, which may have negative effect on image interpretation and diagnostic tasks. In this paper, we propose several multiscale nonlinear thresholding methods for ultrasound speckle suppression. The wavelet coefficients of the logarithm of image are modeled as the sum of a noise-free component plus an independent noise. Assuming that the noise-free component has some local mixture distribution (MD), and the noise is either Gaussian or Rayleigh, we derive the minimum mean squared error (MMSE) and the averaged maximum (AMAP) estimators for noise reduction. We use Gaussian and Laplacian MD for each noise-free wavelet coefficient to characterize their heavy-tailed property. Since we estimate the parameters of the MD using the expectation maximization (EM) algorithm and local neighbors, the proposed MD incorporates some information about the intrascale dependency of the wavelet coefficients. To evaluate our spatially adaptive despeckling methods, we use both real medical ultrasound and synthetically introduced speckle images for speckle suppression. The simulation results show that our method outperforms several recently and the state-of-the-art techniques qualitatively and quantitatively.

In this paper, we proposed novel noise reduction algorithms that can be used to enhance image quality in various medical imaging modalities such as magnetic resonance and multidetector computed tomography. The noisy captured 3-D data are first transformed by discrete complex wavelet transform. Using a nonlinear function, we model the data as the sum of the clean data plus additive Gaussian or Rayleigh noise. We use a mixture of bivariate Laplacian probability density functions for the clean data in the transformed domain. The MAP and minimum mean-squared error (MMSE) estimators allow us to efficiently reduce the noise. The employed prior distribution is mixture and bivariate, and thus accurately characterizes the heavy-tail distribution of clean images and exploits the interscale properties of wavelets coefficients. In addition, we estimate the parameters of the model using local information; as a result, the proposed denoising algorithms are spatially adaptive, i.e., the intrascale dependency of wavelets is also well exploited in the enhancement process. The proposed approach results in significant noise reduction while the introduced distortions are not noticeable as a result of accurate statistical modeling. The obtained shrinkage functions have closed form, are simple in implementation, and efficiently enhances data. Our experiments on CT images show that among our derived shrinkage functions usually BiLapGausMAP produces images with higher peak SNR. However, BiLapGausMMSE is preferred especially for CT images, which have high SNRs. Furthermore, BiLapRayMAP yields better noise reduction performance for low SNR MR datasets such as high-resolution whole heart imaging while BiLapGauMAP results in better performance in MR data with higher intrinsic SNR such as functional cine data.