arXiv subjects

Farokh Marvasti

Publications and source records attributed to Farokh Marvasti.

At least 37 records · Page 2Linked to original sources

arXiv2019

A Fast Iterative Method for Removing Impulsive Noise from Sparse Signals

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.

eess.SP↗

arXiv2018

Forensic Discrimination between Traditional and Compressive Imaging Systems

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.

cs.CV↗

arXiv2018

A Novel Approach to Quantized Matrix Completion Using Huber Loss Measure

In this paper, we introduce a novel and robust approach to Quantized Matrix Completion (QMC). 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: 1- It is differentiable, 2- 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 (GD) technique. Novel and firm theoretical analysis on problem model and convergence of our algorithm to the global solution are provided. Another contribution of our work 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.

stat.ML↗

arXiv2018

Recovering Quantized Data with Missing Information Using Bilinear Factorization and Augmented Lagrangian Method

In this paper, we propose a novel approach in order to recover a quantized matrix with missing information. We propose a regularized convex cost function composed of a log-likelihood term and a Trace norm term. The Bi-factorization approach and the Augmented Lagrangian Method (ALM) are applied to find the global minimizer of the cost function in order to recover the genuine data. We provide mathematical convergence analysis for our proposed algorithm. In the Numerical Experiments Section, we show the superiority of our method in accuracy and also its robustness in computational complexity compared to the state-of-the-art literature methods.

stat.ML↗

arXiv2018

Transduction with Matrix Completion Using Smoothed Rank Function

In this paper, we propose two new algorithms for transduction with Matrix Completion (MC) problem. The joint MC and prediction tasks are addressed simultaneously to enhance the accuracy, i.e., the label matrix is concatenated to the data matrix forming a stacked matrix. Assuming the data matrix is of low rank, we propose new recommendation methods by posing the problem as a constrained minimization of the Smoothed Rank Function (SRF). We provide convergence analysis for the proposed algorithms. The simulations are conducted on real datasets in two different scenarios of randomly missing pattern with and without block loss. The results confirm that the accuracy of our proposed methods outperforms those of state-of-the-art methods even up to 10% in low observation rates for the scenario without block loss. Our accuracy in the latter scenario, is comparable to state-of-the-art methods while the complexity of the proposed algorithms are reduced up to 4 times.

cs.LG↗

arXiv2018

NLOS Mitigation Using Sparsity Feature And Iterative Methods

Well-known methods are employed to localize mobile station (MS) using line of sight (LOS) measurements. These methods may result in large error if they are fed with non LOS (NLOS) measurements. Our proposed algorithm, referred to as Sparse Recovery of NLOS using IMAT (SRNI), considers NLOS as unknown variables and solves the resultant underdetermined system emphasizing on its sparsity feature based on IMAT methods. Simulations are conducted to investigate the performance of SRNI in comparison of other conventional algorithms. Results demonstrate that SRNI is fast enough to deal with large combination of BSs and also accurate in lower number of BSs

eess.SP↗

arXiv2017

Feedback Acquisition and Reconstruction of Spectrum-Sparse Signals by Predictive Level Comparisons

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 (CS) 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.

cs.IT↗

arXiv2017

Multivariate Copula Spatial Dependency in One Bit Compressed Sensing

In this letter, the problem of sparse signal reconstruction from one bit compressed sensing measurements is investigated. To solve the problem, a variational Bayes framework with a new statistical multivariate model is used. The dependency of the wavelet decomposition coefficients is modeled with a multivariate Gaussian copula. This model can separate marginal structure of coefficients from their intra scale dependency. In particular, the drawable Gaussian vine copula multivariate double Lomax model is suggested. The reconstructed signal is derived by variational Bayes algorithm which can calculate closed forms for posterior of all unknown parameters and sparse signal. Numerical results illustrate the effectiveness of the proposed model and algorithm compared with the competing approaches in the literature.

eess.SP↗

arXiv2017

Measurement-Adaptive Sparse Image Sampling and Recovery

This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient information content of image patches. By leveraging texture in space, sparsity locations in DCT domain, and directional decomposition of gradients, the sampler structure consists of a combination of uniform, random, and nonuniform sampling strategies. For reconstruction, we model the recovery problem as a two-state cellular automaton to iteratively restore image with scalable windows from generation to generation. We demonstrate the recovery algorithm quickly converges after a few generations for an image with arbitrary degree of texture. For a given number of measurements, extensive experiments on standard image-sets, infra-red, and mega-pixel range imaging devices show that the proposed measurement matrix considerably increases the overall recovery performance, or equivalently decreases the number of sampled pixels for a specific recovery quality compared to random sampling matrix and Gaussian linear combinations employed by the state-of-the-art compressive sensing methods. In practice, the proposed measurement-adaptive sampling/recovery framework includes various applications from intelligent compressive imaging-based acquisition devices to computer vision and graphics, and image processing technology. Simulation codes are available online for reproduction purposes.

cs.CV↗

arXiv2017

OBTAIN: Real-Time Beat Tracking in Audio Signals

In this paper, we design a system in order to perform the real-time beat tracking for an audio signal. We use Onset Strength Signal (OSS) to detect the onsets and estimate the tempos. Then, we form Cumulative Beat Strength Signal (CBSS) by taking advantage of OSS and estimated tempos. Next, we perform peak detection by extracting the periodic sequence of beats among all CBSS peaks. In simulations, we can see that our proposed algorithm, Online Beat TrAckINg (OBTAIN), outperforms state-of-art results in terms of prediction accuracy while maintaining comparable and practical computational complexity. The real-time performance is tractable visually as illustrated in the simulations.

cs.SD↗

arXiv2017

A Convex Similarity Index for Sparse Recovery of Missing Image Samples

This paper investigates the problem of recovering missing samples using methods based on sparse representation adapted especially for image signals. Instead of $l_2$-norm or Mean Square Error (MSE), a new perceptual quality measure is used as the similarity criterion between the original and the reconstructed images. The proposed criterion called Convex SIMilarity (CSIM) index is a modified version of the Structural SIMilarity (SSIM) index, which despite its predecessor, is convex and uni-modal. We derive mathematical properties for the proposed index and show how to optimally choose the parameters of the proposed criterion, investigating the Restricted Isometry (RIP) and error-sensitivity properties. We also propose an iterative sparse recovery method based on a constrained $l_1$-norm minimization problem, incorporating CSIM as the fidelity criterion. The resulting convex optimization problem is solved via an algorithm based on Alternating Direction Method of Multipliers (ADMM). Taking advantage of the convexity of the CSIM index, we also prove the convergence of the algorithm to the globally optimal solution of the proposed optimization problem, starting from any arbitrary point. Simulation results confirm the performance of the new similarity index as well as the proposed algorithm for missing sample recovery of image patch signals.

cs.LG↗

arXiv2017

Bounds on Discrete Fourier Transform of Random Mask

This paper proposes some bounds on the maximum of magnitude of a random mask in Fourier domain. The random mask is used in random sampling scheme. Having a bound on the maximum value of a random mask in Fourier domain is very useful for some iterative recovery methods that use thresholding operator. In this paper, we propose some different bounds and compare them with the empirical examples.

eess.SP↗

arXiv2017

Using Empirical Covariance Matrix in Enhancing Prediction Accuracy of Linear Models with Missing Information

Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection methods. In sparse linear models, LASSO is well-known in extracting the desired support of the signal and resisting against noisy systems. When sparse models are also suffering from MI, the sparse recovery and inference of the missing models are taken into account simultaneously. In this paper, we will introduce an approach which enjoys sparse regression and covariance matrix estimation to improve matrix completion accuracy, and as a result enhancing feature selection preciseness which leads to reduction in prediction Mean Squared Error (MSE). We will compare the effect of employing covariance matrix in enhancing estimation accuracy to the case it is not used in feature selection. Simulations show the improvement in the performance as compared to the case where the covariance matrix estimation is not used.

stat.ML↗

arXiv2017

Adaptive Singular Value Thresholding

In this paper, we propose an Adaptive Singular Value Thresholding (ASVT) for low rank recovery under affine constraints. Unlike previous iterative methods that the threshold level is independent of the iteration number, in our proposed method, the threshold in adaptively decreases during iterations. The simulation results reveal that we get better performance with this thresholding strategy.

math.OC↗

arXiv2017

Recovery of Missing Samples Using Sparse Approximation via a Convex Similarity Measure

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.

stat.ML↗

arXiv2017

Comparison of Uniform and Random Sampling for Speech and Music Signals

In this paper, we will provide a comparison between uniform and random sampling for speech and music signals. There are various sampling and recovery methods for audio signals. Here, we only investigate uniform and random schemes for sampling and basic low-pass filtering and iterative method with adaptive thresholding for recovery. The simulation results indicate that uniform sampling with cubic spline interpolation outperforms other sampling and recovery methods.

eess.AS↗

arXiv2017

Interpolation of Sparse Graph Signals by Sequential Adaptive Thresholds

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.

cs.IT↗

arXiv2017

Recovery of Sparse and Low Rank Components of Matrices Using Iterative Method with Adaptive Thresholding

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding operator. This algorithm is fast and can be implemented easily. We compare it with one of the most common fast methods in which the rank and sparsity are approximated by $\ell_1$ norm. We also apply it to some real applications where the noise is not so sparse. The simulation results show that it has a suitable performance with low run-time.

math.NA↗