arXiv subjects

Farokh Marvasti

Publications and source records attributed to Farokh Marvasti.

At least 55 records · Page 3Linked to original sources

arXiv2017

New Methods of Enhancing Prediction Accuracy in Linear Models with Missing Data

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.

stat.ML↗

arXiv2016

On Optimum Asymptotic Multiuser Efficiency of Randomly Spread CDMA

We extend the result by Tse and Verdú on the optimum asymptotic multiuser efficiency of randomly spread CDMA with Binary Phase Shift Keying (BPSK) 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 $N\rightarrow\infty$ and the loading factor, $\frac{K}{N}$, 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 (SNR) when $K$ and $N\rightarrow\infty$ and the loading factor, $\frac{K}{N}$, is kept less than $\frac{\log_3K}{2}$. 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 $N\times K$ random matrix whose entries are chosen randomly from a finite set, is a detecting matrix as $K$ and $N\rightarrow \infty$.

cs.IT↗

arXiv2016

Sampling and Distortion Tradeoffs for Indirect Source Retrieval

Consider a continuous signal that cannot be observed directly. Instead, one has access to multiple corrupted versions of the signal. The available corrupted signals are correlated because they carry information about the common remote signal. The goal is to reconstruct the original signal from the data collected from its corrupted versions. The information theoretic formulation of the remote reconstruction problem assumes that the corrupted signals are uniformly sampled and the focus is on optimal compression of the samples. In this paper we revisit this problem from a sampling perspective. We look at the problem of finding the best sampling locations for each signal to minimize the total reconstruction distortion of the remote signal. In finding the sampling locations, one can take advantage of the correlation among the corrupted signals. Our main contribution is a fundamental lower bound on the reconstruction distortion for any arbitrary nonuniform sampling strategy. This lower bound is valid for any sampling rate. Furthermore, it is tight and matches the optimal reconstruction distortion in low and high sampling rates. Moreover, it is shown that in the low sampling rate region, it is optimal to use a certain nonuniform sampling scheme on all the signals. On the other hand, in the high sampling rate region, it is optimal to uniformly sample all the signals. We also consider the problem of finding the optimal sampling locations to recover the set of corrupted signals, rather than the remote signal. Unlike the information theoretic formulation of the problem in which these two problems were equivalent, we show that they are not equivalent in our setting.

cs.IT↗

arXiv2016

Iterative Methods for Sparse Signal Reconstruction from Level Crossings

This letter considers the problem of sparse signal reconstruction from the timing of its Level Crossings (LC)s. We formulate the sparse Zero Crossing (ZC) reconstruction problem in terms of a single 1-bit Compressive Sensing (CS) model. We also extend the Smoothed L0 (SL0) sparse reconstruction algorithm to the 1-bit CS framework and propose the Binary SL0 (BSL0) algorithm for iterative reconstruction of the sparse signal from ZCs in cases where the number of sparse coefficients is not known to the reconstruction algorithm a priori. Similar to the ZC case, we propose a system of simultaneously constrained signed-CS problems to reconstruct a sparse signal from its Level Crossings (LC)s and modify both the Binary Iterative Hard Thresholding (BIHT) and BSL0 algorithms to solve this problem. Simulation results demonstrate superior performance of the proposed LC reconstruction techniques in comparison with the literature.

cs.IT↗

arXiv2016

Fast Methods for Recovering Sparse Parameters in Linear Low Rank Models

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming a low-rank structure for the matrix, one natural solution would be to first apply a matrix completion on the data, and then to solve the resulting compressed sensing problem. In big data applications such as massive MIMO and medical data, the matrix completion step imposes a huge computational burden. Here, we propose to reduce the computational cost of the completion task by ignoring the columns corresponding to zero elements in the sparse vector. To this end, we employ a technique to initially approximate the support of the sparse vector. We further propose to unify the partial matrix completion and sparse vector recovery into an augmented four-step problem. Simulation results reveal that the augmented approach achieves the best performance, while both proposed methods outperform the natural two-step technique with substantially less computational requirements.

cs.LG↗

arXiv2016

Iterative Null-space Projection Method with Adaptive Thresholding in Sparse Signal Recovery and Matrix Completion

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.

stat.ME↗

arXiv2016

Sampling and Distortion Tradeoffs for Bandlimited Periodic Signals

In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for Gaussian bandlimited periodic signals with additive white Gaussian noise are studied. Our emphasis is on characterizing the optimal sampling locations as well as the optimal pre-sampling filter to minimize the reconstruction distortion. We first show that to achieve the optimal distortion, no pre-sampling filter is necessary for any arbitrary sampling rate. Then, we provide a complete characterization of optimal distortion for low and high sampling rates (with respect to the signal bandwidth). We also provide bounds on the reconstruction distortion for rates in the intermediate region. It is shown that nonuniform sampling outperforms uniform sampling for low sampling rates. In addition, the optimal nonuniform sampling set is robust with respect to missing sampling values. On the other hand, for the sampling rates above the Nyquist rate, the uniform sampling strategy is optimal. An extension of the results for random discrete periodic signals is discussed with simulation results indicating that the intuitions from the continuous domain carry over to the discrete domain. Sparse signals are also considered, where it is shown that uniform sampling is optimal above the Nyquist rate.

cs.IT↗

arXiv2016

Dispersion Compensation using High-Positive Dispersive Optical Fibers

The common and traditional method for dispersion compensation in optical domain is concatenating the transmit optical fiber by a compensating optical fiber having high-negative dispersion coefficient. In this paper, we take an opposite direction and show how an optical fiber with high-positive dispersion coefficient can also be used for dispersion compensation. Our optical dispersion compensating structure is the optical implementation of an iterative algorithm in signal processing. The proposed dispersion compensating system is constructed by cascading a number of compensating sub-systems and its compensation capability is improved by increasing the number of embedded sub-systems. We also show that the compensation capability is a trade-off between transmission length and bandwidth. We use simulation results to validate the performance of the introduced dispersion compensating module. Photonic crystal fibers with high-positive dispersion coefficient can be used for constructing the proposed optical dispersion compensating module.

cs.IT↗

arXiv2016

Image Block Loss Restoration Using Sparsity Pattern as Side Information

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.

cs.MM↗

arXiv2016

Comparison of Several Sparse Recovery Methods for Low Rank Matrices with Random Samples

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.

cs.LG↗

arXiv2016

Power Allocation and Measurement Matrix Design for Block CS-Based Distributed MIMO Radars

Multiple-input multiple-output (MIMO) radars offer higher resolution, better target detection, and more accurate target parameter estimation. Due to the sparsity of the targets in space-velocity domain, we can exploit Compressive Sensing (CS) to improve the performance of MIMO radars when the sampling rate is much less than the Nyquist rate. In distributed MIMO radars, block CS methods can be used instead of classical CS ones for more performance improvement, because the received signal in this group of MIMO radars is a block sparse signal in a basis. In this paper, two new methods are proposed to improve the performance of the block CS-based distributed MIMO radars. The first one is a new method for optimal energy allocation to the transmitters, and the other one is a new method for optimal design of the measurement matrix. These methods are based on the minimization of an upper bound of the sensing matrix block-coherence. Simulation results show an increase in the accuracy of multiple targets parameters estimation for both proposed methods.

cs.IT↗

arXiv2015

A Fast and Efficient Algorithm for Reconstructing MR images From Partial Fourier Samples

In this paper, the problem of Magnetic Resonance (MR) image reconstruction from partial Fourier samples has been considered. To this aim, we leverage the evidence that MR images are sparser than their zero-filled reconstructed ones from incomplete Fourier samples. This information can be used to define an optimization problem which searches for the sparsest possible image conforming with the available Fourier samples. We solve the resulting problem using the well-known Alternating Direction Method of Multipliers (ADMM). Unlike most existing methods that work with small over-lapping image patches, the proposed algorithm considers the whole image without dividing it into small blocks. Experimental results prominently confirm its promising performance and advantages over the existing methods.

cs.IT↗

arXiv2014

Multi-Hypothesis Compressed Video Sensing Technique

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.

cs.MM↗

arXiv2014

Reconstruction of Sub-Nyquist Random Sampling for Sparse and Multi-Band Signals

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.

cs.IT↗

arXiv2014

Real-Time Impulse Noise Suppression from Images Using an Efficient Weighted-Average Filtering

In this paper, 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.

cs.CV↗

arXiv2014

Fast restoration of natural images corrupted by high-density impulse noise

In this paper, we suggest a general model for the fixed-valued impulse noise and propose a two-stage method for high density noise suppression while preserving the image details. In the first stage, we apply an iterative impulse detector, exploiting the image entropy, to identify the corrupted pixels and then employ an Adaptive Iterative Mean filter to restore them. The filter is adaptive in terms of the number of iterations, which is different for each noisy pixel, according to the Euclidean distance from the nearest uncorrupted pixel. Experimental results show that the proposed filter is fast and outperforms the best existing techniques in both objective and subjective performance measures.

cs.MM↗

arXiv2013

Iterative Detection with Soft Decision in Spectrally Efficient FDM Systems

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.

cs.IT↗

arXiv2012

Compensating Interpolation Distortion by Using New Optimized Modular Method

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 signal-to-noise ratios 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.

cs.CV↗