1. 
 Mecklenbrauker, C. F., et al.
(författare)

Sequential Bayesian Sparse Signal Reconstruction Using Array Data
 2013

Ingår i: Ieee Transactions on Signal Processing.  1053587X. ; 61:24, s. 63446354

Tidskriftsartikel (refereegranskat)abstract
 In this paper, the sequential reconstruction of source waveforms under a sparsity constraint is considered from a Bayesian perspective. Let the wave field, which is observed by a sensor array, be caused by a spatiallysparse set of sources. A spatially weighted Laplacelike prior is assumed for the source field and the corresponding weighted Least Absolute Shrinkage and Selection Operator (LASSO) cost function is derived. After the weighted LASSO solution has been calculated as the maximum a posteriori estimate at time step, the posterior distribution of the source amplitudes is analytically approximated. The weighting of the Laplacelike prior for time step is then fitted to the approximated posterior distribution. This results in a sequential update for the LASSO weights. Thus, a sequence of weighted LASSO problems is solved for estimating the temporal evolution of a sparse source field. The method is evaluated numerically using a uniform linear array in simulations and applied to data which were acquired from a towed horizontal array during the long range acoustic communications experiment.


2. 
 Panahi, Ashkan, 1986, et al.
(författare)

A novel method of DOA tracking by penalized least squares
 2013

Ingår i: 2013 5th IEEE International Workshop on Computational Advances in MultiSensor Adaptive Processing, CAMSAP 2013.  9781467331463 ; s. 6164

Konferensbidrag (refereegranskat)abstract
 This work develops a new DOA tracking technique by proposing a novel semiparametric method of sequential sparse recovery for a dynamic sparsity model. The proposed method iteratively provides a sequence of spatial spectrum estimates. The final process of estimating direction paths from the spectrum sequence is not considered. However, the simulation results show concentration of the spectrum around the true directions, which simplifies DOA tracking, for example, using a pattern recognition approach. We have also proved analytical results indicating consistency in terms of spectral concentration, which we omit in the interest of space and postpone to a more extensive work. The semiparametric nature of the proposed method avoids highly complex data association and makes the method robust against crossing. The computational complexity per time sample is proportional to grid size, which can be contrasted to a singlesnapshot LASSO solution that has a polynomial complexity order.


3. 
 Panahi, Ashkan, 1986, et al.
(författare)

A numerical implementation of gridless compressed sensing
 2015

Ingår i: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing  Proceedings.  15206149. ; 2015August, s. 33423346

Konferensbidrag (refereegranskat)abstract
 Atomic norm denoising has been recently introduced as a generalization of the Least Absolute Shrinkage and Selection Operator (LASSO) to overcome the problem of offgrid parameters. The method has been found to possess many interesting theoretical properties. However, its implementation has been only discussed in a special case of spectral line estimation by uniform sampling. In this paper, we propose a general numerical method to solve the atomic norm denoising problem. The complexity of the proposed algorithm is proportional to the complexity of a singleparameter search in the parameter space and thus in many interesting cases, including frequency estimation it enjoys fast realization.


4. 
 Panahi, Ashkan, 1986, et al.
(författare)

A robust ℓ1 penalized DOA estimator
 2012

Ingår i: 46th Asilomar Conference on Signals, Systems and Computers..  10586393.  9781467350518 ; s. 20132017

Konferensbidrag (refereegranskat)abstract
 The SPSLASSO has recently been introduced as a solution to the problem of regularization parameter selection in the complexvalued LASSO problem. Still, the dependence on the grid size and the polynomial time of performing convex optimization technique in each iteration, in addition to the deficiencies in the low noise regime, confines its performance for Direction of Arrival (DOA) estimation. This work presents methods to apply LASSO without grid size limitation and with less complexity. As we show by simulations, the proposed methods loose a negligible performance compared to the Maximum Likelihood (ML) estimator, which needs a combinatorial search We also show by simulations that compared to practical implementations of ML, the proposed techniques are less sensitive to the source power difference.


5. 
 Panahi, Ashkan, 1986, et al.
(författare)

Basis pursuit over continuum applied to rangeDoppler estimation problem
 2014

Ingår i: IEEE 8th Sensor Array and Multichannel Signal Processing Workshop, SAM 2014; A Coruna; Spain; 22 June 2014 through 25 June 2014. ; s. 381384

Konferensbidrag (refereegranskat)abstract
 Sparse estimation and compressive sensing techniques have been recently considered for radar estimation problems. It is frequently observed that these methods are robust to model uncertainties and substantially improve performance in scenarios with a low signaltonoise. However, since current sparsitybased techniques are computationally costly and require a suitable discretization (grid), which strongly restricts resolution, they practically receive less attention. In this work, we present an application of a new sparsitybased technique to the specific problem of rangeDoppler estimation. The method, generalizing basis pursuit, is less computationally complex and its performance is independent of the grid selection. We demonstrate that the proposed technique can improve estimation performance in difficult cases, as compared to the SAGE technique.


6. 
 Panahi, Ashkan, 1986, et al.
(författare)

Fast Candidate Points Selection in the LASSO Path
 2012

Ingår i: Ieee Signal Processing Letters.  10709908. ; 19:2, s. 7982

Tidskriftsartikel (refereegranskat)abstract
 The LASSO sparse regression method has recently received attention in a variety of applications from image compression techniques to parameter estimation problems. This paper addresses the problem of regularization parameter selection in this method in a general case of complexvalued regressors and bases. Generally, this parameter controls the degree of sparsity or equivalently, the estimated model order. However, with the same sparsity/model order, the smallest regularization parameter is desired. We relate such points to the nonsmooth points in the path of LASSO solutions and give an analytical expression for them. Then, we introduce a numerically fast method of approximating the desired points by a recursive algorithm. The procedure decreases the necessary number of solutions of the LASSO problem dramatically, which is an important issue due to the polynomial computational cost of the convex optimization techniques. We illustrate our method in the context of DOA estimation.


7. 
 Panahi, Ashkan, 1986, et al.
(författare)

Fast LASSO based DOA tracking
 2011

Ingår i: 4 th IEEE International Workshop on Computational Advances in MultiSensor Adaptive Processing (CAMSAP), 2011.  9781457721052 ; s. 397400

Konferensbidrag (refereegranskat)abstract
 In this paper, we propose a sequential, fast DOA tracking technique using the measurements of a uniform linear sensor array in the far field of a set of narrow band sources. Our approach is based on sparse approximation technique LASSO (Least Absolute Shrincage and Selection Operator), which has recently gained considerable interest for DOA and other estimation problems. Considering the LASSO optimization as a Bayesian estimation, we first define a class of prior distributions suitable for the sparse representation of the model and discuss its relation to the priors over DOAs and waveforms. Inspired by the Kalman filtering method, we introduce a nonlinear sequential filter on this family of distributions. We derive the filter for a simple random walk motion model of the DOAs. The method consists of consecutive implementation of weighted LASSO optimizations using each new measurement and updating the LASSO weights for the next step.


8. 
 Panahi, Ashkan, 1986, et al.
(författare)

Gridless compressive sensing
 2014

Ingår i: 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2014; Florence; Italy; 4 May 2014 through 9 May 2014.  15206149.  9781479928927 ; s. 33853389

Konferensbidrag (refereegranskat)abstract
 The effect of offgrid atoms has become the prominent problem in application of the Compressed Sensing (CS) techniques to the cases where there is an underlying continuous parametrization. In this work, we develop a generalizing CS framework which shows that sampling to a finite grid is not necessary toward compressive estimation. We propose an alternative procedure over infinite dictionaries, which we show to be theoretically consistent in many cases of interest and then propose a robust implementation. We illustrate the general properties of our technique in some difficult practical instances of frequency estimation.


9. 
 Panahi, Ashkan, 1986, et al.
(författare)

Maximum a Posteriori Based Regularization Parameter Selection
 2011

Ingår i: 2011 Ieee International Conference on Acoustics, Speech, and Signal Processing.  15206149.  9781457705397 ; s. 24522455

Konferensbidrag (refereegranskat)abstract
 The l(1) norm regularized least square technique has been proposed as an efficient method to calculate sparse solutions. However, the choice of the regularization parameter is still an unsolved problem, especially when the number of nonzero elements is unknown. In this paper we first design different ML estimators by interpreting the l(1) norm regularization as a MAP estimator with a Laplacian model for data. We also utilize the MDL criterion to decide on the regularization parameter. The performance of these new methods are evaluated in the context of estimating the Directions Of Arrival (DOA) for the simulated data and compared. The simulations show that the performance of the different forms of the MAP estimator are approximately equal in the one snapshot case, where MDL may not work. But for the multiple snapshot case both methods can be used.


10. 
 Panahi, Ashkan, 1986, et al.
(författare)

On the resolution of the LASSObased DOA estimation method
 2011

Ingår i: Proceedings  2011 International ITG Workshop on Smart Antennas, WSA 2011.  9781612840741

Konferensbidrag (refereegranskat)abstract
 This paper investigates the consistency of the LASSObased DOA estimation of the narrowband signals in infinitely high SNR. Such a method provides a robust and accurate approximation of the Maximum Likelihood estimation. However, as we show, unlike the standard techniques such as subspace methods the LASSObased estimation is generally not consistent in high SNRs. In return, considering the true DOA's, we show that the method is consistent for certain configuration of the sources. This approach leads us to relate such a conditional consistency to the resolution concept. We next give a condition to verify the consistency of a given set of directions and simplify it to a computationally fast equivalent algorithm. The results show that the resolution in infinitely high SNR case for m sensors decreases by speed 1 over m.

