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Babu, Prabhu

Open this publication in new window or tab >>Connection between SPICE and Square-Root LASSO for sparse parameter estimation### Babu, Prabhu

### Stoica, Peter

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##### Abstract [en]

##### Keywords

LASSO, Square-Root LASSO, SPICE, Covariance fitting, Sparse parameter estimation
##### National Category

Signal Processing
##### Research subject

Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-209143 (URN)10.1016/j.sigpro.2013.08.011 (DOI)000326912000002 ()
#####

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##### Funder

Swedish Research CouncilEU, European Research Council
Available from: 2013-10-15 Created: 2013-10-15 Last updated: 2018-10-01Bibliographically approved

Department of Electronic and Computer Engineering, HKUST, Hong Kong.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.

In this note we show that the sparse estimation technique named Square-Root LASSO (SR-LASSO) is connected to a previously introduced method named SPICE. More concretely we prove that the SR-LASSO with a unit weighting factor is identical to SPICE. Furthermore we show via numerical simulations that the performance of the SR-LASSO changes insignificantly when the weighting factor is varied. SPICE stands for *sp*arse *i*terative *c*ovariance-based *e*stimation and LASSO for *l*east *a*bsolute *s*hrinkage and *s*election *o*perator.

Open this publication in new window or tab >>Model order estimation via penalizing adaptively the likelihood (PAL)### Stoica, Peter

### Babu, Prabhu

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_some",{id:"formSmash:j_idt184:1:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_1_j_idt188_otherAuthors",{id:"formSmash:j_idt184:1:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_1_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: Signal Processing, ISSN 0165-1684, E-ISSN 1872-7557, Vol. 93, no 11, p. 2865-2871Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Signal Processing
##### Research subject

Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-205725 (URN)10.1016/j.sigpro.2013.03.014 (DOI)000322937700001 ()
#####

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Available from: 2013-08-22 Created: 2013-08-22 Last updated: 2018-10-01Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.

Department of Electronic and Computer Engineering, HKUST, Hong Kong.

This paper introduces a novel rule for model order estimation based on penalizingadatively the likelihood (PAL). The penalty term of PAL, which is data adaptive (as the name suggests), has several unique features: it is "small" (e.g. comparable to AIC penalty) for modelorders, let us say n(0), less than or equal to the true order, denoted by no, and it is "large" (e.g. of the same order as BIC penalty) for n > n(o); furthermore this is true not only as the data sample length increases (which is the case most often considered in the literature) but also asthe signal-to-noise ratio (SNR) increases (the harder case for AIC, BIC and the like); and this "oracle-like" behavior of PAL's penalty is achieved without any knowledge about n(0). Thepaper presents a number of simulation examples to show that PAL has an excellent performance also in non-asymptotic regimes and compare this performance with that of AIC and BIC.

Open this publication in new window or tab >>Parameter estimation of exponential signals: a system identification approach### Stoica, Peter

### Babu, Prabhu

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_some",{id:"formSmash:j_idt184:2:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_2_j_idt188_otherAuthors",{id:"formSmash:j_idt184:2:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_2_j_idt188_otherAuthors",multiple:true}); 2013 (English)In: Digital signal processing (Print), ISSN 1051-2004, E-ISSN 1095-4333, Vol. 23, no 5, p. 1565-1577Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Signal Processing
##### Research subject

Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-205726 (URN)10.1016/j.dsp.2013.05.003 (DOI)000323855500019 ()
#####

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Available from: 2013-08-22 Created: 2013-08-22 Last updated: 2018-10-01Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.

Exponential signals occur in extremely diverse applications and estimation of their parameters is one of the basic problems in applied sciences. Nevertheless there are only a handful of methods for exponential analysis that are recommended in the literature, and even those methods have relatively mediocre performance in more difficult scenarios. In this paper we attempt to correct this situation by making use of a system identification approach. The proposed methodology, which we call EASI (Exponential Analysis via System Identification), is shown to have a satisfactory performance (i.e., high resolution and small statistical variability) for practical data lengths, and this not only for white measurement noise but also in cases with highly correlated noise (which were rarely considered in the previous literature).

Open this publication in new window or tab >>On moving average parameter estimation### Sandgren, Niclas

### Stoica, Peter

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.### Babu, Prabhu

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_some",{id:"formSmash:j_idt184:3:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_3_j_idt188_otherAuthors",{id:"formSmash:j_idt184:3:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_3_j_idt188_otherAuthors",multiple:true}); 2012 (English)Conference paper, Published paper (Refereed)
##### Abstract [en]

##### National Category

Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-184856 (URN)978-146731068-0 (ISBN)
##### Conference

20th European Signal Processing Conference (EUSIPCO), 27-31 Aug, 2012, Bucharest, ROmania
#####

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Available from: 2012-11-15 Created: 2012-11-15 Last updated: 2018-10-01Bibliographically approved

Estimation of the autoregressive moving average (ARMA)parameters of a stationary stochastic process is a problemoften encountered in the signal processing literature. It iswell known that estimating the moving average (MA) parameters is usually more difﬁcult than estimating the autoregressive (AR) part, especially if the zeros are located close tothe unit circle. In this paper, we present four linear methodsfor MA parameter estimation (i.e., methods that involve onlylinear operations) and compare their performances ﬁrst in acase when the zeros are located far away from the unit circleand secondly in a presumably harder case when the zeros arelocated very close to the unit circle

Open this publication in new window or tab >>On the Exponentially Embedded Family (EEF) Rule for Model Order Selection### Stoica, Peter

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.### Babu, Prabhu

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_some",{id:"formSmash:j_idt184:4:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_4_j_idt188_otherAuthors",{id:"formSmash:j_idt184:4:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_4_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: IEEE Signal Processing Letters, ISSN 1070-9908, E-ISSN 1558-2361, Vol. 19, no 9, p. 551-554Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Bayesian information criterion (BIC), exponentially embedded family (EEF), Gaussian mixture model (GMM), generalized likelihood ratio (GLR), model order selection
##### National Category

Computer and Information Sciences
##### Identifiers

urn:nbn:se:uu:diva-179551 (URN)10.1109/LSP.2012.2206583 (DOI)000306520600001 ()
#####

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Available from: 2012-08-20 Created: 2012-08-20 Last updated: 2018-10-01Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.

Model selection is an important task in many signal processing applications. In this letter, we present a generalized likelihood ratio (GLR)-based derivation of the recently proposed EEF rule in an attempt to cast EEF in the main stream of model order selection approaches and provide further insights into its theoretical foundations. We also show that EEF can be expected to behave asymptotically (in the number of data samples) similarly to the Bayesian information criterion (BIC). To evaluate the finite sample performance we consider two numerical examples, including the selection of the number of components in a Gaussian mixture model (GMM), by means of which we show that EEF behaves similarly to BIC.

Open this publication in new window or tab >>On the LIMES approach to spectral analysis of irregularly sampled data### Stoica, Peter

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.### Babu, Prabhu

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_some",{id:"formSmash:j_idt184:5:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_5_j_idt188_otherAuthors",{id:"formSmash:j_idt184:5:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_5_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: Electronics Letters, ISSN 0013-5194, E-ISSN 1350-911X, Vol. 48, no 4, p. 218-219Article in journal (Refereed) Published
##### Abstract [en]

##### National Category

Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-171424 (URN)10.1049/el.2011.3247 (DOI)000300605700017 ()
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Available from: 2012-03-19 Created: 2012-03-19 Last updated: 2018-10-01Bibliographically approved

LIMES (LIkelihood-based Method for Estimation of Spectra) is a recently introduced non-parametric approach for the spectral analysis of regularly or irregularly sampled data. While LIMES is a statistically powerful approach (owing to its maximum-likelihood character), it is computationally rather intensive for large data sets; additionally, the variance of its estimation errors increases somewhat fast as the size of the data set decreases. Provided are simple practical solutions to these two problems of LIMES.

Open this publication in new window or tab >>On the Proper Forms of BIC for Model Order Selection### Stoica, Peter

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.### Babu, Prabhu

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_some",{id:"formSmash:j_idt184:6:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_6_j_idt188_otherAuthors",{id:"formSmash:j_idt184:6:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_6_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 9, p. 4956-4961Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

BIC, model order selection, polynomial trend model
##### National Category

Engineering and Technology
##### Identifiers

urn:nbn:se:uu:diva-182009 (URN)10.1109/TSP.2012.2203128 (DOI)000307790800035 ()
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Available from: 2012-10-08 Created: 2012-10-02 Last updated: 2018-10-01Bibliographically approved

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.

The Bayesian Information Criterion (BIC) is often presented in a form that is only valid in large samples and under a certain condition on the rate at which the Fisher Information Matrix (FIM) increases with the sample length. This form has been improperly used previously in situations in which the conditions mentioned above do not hold. In this correspondence, we describe the proper forms of BIC in several practically relevant cases that do not satisfy the above assumptions. In particular, we present a new form of BIC for high signal-to-noise ratio (SNR) cases. The conclusion of this study is that BIC remains one of the most successful existing rules for model order selection, if properly used.

Open this publication in new window or tab >>Sparse estimation of spectral lines: Grid selection problems and their solutions### Stoica, Peter

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.### Babu, Prabhu

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_some",{id:"formSmash:j_idt184:7:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_7_j_idt188_otherAuthors",{id:"formSmash:j_idt184:7:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_7_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 60, no 2, p. 962-967Article in journal (Refereed) Published
##### Abstract [en]

##### Keywords

Sinusoidal signals, sparse estimation, spectral analysis
##### National Category

Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-165555 (URN)10.1109/TSP.2011.2175222 (DOI)000299434300033 ()
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Available from: 2012-01-09 Created: 2012-01-09 Last updated: 2018-10-01Bibliographically approved

Grid selection for sparse estimation of spectral-line parameters is a critical problem that was in need of a satisfactory solution: assuming the usual case of a uniform spectral grid how should one select the number of grid points, K? We first present a simple practical rule for choosing an initial value (or initial values) of K in a given situation. Then, we go on to explain how the estimation results corresponding to different values of K can be compared with one another and therefore how to select the "best" value of K among those considered. Furthermore, we introduce a method for detecting when a grid is "too rough" and for obtaining refined parameter estimates in such a case.

Open this publication in new window or tab >>Sparse spectral-line estimation for nonuniformly sampled multivariate time series: SPICE, LIKES and MSBL### Babu, Prabhu

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.### Stoica, Peter

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_some",{id:"formSmash:j_idt184:8:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_8_j_idt188_otherAuthors",{id:"formSmash:j_idt184:8:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_8_j_idt188_otherAuthors",multiple:true}); 2012 (English)In: 2012 Proceedings Of The 20th European Signal Processing Conference (EUSIPCO), 2012, p. 445-449Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Series

European Signal Processing Conference, ISSN 2219-5491
##### National Category

Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-184854 (URN)978-146731068-0 (ISBN)
##### Conference

20th European Signal Processing Conference (EUSIPCO 2012), 27-31 Aug, 2012, Bucharest
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Available from: 2012-11-15 Created: 2012-11-15 Last updated: 2018-10-01Bibliographically approved

In this paper we deal with the problem of spectral-line analysis ofnonuniformly sampled multivariate time series for which we introduce two methods: the ﬁrst method named SPICE (sparse iterativecovariance based estimation) is based on a covariance ﬁtting framework whereas the second method named LIKES (likelihood-basedestimation of sparse parameters) is a maximum likelihood technique. Both methods yield sparse spectral estimates and they donot require the choice of any hyperparameters. We numericallycompare the performance of SPICE and LIKES with that of the recently introduced method of multivariate sparse Bayesian learning(MSBL).

Open this publication in new window or tab >>Spectral Analysis of Nonuniformly Sampled Data and Applications### Babu, Prabhu

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_some",{id:"formSmash:j_idt184:9:j_idt188:some",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt184_9_j_idt188_otherAuthors",{id:"formSmash:j_idt184:9:j_idt188:otherAuthors",widgetVar:"widget_formSmash_j_idt184_9_j_idt188_otherAuthors",multiple:true}); 2012 (English)Doctoral thesis, monograph (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Uppsala universitet, 2012. p. 220
##### Keywords

Spectral analysis, array processing, nonuniform sampling, sparse parameter estimation, direction of arrival (DOA) estimation, covariance fitting, sinusoidal parameter estimation, maximum-likelihood, non-parametric approach, exoplanet detection, radial velocity technique, Sudoku
##### National Category

Signal Processing
##### Research subject

Electrical Engineering with specialization in Signal Processing
##### Identifiers

urn:nbn:se:uu:diva-180391 (URN)978-91-506-2300-0 (ISBN)
##### Public defence

2012-10-19, Room 2347, Polacksbacken, Lägerhyddsvägen 2, Uppsala, 13:00 (English)
##### Opponent

### Gustafsson, Fredrik

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##### Supervisors

### Stoica, Peter

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Available from: 2012-10-02 Created: 2012-09-05 Last updated: 2018-10-01Bibliographically approved

Signal acquisition, signal reconstruction and analysis of spectrum of the signal are the three most important steps in signal processing and they are found in almost all of the modern day hardware. In most of the signal processing hardware, the signal of interest is sampled at uniform intervals satisfying some conditions like Nyquist rate. However, in some cases the privilege of having uniformly sampled data is lost due to some constraints on the hardware resources. In this thesis an important problem of signal reconstruction and spectral analysis from nonuniformly sampled data is addressed and a variety of methods are presented. The proposed methods are tested via numerical experiments on both artificial and real-life data sets.

The thesis starts with a brief review of methods available in the literature for signal reconstruction and spectral analysis from non uniformly sampled data. The methods discussed in the thesis are classified into two broad categories - dense and sparse methods, the classification is based on the kind of spectra for which they are applicable. Under dense spectral methods the main contribution of the thesis is a non-parametric approach named LIMES, which recovers the smooth spectrum from non uniformly sampled data. Apart from recovering the spectrum, LIMES also gives an estimate of the covariance matrix. Under sparse methods the two main contributions are methods named SPICE and LIKES - both of them are user parameter free sparse estimation methods applicable for line spectral estimation. The other important contributions are extensions of SPICE and LIKES to multivariate time series and array processing models, and a solution to the grid selection problem in sparse estimation of spectral-line parameters.

The third and final part of the thesis contains applications of the methods discussed in the thesis to the problem of radial velocity data analysis for exoplanet detection. Apart from the exoplanet application, an application based on Sudoku, which is related to sparse parameter estimation, is also discussed.

Linköping University, Department of Electrical Engineering.

Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control.