This paper addresses the problem of clustered multitask distributed estimation under masked measurements, where network nodes observe partial or incomplete data due to sensing limitations, communication constraints, or privacy requirements. We propose a novel extension of the Diffusion LMS (DLMS) algorithm that incorporates node-specific masking and a task-clustered structure. A tailored network-wide optimization problem is formulated to jointly handle masked observations and inter-cluster multitask estimation. Convergence analysis and simulation results demonstrate the effectiveness and robustness of the proposed approach in improving estimation performance under partial observability.

Learning a graph from data is the key to taking advantage of graph signal processing tools. Most of the conventional algorithms for graph learning require complete data statistics, which might not be available in some scenarios. In this work, we aim to learn a graph from incomplete time-series observations. From another viewpoint, we consider the problem of semi-blind recovery of time-varying graph signals where the underlying graph model is unknown. We propose an algorithm based on the method of block successive upperbound minimization (BSUM), for simultaneous inference of the signal and the graph from incomplete data. Simulation results on synthetic and real time-series demonstrate the performance of the proposed method for graph learning and signal recovery.

Abstract Image forensics encompasses a set of scientific tests to investigation of a suspected event via intrinsic clues of imaging pipeline. Traditional image sensing at the Nyquist-Shannon rate as well as the new modality of compressive imaging below the rate are two main types of sensing in photography and imaging applications. Hence, for forensic investigators, it would importantly necessitate the ability to discriminate among images captured by them. However, due to the complex nonlinear nature of imaging processes, investigating imagers’ traces is a difficult task. To this intent, we first systematically model the imaging pipelines as an encoder-decoder pair. For exploring distinguishable traces, we mathematically simplify and linearize the pair for compressive imaging and two main forms of traditional image sensing with or without compression. Our theoretical analyses on the approximate linear models reveal blurring kernels of different imagers have discriminability. To validate it in real-world scenarios, we considered the whole imaging process as an inverse problem and estimated the blurring kernel based on a deconvolution approach, where the discriminability is also justified by information visualization. Then, we designed a pipeline classification system, where a deep convolutional neural network is trained by the estimated blurring kernels to be able to classify the three imaging systems. Our results in compressive imaging identification show an accuracy improvement about 3.7 % in comparison to the best result among compared methods. Implementation codes are available for research and development.

In digital imaging, especially in the process of data acquisition and transmission, images are often affected by impulsive noise. Therefore, it is essential to remove impulsive noise from images before any further processing. Due to the remarkable performance of deep neural networks in different applications of image processing and computer vision, we present an end-to-end fully convolutional neural network to remove impulsive noise from images. To train our network, we generate a customized dataset with various noise densities in which the highly corrupted images are more frequent. Hence, our convolutional neural network is blind since the percentage of impulsive noise is not required as prior knowledge. Moreover, we define a multi-term loss function to train our network. In particular, we define a novel term to impose the sparsity nature of impulsive noise. Experimental results indicate that our deep learning approach significantly outperforms other state-of-the-art methods in terms of reconstruction quality and speed on a system equipped with GPU. Meanwhile, we introduce a fast iterative method, as a post-processing stage, to further improve the reconstruction quality of our neural network. The proposed post-processing algorithm improves the reconstruction quality in only a fraction of a second.

In this letter, the problem of non-coherent direction of arrival (DOA) estimation is investigated exploiting the sign of the measurements in order to resolve the inherent ambiguity of the problem. Although the phase values are inaccurate, the sign of real and imaginary parts of the measurements will most likely remain correct under limited phase errors. Furthermore, a new approach for solving the problem is proposed employing a modified version of the Majorization-Minimization (MM) technique, without any prior information about the number of incident signals. Some theoretical analyses of our proposed algorithm are also provided in the paper. Finally, the simulation results are presented, demonstrating the efficiency of the proposed algorithm in comparison to some state-of-the-art methods in the literature.

Compressed Sensing is targeted at reconstructing a signal from a small set of measurements, if the signal is sparse in some domains. In this respect, a low coherent measurement matrix plays an important role. In this letter, an efficient approximation of ℓ∞-norm based on the soft maximum is introduced to design a low coherent measurement matrix with a controllable spectral norm. The proposed approximation, called Logarithm of Sum of Exponential Absolute values (LSEAp), is convex (similar to ℓ∞-norm) and almost smooth. We design a low coherent measurement matrix with a small spectral norm via minimization of the ℓ∞-norm of the Gram matrix. The resulting problem is not convex but our simulations show that the LSEAp leads to an improved design of the measurement matrix, as compared to current methods.

In this paper, we study the problem of ellipse recovery from blurred shape images. A shape image is a continuous-domain black and white (binary-valued) image in which the points of the same color form a shape. We assume to have a digitized version of the shape image which is a sampled and blurred version of the image using a 2D kernel (the point spread function); the resulting pixels may also be corrupted by additive noise. Our goal in this work is to recover the original continuous-domain image based on the available pixels when the shape image is an ellipse. Our approach is to represent an ellipse as the zero-level-set of a bivariate polynomial of degree 2 and estimate the involved 6 polynomial coefficients based on a deep neural network. Our model is trained end to end on a wide range of blurring setups with varying noise levels. Besides, the network is trained to recover the ellipse even when the available noisy pixels cover only a part of the ellipse. Simulation results validate the performance of the proposed method and indicate its superiority compared to the state of art methods.

In this paper, we propose a new method to reconstruct a signal corrupted by noise where both signal and noise are sparse but in different domains. The main contribution of our algorithm is its low complexity; it has much lower run-time than most other algorithms. The reconstruction quality of our algorithm is both objectively (in terms of PSNR and SSIM) and subjectively better or comparable to other state-of-the-art algorithms. We provide a cost function for our problem, present an iterative method to find its local minimum, and provide the analysis of the algorithm. As an application of this problem, we apply our algorithm for Salt-and-Pepper noise (SPN) and Random-Valued Impulsive Noise (RVIN) removal from images and compare our results with other notable algorithms in the literature. Furthermore, we apply our algorithm for removing clicks from audio signals. Simulation results show that our algorithms are simple and fast, and it outperforms other state-of-the-art methods in terms of reconstruction quality and/or complexity.

While pitch detection has been the focal subject of numerous research efforts for several decades, it is still a challenging task in noisy conditions. In this article, we propose a method to improve the pitch detection accuracy of conventional pitch detection methods. The proposed pitch detection process starts with using the pitch value estimated by a conventional pitch detection method. Then, it extracts pitch candidates according to the most probable types of errors in the initial estimation of high-pitch and low-pitch frames classified by a Deep Convolutional Neural Network (DCNN). Next, a restrained selection procedure is run to find the true pitch value from the set of pitch candidates. In this procedure, we employ two features (harmonic summation and Euclidian deviation), the soft decision of the DCNN, the pitch smoothness feature in successive frames, and the effect of the initial estimation in a cost function. The pitch value which leads to the lowest cost value is chosen as the estimated pitch value. The simulations on CSTR and KEELE databases, in noisy environments with twelve types of noise, were performed. The results show the superiority of the proposed method over the state-of-the-art methods under different SNR conditions.

Recovering low-rank and sparse components from missing observations is an essential problem in various fields. In this paper, we have proposed a method to address the missing low-rank and sparse decomposition problem. We have used the smoothed nuclear norm and the L1norm to impose the low-rankness and sparsity constraints on the components, respectively. Furthermore, we have suggested a linear modeling for the corrupted observations. The problem has been solved with the aid of alternating minimization. Moreover, some simplifications have been applied to the relations to reduce the computational complexity, which makes the algorithm suitable for large-scale problems. To evaluate the proposed method, different simulation scenarios have been devised. The superiority of the suggested scheme over its counterparts has been confirmed on both the recovery accuracy and the convergence speed in various applications.

The matrix decomposing into a sum of low-rank and sparse components has found extensive applications in many areas including video surveillance, computer vision, and medical imaging. In this paper, we propose a new algorithm for recovery of low rank and sparse components of a given matrix. We have also proved the convergence of the proposed algorithm. The simulation results with synthetic and real signals such as image and video signals indicate that the proposed algorithm has a better performance with lower run-time than the conventional methods.

In this paper, we introduce a novel and robust approach to quantized matrix completion. First, we propose a rank minimization problem with constraints induced by quantization bounds. Next, we form an unconstrained optimization problem by regularizing the rank function with Huber loss. Huber loss is leveraged to control the violation from quantization bounds due to two properties: first, it is differentiable; and second, it is less sensitive to outliers than the quadratic loss. A smooth rank approximation is utilized to endorse lower rank on the genuine data matrix. Thus, an unconstrained optimization problem with differentiable objective function is obtained allowing us to advantage from gradient descent technique. Novel and firm theoretical analysis of the problem model and convergence of our algorithm to the global solution are provided. Another contribution of this letter is that our method does not require projections or initial rank estimation, unlike the state-of-the-art. In the Numerical Experiments section, the noticeable outperformance of our proposed method in learning accuracy and computational complexity compared to those of the state-of-the-art literature methods is illustrated as the main contribution.

The problem of finding the optimal node density for reconstructing a stochastic signal from its noisy samples in sensor networks is considered. The signal could be nonstationary and nonbandlimited. A weight is assigned to each location that indicates the relative importance of the signal at that location. It is shown that when the number of samples is very large, the optimal density of the samples at each location is proportional to the square root of the weight associated to that location.

This paper presents a low complexity while accurate Heart Rate (HR) estimation technique from signals captured by Photoplethysmographic (PPG) sensors worn on the wrist during intensive physical exercise. Wrist-type PPG signals experience severe Motion Artifacts (MA) that hinder efficient HR estimation especially during intensive physical exercises. To suppress the motion artifacts efficiently, simultaneous 3 dimensional acceleration signals are used as reference MAs. The proposed method achieves an Average Absolute Error (AAE) of 1.19 Beats Per Minute (BPM) on the 12 benchmark PPG recordings in which subjects run at speeds of up to 15 km/h. This method also achieves an AAE of 2.17 BPM on the whole benchmark database of 23 recordings that include both running and arm movement activities. This performance is comparable with state-of-the-art algorithms while at a significantly reduced computational cost which makes its standalone implementation on wearable devices feasible. The proposed algorithm achieves an average processing time of 32 milliseconds per input frames of length 8 seconds (2 channel PPG and 3D ACC signals) on a 3.2 GHz processor.

Adaptive thresholding methods have proved to yield a high signal‐to‐noise ratio (SNR) and fast convergence in sparse signal recovery. The robustness of a class of iterative sparse recovery algorithms, such as the iterative method with adaptive thresholding, has been found to outperform the state‐of‐art methods in respect of reconstruction quality, convergence speed, and sensitivity to noise. In this study, the authors introduce a new method for compressed sensing, using the sensing matrix and measurements. In our method, they iteratively threshold the signal and project the thresholded signal onto the translated null space of the sensing matrix. The threshold level is assigned adaptively. The results of the simulations reveal that the authors’ proposed method outperforms other methods in the signal reconstruction (in terms of the SNR). This performance advantage is noticeable when the number of available measurements approaches twice the sparsity number.

In this letter, we propose a new accurate approach for target localization in multiple-input multiple-output (MIMO) radars, which exploits the sparse spatial distribution of targets to reduce the sampling rate. We express the received signal of a MIMO radar in terms of the deviations of target parameters from the grid points in the form of a block sparse signal using the expansion around all the neighbor points. Applying a block sparse recovery method, we can estimate both the grid-point locations of targets and these deviations. The proposed approach can yield more accurate localization with higher detection probability compared with its counterparts. Moreover, the proposed approach can reduce the computational complexity.

This letter investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavytailed impulsive noise is well modeled with stable distributions. Since there is no explicit formula for the probability density function of SαS distribution, alternative approximations are used, such as, generalized Gaussian distribution, which imposes ℓp-norm fidelity on the residual error. In this letter, we exploit a continuous mixed norm (CMN) for robust sparse recovery instead of ℓp-norm. We show that in blind conditions, i.e., in the case where the parameters of the noise distribution are unknown, incorporating CMN can lead to near-optimal recovery. We apply alternating direction method of multipliers for solving the problem induced by utilizing CMN for robust sparse recovery. In this approach, CMN is replaced with a surrogate function and the majorization-minimization technique is incorporated to solve the problem. Simulation results confirm the efficiency of the proposed method compared to some recent algorithms for robust sparse recovery in impulsive noise.

In this letter, we propose a sparsity promoting feedback acquisition and reconstruction scheme for sensing, encoding and subsequent reconstruction of spectrally sparse signals. In the proposed scheme, the spectral components are estimated utilizing a sparsity-promoting, sliding-window algorithm in a feedback loop. Utilizing the estimated spectral components, a level signal is predicted and sign measurements of the prediction error are acquired. The sparsity promoting algorithm can then estimate the spectral components iteratively from the sign measurements. Unlike many batch-based compressive sensing algorithms, our proposed algorithm gradually estimates and follows slow changes in the sparse components utilizing a sliding-window technique. We also consider the scenario in which possible flipping errors in the sign bits propagate along iterations (due to the feedback loop) during reconstruction. We propose an iterative error correction algorithm to cope with this error propagation phenomenon considering a binary-sparse occurrence model on the error sequence. Simulation results show effective performance of the proposed scheme in comparison with the literature.

The authors propose asynchronous level crossing (LC) A/D converters for low redundancy voice sampling. They propose to utilise the family of iterative methods with adaptive thresholding (IMAT) for reconstructing voice from non‐uniform LC and adaptive LC (ALC) samples thereby promoting sparsity. The authors modify the basic IMAT algorithm and propose the iterative method with adaptive thresholding for level crossing (IMATLC) algorithm for improved reconstruction performance. To this end, the authors analytically derive the basic IMAT algorithm by applying the gradient descent and gradient projection optimisation techniques to the problem of square error minimisation subjected to sparsity. The simulation results indicate that the proposed IMATLC reconstruction method outperforms the conventional reconstruction method based on low‐pass signal assumption by 6.56 dBs in terms of reconstruction signal‐to‐noise ratio (SNR) for LC sampling. In this scenario, IMATLC outperforms orthogonal matching pursuit, least absolute shrinkage and selection operator and smoothed L0 sparsity promoting algorithms by average amounts of 12.13, 10.31, and 10.28 dBs, respectively. Finally, the authors compare the performance of the proposed LC/ALC‐based A/Ds with the conventional uniform sampling‐based A/Ds and their random sampling‐based counterparts both in terms of perceptual evaluation of speech quality and reconstruction SNR.

In this study, the authors consider the designing of a new set of uniquely decodable codes for uncoded synchronous overloaded code division multiple access for the number of codes exceeding the assigned code length. For the construction, the proposed recursive method at iteration‐ k generates a matrix that can be classified into k orthogonal subsets of different dimensions. Out of them, all besides the largest (binary Hadamard) one are ternary in nature. There resides an inbuilt twin tree structured cross‐correlation hierarchy that facilitates an advantageous balance between the auto and intergroup cross‐correlation for the signatures in a subset. This opportunity is further leveraged by the proposed multi‐stage detector to maintain the uniquely decodable (errorless) nature of the matrices for noiseless transmission. The simple logic of matched filtering serving as the basic designing block of the decoder provides an enormous saving over the complexity of optimum maximum likelihood decoder. For the noisy channel, the authors derive the theoretical expression of the average bit error rate for the individual subset. Moreover, the authors explain the role of the two factors (cardinality of the subset, and net level of interference) in being responsible for the non‐uniformity in the order of their error performance.

This letter considers the problem of casual heart rate tracking during intensive physical exercise using simultaneous 2 channel photoplethysmographic (PPG) and 3 dimensional (3D) acceleration signals recorded from wrist. This is a challenging problem because the PPG signals recorded from wrist during exercise are contaminated by strong Motion Artifacts (MAs). In this work, a novel algorithm is proposed which consists of two main steps of MA Cancellation and Spectral Analysis. The MA cancellation step cleanses the MA-contaminated PPG signals utilizing the acceleration data and the spectral analysis step estimates a higher resolution spectrum of the signal and selects the spectral peaks corresponding to HR. Experimental results on datasets recorded from 12 subjects during fast running at the peak speed of 15 km/hour showed that the proposed algorithm achieves an average absolute error of 1.25 beat per minute (BPM). These experimental results also confirm that the proposed algorithm keeps high estimation accuracies even in strong MA conditions.

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix A and sparse domain matrix Φ, i.e., D = AΦ, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix D. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.

In this paper, we investigate the achievable energy efficiency of cognitive radio networks where two main modes are of interest, namely, spectrum sharing (known as underlay paradigm) and spectrum sensing (or interweave paradigm). In order to improve the energy efficiency, we formulate a new multiobjective optimization problem that jointly maximizes the ergodic capacity and minimizes the average transmission power of the secondary user network while limiting the average interference power imposed on the primary user receiver. The multiobjective optimization will be solved by first transferring it into a single objective problem (SOP), namely, a power minimization problem, by using the ε-constraint method. The formulated SOP will be solved using two different methods. Specifically, the minimum power allocation at the secondary transmitter in a spectrum sharing fading environment are obtained using the iterative search-based solution and augmented Lagrangian approach for single and multiple secondary links, respectively. The significance of having extra side information and also imperfect side information of cross channels at the secondary transmitter are investigated. The minimum power allocations under perfect and imperfect sensing schemes in interweave cognitive radio networks are also found. Our numerical results provide guidelines for the design of future cognitive radio networks.

In this paper, we present a compressive sampling and multihypothesis (MH) reconstruction strategy for video sequences that has a rather simple encoder, while the decoding system is not that complex. We introduce a convex cost function that incorporates the MH technique with the sparsity constraint and the Tikhonov regularization. Consequently, we derive a new iterative algorithm based on these criteria. This algorithm surpasses its counterparts (Elasticnet and Tikhonov) in recovery performance. Besides, it is computationally much faster than Elasticnet and comparable with Tikhonov. Our extensive simulation results confirm these claims.

Overloaded code division multiple access being the only means of the capacity extension for conventional code division multiple access accommodates more number of signatures than the spreading gain. Recently, ternary Signature Matrices with Orthogonal Subsets (SMOS) has been proposed, where the capacity maximization is 200%. The proposed multi-user detector using matched filter exploits the twin tree hierarchy of correlation among the subsets to guarantee the errorless recovery. In this paper, we feature the non-ternary version of SMOS (i.e., 2k-ary SMOS) of same capacity, where the binary alphabets in all the k constituent (orthogonal) subsets are unique. Unlike ternary, the tree hierarchy for 2k-ary SMOS is non-uniform. However, the errorless detection of the multi-user detector remains undeviated. For noisy transmission, simulation results show the error performance of the right child for each subset of 2k-ary to be significantly improved over the left. The optimality of the right child of the largest (Hadamard) subset is also discovered. At higher loading, for larger and smaller subsets the superiority is reported for the 2k-ary and ternary, respectively, and the counter-intuitive deviations observed for the lower loading scenarios are logically explained. For the overall capacity maximization being 150%, superiority is featured by the 2k-ary, but beyond, it becomes a conditional entity. Copyright © 2016 John Wiley & Sons, Ltd.

Level‐crossing (LC) analog‐to‐digital (A/D) converters can efficiently sample certain classes of signals. An LC A/D converter is a real‐time asynchronous system, which encodes the information of an analog signal into a sequence of non‐uniformly spaced time instants. In particular, this class of A/D converters uses an asynchronous data conversion approach, which is a power efficient technique. In this study, the authors propose adaptive and multi‐level adaptive LC sampling models as alternatives to conventional LC schemes and apply an iterative algorithm to improve the reconstruction quality of LC A/D converters. This simulation results show that multi‐level adaptive LC outperforms conventional A/D converters such as sigma‐delta A/D converters in terms of performance and computational complexity.

In this letter, we propose a method for real-time high density impulse noise suppression from images. In our method, we first apply an impulse detector to identify the corrupted pixels and then employ an innovative weighted-average filter to restore them. The filter takes the nearest neighboring interpolated image as the initial image and computes the weights according to the relative positions of the corrupted and uncorrupted pixels. Experimental results show that the proposed method outperforms the best existing methods in both PSNR measure and visual quality and is quite suitable for real-time applications.

We extend the result by Tse and Verdú on the optimum asymptotic multiuser efficiency of randomly spread code division multiple access (CDMA) with binary phase shift keying input. Random Gaussian and random binary antipodal spreading are considered. We obtain the optimum asymptotic multiuser efficiency of a K-user system with spreading gain N when K and N → ∞ and the loading factor, (K/N), grows logarithmically with K under some conditions. It is shown that the optimum detector in a Gaussian randomly spread CDMA system has a performance close to the single user system at high signal-to-noise ratio when K and N → ∞ and the loading factor, (K/N), is kept less than (log3K/2). Random binary antipodal matrices are also studied and a lower bound for the optimum asymptotic multiuser efficiency is obtained. Furthermore, we investigate the connection between detecting matrices in the coin weighing problem and optimum asymptotic multiuser efficiency. We obtain a condition such that for any binary input, an N × K random matrix, whose entries are chosen randomly from a finite set, is a detecting matrix as K and N → ∞.

We propose a new image recovery method to improve the resolution in microwave imaging applications. Scattered field data obtained from a simplified breast model with closely located targets is used to formulate an electromagnetic inverse scattering problem, which is then solved using the Distorted Born Iterative Method (DBIM). At each iteration of the DBIM method, an underdetermined set of linear equations is solved using our proposed sparse recovery algorithm, IMATCS. Our results demonstrate the ability of the proposed method to recover small targets in cases where traditional DBIM approaches fail. Furthermore, in order to regularize the sparse recovery algorithm, we propose a novel L(2) -based approach and prove its convergence. The simulation results indicate that the L(2)-regularized method improves the robustness of the algorithm against the ill-posed conditions of the EM inverse scattering problem. Finally, we demonstrate that the regularized IMATCS-DBIM approach leads to fast, accurate and stable reconstructions of highly dense breast compositions.

We derive some bounds on the Optimum Asymptotic Multiuser Efficiency (OAME) of randomly spread CDMA as extensions of the result by Tse and Verdú. To this end, random Gaussian and random binary antipodal spreading are considered. Furthermore, the input signal is assumed to be Binary Phase Shift Keying (BPSK). It is shown that in a CDMA system with K-user and N chips when K and N → 8 and the loading factor, K over N, grows logarithmically with K, the OAME converges to 1 almost surely under some condition. It is also shown that a Gaussian randomly spread CDMA system has a performance close to the single user system at high Signal to Noise Ratio (SNR) when the loading factor is kept less than log3K over 2. Moreover, for random binary antipodal matrices, we show that the loading factor cannot grow faster than equation.

In this study, the authors explore a generalised scheme for the synchronous code division multiple access (CDMA). In this scheme, unlike the standard CDMA systems, each user has different codewords for communicating different messages. Two main problems are investigated. The first problem concerns whether uniquely detectable overloaded matrices (an injective matrix, i.e. the inputs and outputs are in one‐to‐one correspondence depending on the input alphabets) exist in the absence of additive noise, and if so, whether there are any practical optimum detectors for such input codewords. The second problem is about finding tight bounds for the sum channel capacity. In response to the first problem, the authors have constructed uniquely detectable matrices for the generalised scheme and the authors have developed practical maximum likelihood detection algorithms for such codes. In response to the second problem, lower bounds and conjectured upper bounds are derived. The results of this study are superior to other standard overloaded CDMA codes since the generalisation can support more users than the previous schemes.

In this study, the performance of a spectral‐amplitude‐coding optical code division multiple access (SAC‐OCDMA) system in the asynchronous regime is evaluated using a Gaussian approximation of the decision variable for codes with fixed cross‐correlation used in SAC‐OCDMA systems. The authors consider the effect of phase‐induced intensity noise (PIIN), thermal noise and shot noise. Moreover, the validity of the Gaussian approximation is confirmed by a Kolmogorov–Smirnov fitness test. For sake of comparison, the bit error rate (BER) of the asynchronous SAC‐OCDMA system is also plotted numerically in comparison with the BER of the synchronous SAC‐OCDMA. They show that a SAC‐OCDMA system without any time management for the users, that is, the asynchronous regime, has a better performance than the synchronous SAC‐OCDMA when PIIN effect exists.

The objective of this study is to design sub‐optimal signature matrices for binary inputs for an overloaded code division multiple access (CDMA) system as developed by this author group. In this study, the authors propose to use the sum capacity, the bit error rate and distance criteria as objective functions for signature matrix optimisation. Three optimisation techniques, the genetic algorithm, the particle swarm optimisation and the conjugate gradient (CG) are exploited in this work. Since the optimisation computational complexity increases by matrix dimensions, it is practically impossible to directly optimise the large signature matrices. In order to address this problem, a method is proposed to enlarge small‐scale signature matrices. It is also proved that the sum channel capacity of the enlarged matrix is scaled by its enlargement factor. The results indicate that this proposed signature matrices provide higher sum capacity than the commonly used signature matrices. The authors also address that this matrices are applicable for highly overloaded CDMA systems.

In this study, the authors investigate the performance of optical code‐division multiple access (OCDMA) systems with belief propagation (BP)‐based receivers. They propose three receivers for the optical fibre channel that provide a trade‐off between detecting complexity and system performance. The first proposed receiver achieves a performance very close to the so‐called known interference lower bound. The second receiver exhibits a considerably less complexity at the expense of a slight degradation in performance. They show that the third BP‐based receiver, which is a simplified version of the second receiver, is surprisingly the same as the so‐called multistage detector in OCDMA systems. They then study the problem of finding proper spreading codes for the proposed receivers. BP‐based receivers perform well if the graph corresponding to the spreading matrix has no short cycles. The probability of existence of short cycles directly depends on the sparsity of the spreading matrix. Therefore they look for sparse spreading matrices that are also uniquely detectable, that is, the corresponding input data vectors and the output spread vectors are in one‐to‐one correspondence. The existence of random uniquely detectable matrices (for which the elements are binary with equal probability) has already been proved by Edrös and Rényi when the dimensions of matrix tend to infinity. In this study, they prove the existence of sparse uniquely detectable spreading matrices in the large system limit, when the number of users and the number of chips approach infinity and their ratio is kept constant. For finite length systems, they propose to use optical codes with one chip interference between codes and show that they exhibit a better performance than random sparse codes.

In this paper, we prove the existence of capacity achieving linear codes with random binary sparse generating matrices over the Binary Symmetric Channel (BSC). The results on the existence of capacity achieving linear codes in the literature are limited to the random binary codes with equal probability generating matrix elements and sparse parity-check matrices. Moreover, the codes with sparse generating matrices reported in the literature are not proved to be capacity achieving for channels other than Binary Erasure Channel. As opposed to the existing results in the literature, which are based on optimal maximum a posteriori decoders, the proposed approach is based on a different decoder and consequently is suboptimal. We also demonstrate an interesting trade-off between the sparsity of the generating matrix and the error exponent (a constant which determines how exponentially fast the probability of error decays as block length tends to infinity). Based on our results, we also propose a channel coding rate achievable by linear codes at a given block length and error probability. Moreover, we prove the existence of capacity achieving linear codes with a given (arbitrarily low) density of ones on rows of the generating matrix. In addition to proving the existence of capacity achieving sparse codes, an important conclusion of our paper is to prove that any arbitrarily selected sequence of sparse generating matrices is capacity achieving with high probability.

In this paper, we introduce a new class of signature matrices for overloaded synchronous CDMA systems that have a very low complexity decoder. While overloaded systems are more efficient from the bandwidth point of view, the Maximum Likelihood (ML) implementation for decoding is impractical even for moderate dimensions. Simulation results show that the performance of the proposed decoder is very close to that of the ML decoder. Indeed, the proposed decoding scheme needs neither multiplication nor addition and requires only a few comparisons . Furthermore, the computational complexity and the probability of error vs. Signal to Noise Ratios (SNR) are derived analytically.

In this paper, we explore some of the fundamentals of synchronous Code Division Multiple Access (CDMA) as applied to wireless and optical communication systems under very general settings (of any size) for the user symbols and the signature matrix entries. The channel is modeled by real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether uniquely detectable overloaded matrices exist in the absence of additive noise under these general settings, and if so, whether there are any practical optimum detection algorithms. The second one is about the bounds for the sum channel capacity when user data and signature matrices employ any real or complex alphabets (finite or infinite). In response to the first problem, we have developed practical maximum likelihood detection algorithms for overloaded CDMA systems for a large class of alphabets. In response to the second problem, a general theorem has been developed in which the sum capacity lower bounds with respect to the number of users, spreading gain, and signal-to-noise ratio can be derived. To show the power and utility of the main theorem, a number of sum capacity bounds for special cases are evaluated. An important conclusion of this paper is that the lower and upper bounds of the sum capacity for small/medium-size CDMA systems depend on both the input and the signature symbols; this is contrary to the asymptotic results for large-scale systems reported in the literature (also confirmed in this paper) where the signature symbols and statistics disappear for signature matrices and input vectors with i.i.d. entries. Furthermore, upper and asymptotic bounds are derived and compared to other derivations.

The problem of extracting low-dimensional structure from high-dimensional data arises in many applications such as machine learning, statistical pattern recognition, wireless sensor networks, and data compression. If the data is restricted to a lower dimensional subspace, then simple algorithms using linear projections can find the subspace and consequently estimate its dimensionality. However, if the data lies on a low-dimensional but nonlinear space (e.g., manifolds), then its structure may be highly nonlinear and, hence, linear methods are doomed to fail. In this paper, we introduce a new technique for dimensionality reduction based on point-wise operators. More precisely, let be a matrix of rank and assume that the matrix is generated by taking the elements of to some real power . In this paper, we show that based on the values of the data matrix , one can estimate the value and, therefore, the underlying low-rank matrix ; i.e., we are reducing the dimensionality of by using point-wise operators. Moreover, the estimation algorithm does not need to know the rank of . We also provide bounds on the quality of the approximation and validate the stability of the proposed algorithm with simulations in noisy environments.

In this paper, capacity inner and outer bounds are established for multiuser channels with Channel State Information (CSI) known non-causally at the transmitters: The Multiple Access Channel (MAC), the Broadcast Channel (BC) with common information, and the Relay Channel (RC). For each channel, the actual capacity region is also derived in some special cases. Specifically, it is shown that for some deterministic models with non-causal CSI at the transmitters, similar to Costa's Gaussian channel, the availability of CSI at the deterministic receivers does not affect the capacity region.

In this paper, we establish the connection between the Orthogonal Optical Codes (OOC) and binary compressed sensing matrices. We also introduce deterministic bipolar m × n RIP fulfilling ±1 matrices of orderksuch thatm≤O(k(log2n)( log2k)/( ln log2k)). The columns of these matrices are binary BCH code vectors where the zeros are replaced by -1. Since the RIP is established by means of coherence, the simple greedy algorithms such as Matching Pursuit are able to recover the sparse solution from the noiseless samples. Due to the cyclic property of the BCH codes, we show that the FFT algorithm can be employed in the reconstruction methods to considerably reduce the computational complexity. In addition, we combine the binary and bipolar matrices to form ternary sensing matrices ({0,1,-1} elements) that satisfy the RIP condition.

This paper investigates the capacity problem for some multiple-access scenarios with cooperative transmitters. First, a general Multiple-Access Channel (MAC) with common information, i.e., a scenario where p transmitters send private messages and also a common message to q receivers and each receiver decodes all of the messages, is considered. The capacity region of the discrete memoryless channel is characterized. Then, the general Gaussian fading MAC with common information wherein partial Channel State Information (CSI) is available at the transmitters (CSIT) and perfect CSI is available at the receivers (CSIR) is investigated. A coding theorem is proved for this model that yields an exact characterization of the throughput capacity region. Finally, a two-transmitter/one-receiver Gaussian fading MAC with conferencing encoders with partial CSIT and perfect CSIR is studied and its capacity region is determined. For the Gaussian fading models with CSIR only (transmitters have no access to CSIT), some numerical examples and simulation results are provided for Rayleigh fading.

Among the many attacks against watermarked data, the gain attack is less supported with countermeasures. The effectiveness of this attack becomes more evident in quantization-based embedding algorithms such as Dither Modulation (DM). In this paper, the general solution for both block and sample type DM schemes that are robust against gain attacks is considered. Among the solutions, we concentrate on a subclass of the algorithms which are insensitive to additive noise attacks; i.e., we introduce watermarking schemes which are both robust against gain and additive noise attacks. The simulation results confirm the desired performance of the final algorithm against these attacks while outperform other gain invariant schemes.

In this paper we propose a new model for the near-far effect in a CDMA system. We derive upper and lower bounds for the maximum near-far effect for errorless transmission. Using these bounds, we propose some near-far resistant codes. Also a very low complexity ML decoder for a subclass of the proposed codes is suggested.

Lower and upper bounds are derived for the sum capacity of synchronous CDMA where the signature matrix and input alphabets are binary or (2p + 1)-ary, in two cases of noiseless and noisy channels. The bounds are very tight in some regions. Interestingly, simulations show that the formulas for noisy systems tend to the ones for noiseless system as noise tends to 0 while it cannot be deduced easily from the formulas. The results give good insights about the extent of the number of users in which errorless communication is possible for a system with a given chip rate.

In this paper, we study the two-user Gaussian fading Multiple Access Channel (MAC) with cooperative encoders. Two different scenarios are studied: the Gaussian fading MAC with a common message, and the Gaussian fading MAC with conferencing encoders. The throughput capacity region of these channels with partial Channel State Information (CSI) at the transmitters (CSIT) and perfect CSI at the receiver (CSIR) is established. For the Gaussian fading systems with only CSIR (transmitters have no access to CSIT), some numerical examples and simulation results are provided for Rayleigh fading models.

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.

In this paper, a novel quantization based watermarking method is proposed. For blind detection, a set of nonlinear convex functions based on geometric mean are investigated. In order to achieve minimum distortion, the optimum function set is found. The algorithm is implemented on the approximation coefficients of wavelet transform for natural images. In order to make the algorithm more robust and imperceptible, a new transform domain called Point to Point Graph (PPG), which converts a 1-D signal to a 2-D one, has been used. The error probability of the proposed scheme is analytically investigated. Simulation results show that this algorithm has great robustness against common attacks such as AWGN, JPEG and rotation in comparison with recent methods presented so far.

In this paper, a semi-blind multiplicative watermarking approach for audio and speech signals has been presented. At the receiver end, the optimal maximum likelihood (ML) detector aided by the channel side information for Gaussian and Laplacian signals in noisy environment is designed and implemented. The performance of the proposed scheme is analytically calculated and verified by simulation. Then, we adapt the proposed scheme to speech and audio signals. To improve robustness, the algorithm is applied to low frequency components of the host signal. Besides, the power of the watermark is controlled elegantly to have inaudibility using perceptual evaluation of audio quality (PEAQ) and perceptual evaluation of speech quality (PESQ) algorithms. Experimental results over several audio and speech signals show the higher robustness of the proposed technique in comparison with a recent watermarking scheme.

In this paper we introduce a new class of codes for over-loaded synchronous wireless CDMA systems which increases the number of users for a fixed number of chips without introducing any errors. In addition these codes support active user detection. We derive an upper bound on the number of users with a fixed spreading factor. Also we propose an ML decoder for a subclass of these codes that is computationally implementable. Although for our simulations we consider a scenario that is worse than what occurs in practice, simulation results indicate that this coding/decoding scheme is robust against additive noise. As an example, for 64 chips and 88 users we propose a coding/decoding scheme that can obtain an arbitrary small probability of error which is computationally feasible and can detect active users. Furthermore, we prove that for this to be possible the number of users cannot be beyond 230.

In this paper, a novel scaling based information hiding approach robust against noise and gain attack is presented. The host signal is assumed to be stationary Gaussian modeled with a first-order autoregressive process. For data embedding, the host signal is divided into two parts. One part is manipulated while the other part is kept unchanged for parameter estimation. The decoding scheme using the ratio of samples is suitable for highly correlated signals in which the decoding process is difficult. By calculating the distribution of the ratio, the performance of the maximum likelihood decoder is analytically studied. The proposed algorithm is applied to several artificial Gaussian autoregressive signals to verify the validity of our results.

In this paper, a new blind scaling based watermarking approach is presented. The host signal is assumed to be stationary Gaussian with first-order autoregressive model. Partitioning the host signal into two separate parts, the data is embedded in one part and the other is kept unchanged for blind parameter estimation. Driving the distribution of the decision variable we have suggested a maximum likelihood decoding algorithm which is independent of the host signal distribution and can be applied for any transform domains. The proposed algorithm is applied to both artificial Gaussian autoregressive signals as well as various test images. Experimental results confirm the independence of the decoder performance to the host signal distribution and its great robustness against common attacks.

In this paper, we obtain a family of lower bounds for the sum capacity of code-division multiple-access (CDMA) channels assuming binary inputs and binary signature codes in the presence of additive noise with an arbitrary distribution. The envelope of this family gives a relatively tight lower bound in terms of the number of users, spreading gain, and the noise distribution. The derivation methods for the noiseless and the noisy channels are different but when the noise variance goes to zero, the noisy channel bound approaches the noiseless case. The behavior of the lower bound shows that for small noise power, the number of users can be much more than the spreading gain without any significant loss of information (overloaded CDMA). A conjectured upper bound is also derived under the usual assumption that the users send out equally likely binary bits in the presence of additive noise with an arbitrary distribution. As the noise level increases, and/or, the ratio of the number of users and the spreading gain increases, the conjectured upper bound approaches the lower bound. We have also derived asymptotic limits of our bounds that can be compared to a formula that Tanaka obtained using techniques from statistical physics; his bound is close to that of our conjectured upper bound for large scale systems.

In this paper, we introduce a new class of codes for overloaded synchronous wireless and optical code-division multiple-access (CDMA) systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of a binary overloaded CDMA are derived that can predict the existence of such overloaded codes. We also propose a simplified maximum likelihood method for decoding these types of overloaded codes. Although a high percentage of the overloading factor degrades the system performance in noisy channels, simulation results show that this degradation is not significant. More importantly, for moderate values ofEb/N0(in the range of 6-10 dB) or higher, the proposed codes perform much better than the binary Welch bound equality sequences.

In this paper, two blind audio watermarking methods using correlated quantization for data embedding with histogram-based detector have been proposed. First, a novel mapping called the point-to-point graph (PPG) is introduced. In this mapping, the value of samples is important as well as the correlation among them. As this mapping increases the dimension of the signal, the data embedding procedure (quantization) will be diversified more securely than that of the 1-D domains such as the time or frequency domains. Hence, two watermarking techniques coined as hard and soft quantization methods based on the quantization of the PPG point radii are suggested. The performance of both techniques is analyzed by obtaining the radii distribution of PPG points after watermarking. Experimental results against AWGN attack confirm the validity of theoretical analysis. Moreover, the robustness of the proposed methods against other common attacks such as echo, low pass, resampling, and MP3 are investigated through extensive simulations.

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.

In this paper a new class of invertible watermarking approach based on quantization has been introduced. Based on the necessary conditions (blindness, reversibility and imperceptibility), a set of linear convex functions which satisfy these requirements are found. Then the optimum of this function set with the least distortion has been selected. The main advantage of this method is that the inserted distortion can be easily controlled by adjusting quantization levels. The low computational complexity is another advantage of this method. Experimental results show that the proposed algorithm achieves higher embedding capacity while its distortion is lower than other invertible watermarking techniques.

In this paper, a new multiplicative image watermarking system is presented. As 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 the most energetic directional subband. By modeling general gaussian distribution (GGD) for the contourlet coefficients, the distribution of watermarked noisy coefficients is analytically calculated. At the receiver, based on the maximum likelihood (ML) decision rule, the optimal detector is proposed. Experimental results show the imperceptibility and high robustness of the proposed method against Additive White Gaussian Noise (AWGN) and JPEG compression attacks.

In this paper we introduce a new class of codes for over-loaded synchronous wireless and optical CDMA systems which increases the number of users for fixed number of chips without introducing any errors. Equivalently, the chip rate can be reduced for a given number of users, which implies bandwidth reduction for downlink wireless systems. An upper bound for the maximum number of users for a given number of chips is derived. Also, lower and upper bounds for the sum channel capacity of an overloaded CDMA are derived that can predict the existence of such overloaded codes. Although a high percentage of the overloading factor degrades the system performance in noisy channels, simulation results show that this degradation is not significant.

In this paper we propose a new method for image noise reduction based on wavelet transform. In this method we introduce an improved version of thresholding neural networks (TNN) by utilizing a new class of smooth nonlinear thresholding functions as the activation function. Using this approach we will find the best thresholds in the sense of minimum mean square error (MMSE). Then using TNN with obtained thresholds, we employ a cycle-spinning-based technique to reduce image artifacts. Experimental results indicate that the proposed method outperforms several other established wavelet denoising techniques, in terms of peak-signal-to-noise-ratio (PSNR) and visual quality.

Long Reed-Solomon codes over the prime field GF(216+1) are proposed as a low overhead channel code for reliable transmission of video over noisy and lossy channels. The added redundancy is near optimal from the information theoretic point of view contrary to the conventionally used intra-coding and sync (marker) insertion in video transmission that are not justified theoretically. Compared to known source-channel coding methods, we have achieved the quality of the output of source coder by providing nearly error free transmission. (By nearly error free we mean an arbitrarily small error probability.) The price paid for such remarkable video quality improvement and relatively low complexity is long delay due to long codes. However, the incurred delay is justifiable for Internet low bit video transmission and in high quality video broadcasting systems like streaming MPEG2 video where each encoder and decoder may have three frames delay. The proposed method surpasses the previous works for video transmission over binary symmetric channels, bursty channels, and packet loss channels. Also we propose a nearly error free transmission system for Gaussian channels for completeness of the work. We have also proposed short codes, which with larger overhead provide nearly error free transmission, and still outperform the previous works

A hybrid video codec, where the intraframe pictures are wavelet-based coded and the interframe pictures are coded with a standard H.263 codec is proposed. We show that intraframe-wavelet coded pictures not only improve the quality of I-pictures but also result in lower distorted prediction pictures that outperforms a pure H.263 video codec.

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.

We propose a novel decoding technique for DFT-based error control codes, which is robust against quantization and additive noise. The proposed algorithm simultaneously determines the number and the positions of the corrupted samples. We show that in contrast to conventional decoding techniques, the proposed decoding method is stable in the presence of quantization and additive noise.

It is well known that clipping the OFDM signals in digital part of the transmitter is one of the simplest methods to reduce the peak to mean envelop power ratio. However, it suffers from additional clipping distortion, peak regrowth after digital to analog conversion, and out-of-band distortion. Recently, to combat the effect of in-band distortion and peak regrowth, it is proposed that before clipping, oversampling is performed by padding the modulating sequence with zeros. In this paper, we propose a robust DFT-based method (DBM) to reconstruct the clipped samples and mitigate the clipping distortion in the presence of channel noise at the expense of bandwidth expansion. We show through extensive simulations that by slightly increasing the bandwidth of the system, we can significantly improve the performance while limiting the maximum of the analog signal. Furthermore, we compare the performance of the DBM and the channel coding methods. It can be seen that for lower bandwidth expansions, the DBM outperforms the channel coding methods at moderate SNR values while for higher bandwidth expansions, the channel coding methods seem to be more efficient. Furthermore, we introduce a hybrid system which outperforms both the DBM and the channel coding methods at most SNR values.

Almost any system for the detection of asymptomatic circulating emboli by Doppler ultrasound employs the fast Fourier Transform (FFT). However, the FFT is not ideally suited to study short-lived embolic signals. The wavelet transform (WT) is an optimized way of analyzing short-lived signals and performs better than the FFT in some respects. We propose a detection method based on the discrete wavelet transform (DWT) and study some parameters, which might be useful for describing embolic signals. We used 2 independent data sets, comprising 100 low intensity embolic signals, 100 various type of artifacts and 100 Doppler speckle. 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. 98 out of 100 embolic signals were detected as embolic signals for the first data set. 95 out of 100 embolic signals were detected for the second data set when the same threshold values were used.

The magnitude spectrum of speech is sampled to extract the extremum (maximum) points representing the underlying sine-wave amplitudes. The resulting nonuniform samples are, first, interpolated using a cubic spline function and, then, modelled by an all-pole magnitude spectrum. The gain factor and the line spectral frequency (LSF) domain representation of the coefficients of the all-pole model are quantized at the encoder. A faithful reconstruction of the spectral extremum envelope is obtained at the decoder using the dequantized all-pole model parameters.

A new method to recover (8/spl times/8) block losses for JPEG compressed images is proposed, which can be used in wireless UMTS and asynchronous transfer mode (ATM) networks. The problem of image reconstruction with (8/spl times/8) block losses is transformed to a system of linear equations using two-dimensional trigonometric polynomials. The simulation results show the feasibility of this method. The sensitivity analysis of the proposed method shows that this method is robust against additive noise.

We present a novel class of forward error correcting codes constructed using the discrete Walsh transform. They are a class of double-error correcting codes defined on the field of real numbers. An iterative decoding algorithm for Walsh transform codes is developed and implemented. The error correcting performance of Walsh transform codes over an AWGN channel is evaluated. Selected Walsh transform code parameters are compared to those of the well-known BCH and RS codes.

We discuss the split band code-excited linear prediction (SB-CELP) speech coder which employs an iterative version of the harmonic sinusoidal coding algorithm to encode the periodic contents of speech signal. The speech spectrum is split into two frequency regions of harmonic and random components and a reliable fundamental frequency is estimated for the harmonic region using both speech and its linear predictive (LP) residual spectrum. The resulting sinusoidal parameters are interpolated to reconstruct the periodicity in speech waveform. The level of periodicity is controlled by computing a cutoff frequency between the harmonic and random regions of spectrum. The random part of spectrum and unvoiced speech are processed using the CELP coding algorithm. The SB-CELP speech coder which combines the powerful features of the sinusoidal and CELP coding algorithms yields a high quality synthetic speech at 4.05 kb/s.

Images transmitted via ATM networks suffer from quality degradation due to buffer overflow or cell header errors which cause ATM cells to be lost. This paper presents a new approach to conceal the errors in the received images by the application of novel error recovery techniques to the decomposed DCT-coefficient subimages of the corrupted image. These techniques were developed to recover images corrupted by impulsive noise. Since decomposing the corrupted image into the DCT-coefficient subimages generates low resolution images corrupted by impulsive noise, all the techniques used to recover images corrupted by impulsive noise can be used to recover the subimages and hence the corrupted image. We study the performance of new techniques to recover the corrupted subimages. The quality of the recovered image using these techniques is better than the quality obtained by many classical error concealment techniques.

Describes the interpolation of low-pass signals from a class of stable sampling sets at half the Nyquist rate. Practical reconstruction algorithms are also suggested.

We note that the arrangement of the rows or the block wavelet transform (BWT) matrix as given by Cetin, Gerek and Ulukus (see ibid. vol.3, no.6, p.433, 1993) is not in an increasing order of frequency as implied by the equations and figures in the same paper. The rows of the matrix are rearranged to follow an increasing order of frequency.

We describe the interpolation of low pass signals from a class of stable sampling sets at half the Nyquist rate. We also develop formulas based on Lagrange interpolation and suggest practical reconstruction algorithms.

The power spectrum of a signal derived by random nonuniform sampling of an analog signal (random or deterministic) is analyzed in terms of the power spectrum of the analog signal. It is shown that the spectrum consists of the original signal with a background white noise. The same analysis holds for uniform samples with time jitter and PAM with some missing samples. We show finally that the power spectrum of random pulse sequence is proportional to the power spectrum of the pulse.

We show that the problem presented in the above letter [1] by Papoulis has been proved by others [3]-[6] using different methods. We present a much simpler proof which covers random and deterministic signals with uniform or nonuniform sampling.

In this correspondence we show that the above paper is a rediscovery of what was known since 1973 [1]. The contents of the paper have been published in various forms in the literature. The more general case of a periodic wave crossing has already been considered, which covers the special case of a sine wave crossing.