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A Field Guide to Forward-Backward Splitting with a FASTA Implementation [article]

Tom Goldstein, Christoph Studer, Richard Baraniuk
2016 arXiv   pre-print
This article is an introductory review of forward-backward splitting with a special emphasis on practical implementation concerns.  ...  FASTA provides a simple interface for applying forward-backward splitting to a broad range of problems.  ...  Applications of Forward-Backward Splitting In this section we study a variety of problems, and discuss how they are formulated and solved using forward-backward splitting.  ... 
arXiv:1411.3406v6 fatcat:nzcvvhninzgzpa2m2w5dq7ccdq

Real-Valued 2D MUSIC Algorithm Based on Modified Forward/Backward Averaging Using an Arbitrary Centrosymmetric Polarization Sensitive Array

Weijian Si, Yan Wang, Changbo Hou, Hong Wang
2017 Sensors  
In subspace-based algorithms based on TSA, by utilizing the forward/backward (FB) averaging technique, the complex covariance matrix is converted into a real-valued matrix, thus the eigenvalue decomposition  ...  The modified forward/backward averaging, which can be applied to the PSA, is presented.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/s17102241 pmid:28961205 pmcid:PMC5676623 fatcat:o5sqeurx7va5bpxj4liqmezqn4

A DOA Estimation Method with Kronecker Subspace for Coherent Signals

Masaaki Inoue, Kazunori Hayashi, Hiroki Mori, Toshihisa Nabetani
2018 IEEE Communications Letters  
The simulation proves the possibility of estimating forward-backward averaged correlation matrix via proposed approach.  ...  A new representation of forwardbackward averaging technique was offered for the usage of adaptive subspace tracking methods.  ...  There is a need, therefore, to adapt a forward-backward averaging technique for the case of subspace tracking algorithms application.  ... 
doi:10.1109/lcomm.2018.2870824 fatcat:nt7d7jhv3raezhvfpdlppprhcm

Angles Of Arrival Estimation With Unitary Partial Propagator

Youssef Khmou, Said Safi
2014 Zenodo  
Monte Carlo simulations proved the performance of the UPP spectrum comparatively with Forward Backward Partial Propagator (FBPP) and Unitary Propagator (UP).  ...  In this paper, we investigated the effect of real valued transformation of the spectral matrix of the received data for Angles Of Arrival estimation problem.  ...  CONCLUSIONIn this paper, we have proposed a unitary transformation of Partial Propagator (UPP) operator for narrowband Direction Of Arrival (DOA) estimation using Uniform Linear Array (ULA).  ... 
doi:10.5281/zenodo.1094048 fatcat:lepdjcwlyncplk74uahyf3v5wu

Higher-Order SVD-Based Subspace Estimation to Improve the Parameter Estimation Accuracy in Multidimensional Harmonic Retrieval Problems

Martin Haardt, Florian Roemer, Giovanni Del Galdo
2008 IEEE Transactions on Signal Processing  
We show how the concepts of forward-backward averaging and the mapping of centro-Hermitian matrices to real-valued matrices of the same size can be extended to tensors.  ...  Significant improvements of the resulting parameter estimation accuracy are achieved if there is at least one of the dimensions, which possesses a number of sensors that is larger than the number of sources  ...  FORWARD-BACKWARD AVERAGING AND -D UNITARY TENSOR-ESPRIT Many high-resolution parameter estimation schemes use forward-backward averaging as a preprocessing step in order to enhance the estimation accuracy  ... 
doi:10.1109/tsp.2008.917929 fatcat:df7jbrfppfcxbk4ktzunhifg2i

Unitary root-MUSIC with a real-valued eigendecomposition: a theoretical and experimental performance study

M. Pesavento, A.B. Gershman, M. Haardt
2000 IEEE Transactions on Signal Processing  
A real-valued (unitary) formulation of the popular root-MUSIC direction-of-arrival (DOA) estimation technique is considered.  ...  Based on a unitary transformation [1], Haardt and Nossek developed a unitary ESPRIT algorithm [4]-an efficient variant of ESPRIT [8] exploiting the centro-Hermitian property of the forward-backward covariance  ...  Sometimes, forward-backward averaging has been found to cause a certain degradation of asymptotic performances of direction finding techniques [14] .  ... 
doi:10.1109/78.839978 fatcat:patoprunhna3lb2imaxr5vfqwu

Improved Unitary Root-MUSIC for DOA Estimation Based on Pseudo-Noise Resampling

Cheng Qian, Lei Huang, H. C. So
2014 IEEE Signal Processing Letters  
A novel pseudo-noise resampling (PR) based unitary root-MUSIC algorithm for direction-of-arrival (DOA) estimation is derived in this letter.  ...  Index Terms-Direction-of-arrival (DOA) estimation, pseudonoise resampling (PR), small sample size, unitary root-music.  ...  So Abstract-A novel pseudo-noise resampling (PR) based unitary root-MUSIC algorithm for direction-of-arrival (DOA) estimation is derived in this letter.  ... 
doi:10.1109/lsp.2013.2294676 fatcat:qe6kpx2ssnartdkbdu7a4mhbwa

Tensor subspace Tracking via Kronecker structured projections (TeTraKron) for time-varying multidimensional harmonic retrieval

Yao Cheng, Florian Roemer, Olaa Khatib, Martin Haardt
2014 EURASIP Journal on Advances in Signal Processing  
In addition, we incorporate forward-backward-averaging and find a similar link between the real-valued matrix-based and tensor-based subspace estimation.  ...  Moreover, incorporating forward-backward-averaging leads to an improved accuracy of the subspace tracking, and only real-valued processing is involved.  ...  by the TeTraKron-based subspace tracking algorithms are used for direction-of-arrival estimation.  ... 
doi:10.1186/1687-6180-2014-123 fatcat:tcrgbnhwwras3otbhfe5sq4yjq

Unitary cyclic ESPRIT-like direction finding

ZhiGang Liu, JinKuan Wang
2010 Science China Information Sciences  
A unitary formulation of cyclic ESPRIT algorithm, with uniform linear array (ULA) configuration, is proposed by constructing the forward backward cyclic autocorrelation matrix by Hermitian mapping.  ...  This approach not only substantially reduces the computational complexity via real-valued decomposition, but also outperforms the forward backward spatial smoothing algorithm for uncorrelated or correlated  ...  In [1] , Huarng and Yeh presented a real-valued variant of spectral MUSIC based on a unitary transformation.  ... 
doi:10.1007/s11432-010-4057-y fatcat:gq5ht7op2ffixfyji3zcq7sa6y

Accurate DOA Estimation Based on Real-Valued Singular Value Decomposition [article]

Hui Cao, Qi Liu
2020 arXiv   pre-print
In this paper, an accurate direction-of-arrival (DOA) estimator is developed based on the real-valued singular value decomposition (SVD) of covariance matrix.  ...  The singular vector is then utilized with a weighted least squares (WLS) method to achieve DOA estimation.  ...  [10] considers a realvalued (unitary) formulation of the root-MUSIC DOA (U-root-MUSIC) estimation technique while [11] presents a second forward-backward (SFB) averaging technique to transform the  ... 
arXiv:2004.04901v1 fatcat:u5p4will35b3zkdytyugl6np6y

Structured least squares to improve the performance of ESPRIT-type algorithms

M. Haardt
1997 IEEE Transactions on Signal Processing  
ESPRIT-type (spatial) frequency estimation techniques obtain their frequency estimates from the solution of a highly structured, overdetermined system of equations (the so-called invariance equation).  ...  If SLS is initialized with the least squares solution of the invariance equation, only one "iteration," i.e., the solution of one linear system of equations, is performed to achieve a significant improvement  ...  In this experiment, all algorithms were implemented with forward-backward averaging.  ... 
doi:10.1109/78.558508 fatcat:jnvnxwg6lfg4fltufwmykajrlu

Tensor-Based Spatial Smoothing (TB-SS) Using Multiple Snapshots

Arpita Thakre, Martin Haardt, Florian Roemer, K. Giridhar
2010 IEEE Transactions on Signal Processing  
Tensor-based spatial smoothing (TB-SS) is a preprocessing technique for subspace-based parameter estimation of damped and undamped harmonics.  ...  Index Terms-Damped harmonics, direction of arrival (DOA) estimation, higher-order tensor, higher-order singular value decomposition (HOSVD), multidimensional signal processing, multilinear algebra, parameter  ...  Lathauwer for providing a MATLAB implementation of the HOOI algorithm.  ... 
doi:10.1109/tsp.2010.2043141 fatcat:2tmvl2zqkvaudkjnb5dgqev7gy

Unitary ESPRIT: how to obtain increased estimation accuracy with a reduced computational burden

M. Haardt, J.A. Nossek
1995 IEEE Transactions on Signal Processing  
ESPRIT is a high-resolution signal parameter estimation technique based on the translational invariance structure of a sensor array.  ...  Furthermore, Unitary ESPRIT incorporates forward-backward averaging, leading to an improved performance compared to the standard ESPRIT algorithm, especially for correlated source signals.  ...  Viberg, Gothenburg, Sweden, for his helpful comments regarding the contents of this paper.  ... 
doi:10.1109/78.382406 fatcat:hzwbipb22ffvfejrpq4cpmvoyu

A MSWF root‐MUSIC based on Pseudo‐noise resampling technique

M. Johnny, M. R. Aref
2021 Electronics Letters  
Also, the MSWF root-MUSIC based on the pseudo-noise resampling process for estimating the direction of arrival (DOA) of signals is proposed.  ...  When all the DOA estimators fail to pass the hypothesis test, the criterion based on the Gaussian weight average of the root estimator bank is introduced.  ...  To reduce the complexity, real valued estimators including unitary root-MUSIC [8] , unitary root-MUSIC with second forward/backward averaging [9] and unitary ES-PRIT were proposed.  ... 
doi:10.1049/ell2.12220 fatcat:4d3i5r65indedhepj7rtagx3ou

Combination of weighted ℓ2,1 minimization with unitary transformation for DOA estimation

Chundi Zheng, Gang Li, Xiqin Wang
2013 Signal Processing  
estimation.  ...  Simulations demonstrate that the proposed method can achieve better performance in terms of resolution and estimation accuracy.  ...  Introduction As a fundamental problem in the field of array signal processing, direction-of-arrival (DOA) estimation has a wide range of applications that encompass electromagnetics, acoustics, underwater  ... 
doi:10.1016/j.sigpro.2013.03.028 fatcat:r44jnty77jbl5ef2zqukdjncma
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