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 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.

In this study, a two‐way full‐duplex amplify‐and‐forward relay network is considered in which two multi‐antenna fullduplex user nodes manage to exchange their information via a full‐duplex multi‐antenna relay. The users and relay can concurrently transmit their symbols in all time slots in the same frequency band, which leads to self‐interference (SI) at all nodes. The joint beamforming algorithm is used in which the relay and users beamforming matrices are updated in each time slot to suppress the SI. This algorithm needs the channel state information (CSI) of all previous time slots, so the complexity increases as time lapses. To decrease the complexity, an algorithm is proposed in which the beamforming matrix is computed recursively. Moreover, the channel estimation error is considered when the relay and users have partial CSI. Thus, a robust algorithm, i.e. an algorithm that takes the estimation error into account is proposed to decrease the effect of estimation error. The proposed algorithm has been evaluated in terms of mean square error, achievable sum rate and BER for various values of the estimation error variances and compared with the non‐robust algorithm. The results show that the superiority of the recursive robust algorithm in terms of SNR and 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.

This letter presents the sparse vector signal detection from one bit compressed sensing measurements, in contrast to the previous works that deal with scalar signal detection. Available results are extended to the vector case and the generalized likelihood ratio test (GLRT) detector and the optimal quantizer design are obtained. A double-detector scheme is introduced, in which a sensor level threshold detector is integrated into network level GLRT to improve the performance. The detection criteria of oracle and clairvoyant detectors are also derived. Simulation results show that with careful design of the threshold detector, the overall detection performance of double-detector scheme would be better than the sign-GLRT proposed in [J. Fang et al., “One-bit quantizer design for multisensor GLRT fusion,” IEEE Signal Process. Lett., vol. 20, no. 3, pp. 257-260, Mar. 2013] and close to oracle and clairvoyant detectors. The proposed detector is applied to spectrum sensing and the results are near the well-known energy detector, which uses the real valued data, while the proposed detector only uses the sign of the data.

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.

Using a novel block iterative Bayesian algorithm (Block-IBA), this paper presents a new impulsive noise reduction method for OFDM systems. The method utilizes the guard band null subcarriers and data subcarriers for the impulsive noise estimation and cancellation. Unlike some other general OFDM transceivers which use time-domain interleaving (TDI) to cancel impulsive noise, we design a specific receiver for bursty impulsive noise channels that removes the delay due to TDI and saves memory space. The Block-IBA first estimates the variance and the transition matrix of Markov chain model for the impulsive noise. It then iteratively estimates the amplitudes and positions of the block-sparse impulsive noise using the steepest-ascent based expectation-maximization (EM), and optimally selects the nonzero elements of the block-sparse impulsive noise by adaptive thresholding. Numerical experiments show that the proposed receiver outperforms existing receivers under the block-sparse impulsive noise environment.

This paper presents a novel iterative Bayesian algorithm, Block Iterative Bayesian Algorithm (Block-IBA), for reconstructing block-sparse signals with unknown block structures. Unlike the other existing algorithms for block sparse signal recovery which assume the cluster structure of the non-zero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to capture the burstiness (block structure) of the impulsive noise in practical applications such as Power Line Communication (PLC). The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal based on Expectation-Maximization (EM) algorithm which is also optimized with the steepest-ascent method. Simulation results show the effectiveness of our algorithm for block-sparse signal recovery.

We propose a new adaptive filtering algorithm in system identification applications which is based on a continuous mixed p-norm. It enjoys the advantages of various error norms since it combines p-norms for 1 ≤ p ≤ 2. The mixture is controlled by a continuous probability density-like function of p which is assumed to be uniform in our derivations in this letter. Two versions of the suggested algorithm are developed. The robustness of the proposed algorithms against impulsive noise are demonstrated in a system identification simulation.

In this paper, we suggest to use a steepest descent algorithm for learning a parametric dictionary in which the structure or atom functions are known in advance. The structure of the atoms allows us to find a steepest descent direction of parameters instead of the steepest descent direction of the dictionary itself. We also use a thresholded version of Smoothed-ℓ0(SL0) algorithm for sparse representation step in our proposed method. Our simulation results show that using atom structure similar to the Gabor functions and learning the parameters of these Gabor-like atoms yield better representations of our noisy speech signal than non parametric dictionary learning methods like K-SVD, in terms of mean square error of sparse representations.

We propose an ℓ1criterion for dictionary learning for sparse signal representation. Instead of directly searching for the dictionary vectors, our dictionary learning approach identifies vectors that are orthogonal to the subspaces in which the training data concentrate. We study conditions on the coefficients of training data that guarantee that ideal normal vectors deduced from the dictionary are local optima of the criterion. We illustrate the behavior of the criterion on a 2D example, showing that the local minima correspond to ideal normal vectors when the number of training data is sufficient. We conclude by describing an algorithm that can be used to optimize the criterion in higher dimension.

In this paper, we suggest to use a modified version of Smoothed-lscr0(SL0) algorithm in the sparse representation step of iterative dictionary learning algorithms. In addition, we use a steepest descent for updating the non unit column-norm dictionary instead of unit column-norm dictionary. Moreover, to do the dictionary learning task more blindly, we estimate the average number of active atoms in the sparse representation of the training signals, while previous algorithms assumed that it is known in advance. Our simulation results show the advantages of our method over K-SVD in terms of complexity and performance.

In this paper, we propose a Bayesian pursuit algorithm for sparse representation. It uses both the simplicity of the pursuit algorithms and optimal Bayesian framework to determine active atoms in sparse representation of a signal. We show that using Bayesian Hypothesis testing to determine the active atoms from the correlations leads to an efficient activity measure. Simulation results show that our suggested algorithm has better performance among the algorithms which have been implemented in our simulations in most of the cases.

In this paper, a new approach for decoding real-field codes based on finding sparse solutions of underdetermined linear systems is proposed. This algorithm iteratively estimates the positions and the amplitudes of the sparse errors (or noise impulses) using an expectation-maximization (EM) algorithm. Iterative estimation of amplitudes is done in the expectation step (E-step), while iterative estimation of error positions is done in the maximization step (M-step). Simulation results show 1-2 dB improvement over linear programming (LP) which has been previously used for error correction.

In this letter, we address the theoretical limitations in estimating the mixing matrix in noisy sparse component analysis (SCA) for the two-sensor case. We obtain the Cramer-Rao lower bound (CRLB) error estimation of the mixing matrix. Using the Bernouli-Gaussian (BG) sparse distribution, and some simple assumptions, an approximation of the Fisher information matrix (FIM) is calculated. Moreover, this CRLB is compared to some of the main methods of mixing matrix estimation in the literature.