Seyed Javad Heydari, Mahmoud Ferdosizade Naeiny, Farokh Marvasti
In Spectrally Efficient Frequency Division Multiplexing systems the input data stream is divided into several adjacent subchannels where the distance of the subchannels is less than that of Orthogonal Frequency Division Multiplexing(OFDM)systems. Since the subcarriers are not orthogonal in SEFDM systems, they lead to interference at the receiver side. In this paper, an iterative method is proposed for interference compensation for SEFDM systems. In this method a soft mapping technique is used after each iteration block to improve its performance. The performance of the proposed method is comparable to that of Sphere Detection(SD)which is a nearly optimal detection method.
K. Alishahi, S. Dashmiz, P. Pad, F. Marvasti, M. H. Shafinia, M. Mansouri
In this paper, we explore the mystery of synchronous CDMA as applied to wireless and optical communication systems under very general settings for the user symbols and the signature matrix entries. The channel is modeled with real/complex additive noise of arbitrary distribution. Two problems are addressed. The first problem concerns whether overloaded error free codes exist in the absence of additive noise under these general settings, and if so whether there are any practical optimum decoding algorithms. The second one is about the bounds for the sum channel capacity when user data and signature codes employ any real or complex alphabets (finite or infinite). In response to the first problem, we have developed practical Maximum Likelihood (ML) decoding 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 and spreading gain and Signal-to-Noise Ratio (SNR) can be derived as special cases for a given CDMA system. To show the power and utility of the main theorem, a number of sum capacity bounds for special cases are simulated. 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 in the asymptotic sum capacity. Moreover, these questions are investigated for the case when not all users are active. Furthermore, upper and asymptotic bounds are derived and numerically evaluated and compared to other derivations.
Pedram Pad, Mahdi Soltanolkotabi, Saeed Hadikhanlou, Arash Enayati, Farokh Marvasti
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.
Sahar Sadrizadeh, Nematollah Zarmehi, Ehsan Asadi, Hamidreza Abin, Farokh Marvasti
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 problem investigated in this paper arises in different applications such as impulsive noise removal from images, audios and videos, decomposition of low-rank and sparse components of matrices, and separation of texts from images. First, we provide a cost function for our problem and then present an iterative method to find its local minimum. The analysis of the algorithm is also provided. As an application of this problem, we apply our algorithm for impulsive noise 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 is simple and fast, and it outperforms other state-of-the-art methods in terms of reconstruction quality and/or complexity.
Seyed Majid Naji, Azra Abtahi, Farokh Marvasti
The brain, as the source of inspiration for Artificial Neural Networks (ANN), is based on a sparse structure. This sparse structure helps the brain to consume less energy, learn easier and generalize patterns better than any other ANN. In this paper, two evolutionary methods for adopting sparsity to ANNs are proposed. In the proposed methods, the sparse structure of a network as well as the values of its parameters are trained and updated during the learning process. The simulation results show that these two methods have better accuracy and faster convergence while they need fewer training samples compared to their sparse and non-sparse counterparts. Furthermore, the proposed methods significantly improve the generalization power and reduce the number of parameters. For example, the sparsification of the ResNet47 network by exploiting our proposed methods for the image classification of ImageNet dataset uses 40 % fewer parameters while the top-1 accuracy of the model improves by 12% and 5% compared to the dense network and their sparse counterpart, respectively. As another example, the proposed methods for the CIFAR10 dataset converge to their final structure 7 times faster than its sparse counterpart, while the final accuracy increases by 6%.
Mohammad Amin Fakharian, Ashkan Esmaeili, Farokh Marvasti
In this paper, prediction for linear systems with missing information is investigated. New methods are introduced to improve the Mean Squared Error (MSE) on the test set in comparison to state-of-the-art methods, through appropriate tuning of Bias-Variance trade-off. First, the use of proposed Soft Weighted Prediction (SWP) algorithm and its efficacy are depicted and compared to previous works for non-missing scenarios. The algorithm is then modified and optimized for missing scenarios. It is shown that controlled over-fitting by suggested algorithms will improve prediction accuracy in various cases. Simulation results approve our heuristics in enhancing the prediction accuracy.
Ashkan Esmaeili, Ehsan Asadi, Farokh Marvasti
Adaptive thresholding methods have proved to yield high SNRs and fast convergence in finding the solution to the Compressed Sensing (CS) problems. Recently, it was observed that the robustness of a class of iterative sparse recovery algorithms such as Iterative Method with Adaptive Thresholding (IMAT) has outperformed the well-known LASSO algorithm in terms of reconstruction quality, convergence speed, and the sensitivity to the noise. In this paper, we introduce a new method towards solving the CS problem. The logic of this method is based on iterative projections of the thresholded signal onto the null-space of the sensing matrix. The thresholding is carried out by recovering the support of the desired signal by projection on thresholding subspaces. The simulations reveal that the proposed method has the capability of yielding noticeable output SNR values with about as many samples as twice the sparsity number, while other methods fail to recover the signals when approaching the algebraic bound for the number of samples required. The computational complexity of our method is also comparable to other methods as observed in the simulations. We have also extended our Algorithm to Matrix Completion (MC) scenarios and compared its efficiency to other well-reputed approaches for MC in the literature.
Masoumeh Azghani, Mostafa Karimi, Farokh Marvasti
In this paper, we present a compressive sampling and Multi-Hypothesis (MH) reconstruction strategy for video sequences which 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 the recovery performance. Besides it is computationally much faster than the Elasticnet and comparable to the Tikhonov. Our extensive simulation results confirm these claims.
Amir Zandieh, Alireza Zareian, Masoumeh Azghani, Farokh Marvasti
As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling rates. Hence, lower sampling rates (i.e., sub-Nyquist) are considered to be cost efficient. A well-known approach is to consider sparse signals that have fewer nonzero frequency components compared to the highest frequency component. For the prior knowledge of the sparse positions, well-established methods already exist. However, there are applications where such information is not available. For such cases, a number of approaches have recently been proposed. In this paper, we propose several random sampling recovery algorithms which do not require any anti-aliasing filter. Moreover, we offer certain conditions under which these recovery techniques converge to the signal. Finally, we also confirm the performance of the above methods through extensive simulations.
Hossein Hosseini, Ali Goli, Neda Barzegar Marvasti, Masoume Azghani, Farokh Marvasti
In this paper, we propose a method for image block loss restoration based on the notion of sparse representation. We use the sparsity pattern as side information to efficiently restore block losses by iteratively imposing the constraints of spatial and transform domains on the corrupted image. Two novel features, including a pre-interpolation and a criterion for stopping the iterations, are proposed to improve the performance. Also, to deal with practical applications, we develop a technique to transmit the side information along with the image. In this technique, we first compress the side information and then embed its LDPC coded version in the least significant bits of the image pixels. This technique ensures the error-free transmission of the side information, while causing only a small perturbation on the transmitted image. Mathematical analysis and extensive simulations are performed to validate the method and investigate the efficiency of the proposed techniques. The results verify that the proposed method outperforms its counterparts for image block loss restoration.
Amirhossein Javaheri, Hadi Zayyani, Farokh Marvasti
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index, which is convex and error-sensitive. The optimization problem incorporating this criterion, is then solved via Alternating Direction Method of Multipliers (ADMM). Simulation results show the efficiency of the proposed method for missing sample recovery of 1D patch vectors and inpainting of 2D image signals.
Ashkan Esmaeili, Farokh Marvasti
In this paper, we will investigate the efficacy of IMAT (Iterative Method of Adaptive Thresholding) in recovering the sparse signal (parameters) for linear models with missing data. Sparse recovery rises in compressed sensing and machine learning problems and has various applications necessitating viable reconstruction methods specifically when we work with big data. This paper will focus on comparing the power of IMAT in reconstruction of the desired sparse signal with LASSO. Additionally, we will assume the model has random missing information. Missing data has been recently of interest in big data and machine learning problems since they appear in many cases including but not limited to medical imaging datasets, hospital datasets, and massive MIMO. The dominance of IMAT over the well-known LASSO will be taken into account in different scenarios. Simulations and numerical results are also provided to verify the arguments.
Mahdi Boloursaz Mashhadi, Maryam Fallah, Farokh Marvasti
This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by the findings on sparse signal reconstruction, we consider the graph signal to be rather sparse/compressible in the Graph Fourier Transform (GFT) domain and propose the Iterative Method with Adaptive Thresholding for Graph Interpolation (IMATGI) algorithm for sparsity promoting interpolation of the underlying graph signal.We analytically prove convergence of the proposed algorithm. We also demonstrate efficient performance of the proposed IMATGI algorithm in reconstructing randomly generated sparse graph signals. Finally, we consider the widely desirable application of recommendation systems and show by simulations that IMATGI outperforms state-of-the-art algorithms on the benchmark datasets in this application.
Mahmoud Essalat, Mahdi Boloursaz Mashhadi, Farokh Marvasti
PPG based heart rate (HR) monitoring has recently attracted much attention with the advent of wearable devices such as smart watches and smart bands. However, due to severe motion artifacts (MA) caused by wristband stumbles, PPG based HR monitoring is a challenging problem in scenarios where the subject performs intensive physical exercises. This work proposes a novel approach to the problem based on supervised learning by Neural Network (NN). By simulations on the benchmark datasets [1], we achieve acceptable estimation accuracy and improved run time in comparison with the literature. A major contribution of this work is that it alleviates the need to use simultaneous acceleration signals. The simulation results show that although the proposed method does not process the simultaneous acceleration signals, it still achieves the acceptable Mean Absolute Error (MAE) of 1.39 Beats Per Minute (BPM) on the benchmark data set.
Ali Taimori, Farokh Marvasti
Compressive sensing is a new technology for modern computational imaging systems. In comparison to widespread conventional image sensing, the compressive imaging paradigm requires specific forensic analysis techniques and tools. In this regards, one of basic scenarios in image forensics is to distinguish traditionally sensed images from sophisticated compressively sensed ones. To do this, we first mathematically and systematically model the imaging system based on compressive sensing technology. Afterwards, a simplified version of the whole model is presented, which is appropriate for forensic investigation applications. We estimate the nonlinear system of compressive sensing with a linear model. Then, we model the imaging pipeline as an inverse problem and demonstrate that different imagers have discriminative degradation kernels. Hence, blur kernels of various imaging systems have utilized as footprints for discriminating image acquisition sources. In order to accomplish the identification cycle, we have utilized the state-of-the-art Convolutional Neural Network (CNN) and Support Vector Machine (SVM) approaches to learn a classification system from estimated blur kernels. Numerical experiments show promising identification results. Simulation codes are available for research and development purposes.
Mahdi Soltanolkotabi, Arash Amini, Farokh Marvasti
Wireless OFDM channels can be approximated by a time varying filter with sparse time domain taps. Recent achievements in sparse signal processing such as compressed sensing have facilitated the use of sparsity in estimation, which improves the performance significantly. The problem of these sparse-based methods is the need for a stable transformation matrix which is not fulfilled in the current transmission setups. To assist the analog filtering at the receiver, the transmitter leaves some of the subcarriers at both edges of the bandwidth unused which results in an ill-conditioned DFT submatrix. To overcome this difficulty we propose Adaptive Thresholding for Sparse Signal Detection (ATSSD). Simulation results confirm that the proposed method works well in time-invariant and specially time-varying channels where other methods may not work as well.
Arash Amini, Farokh Marvasti
In this paper we introduce deterministic $m\times n$ RIP fulfilling $\pm 1$ matrices of order $k$ such that $\frac{\log m}{\log k}\approx \frac{\log(\log_2 n)}{\log(\log_2 k)}$. The columns of these matrices are binary BCH code vectors that their zeros are replaced with -1 (excluding the normalization factor). The samples obtained by these matrices can be easily converted to the original sparse signal; more precisely, for the noiseless samples, the simple Matching Pursuit technique, even with less than the common computational complexity, exactly reconstructs the sparse signal. In addition, using Devore's binary matrices, we expand the binary scheme to matrices with $\{0,1,-1\}$ elements.
Amirhossein Javaheri, Arash Amini, Farokh Marvasti, Daniel P. Palomar
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.
Reza K. Farsani, Farokh Marvasti
In this paper, capacity inner and outer bounds are established for the 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.
Ali Ayremlou, Mohammad Tofighi, Farokh Marvasti
A modular method was suggested before to recover a band limited signal from the sample and hold and linearly interpolated (or, in general, an nth-order-hold) version of the regular samples. In this paper a novel approach for compensating the distortion of any interpolation based on modular method has been proposed. In this method the performance of the modular method is optimized by adding only some simply calculated coefficients. This approach causes drastic improvement in terms of SNRs with fewer modules compared to the classical modular method. Simulation results clearly confirm the improvement of the proposed method and also its superior robustness against additive noise.