Regularized &lt;formula formulatype="inline"&gt;&lt;tex Notation="TeX"&gt;$M$&lt;/tex&gt; &lt;/formula&gt;-Estimators of Scatter Matrix

Ollila, Esa; Tyler, David E.

doi:10.1109/tsp.2014.2360826

Cited by 91 publications

(9 citation statements)

References 34 publications

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“…When D > N , these estimators are undefined [69,104], and even when D ≤ N they may be ill-conditioned. It is thus common to regularize them [82,100].…”

Section: F Robust Covariancesmentioning

confidence: 99%

An Overview of Robust Subspace Recovery

2018

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This paper will serve as an introduction to the body of work on robust subspace recovery. Robust subspace recovery involves finding an underlying low-dimensional subspace in a dataset that is possibly corrupted with outliers. While this problem is easy to state, it has been difficult to develop optimal algorithms due to its underlying nonconvexity. This work emphasizes advantages and disadvantages of proposed approaches and unsolved problems in the area.

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“…When D > N , these estimators are undefined [69,104], and even when D ≤ N they may be ill-conditioned. It is thus common to regularize them [82,100].…”

Section: F Robust Covariancesmentioning

confidence: 99%

An Overview of Robust Subspace Recovery

2018

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“…Symmetric α-stable random vectors belong to the larger class of complex elliptically symmetric (CES) distributed random vectors [51][52][53]. CES distributions comprise, e.g., complex normal, complex t-, complex K-, generalized Gaussian, and inverse Gaussian distributions that are used to model radar clutter.…”

Section: Statistics For Distributed Scatterersmentioning

confidence: 99%

InSAR Deformation Analysis with Distributed Scatterers: A Review Complemented by New Advances

Even

Schulz

2018

Remote Sensing

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Interferometric Synthetic Aperture Radar (InSAR) is a powerful remote sensing technique able to measure deformation of the earth's surface over large areas. InSAR deformation analysis uses two main categories of backscatter: Persistent Scatterers (PS) and Distributed Scatterers (DS). While PS are characterized by a high signal-to-noise ratio and predominantly occur as single pixels, DS possess a medium or low signal-to-noise ratio and can only be exploited if they form homogeneous groups of pixels that are large enough to allow for statistical analysis. Although DS have been used by InSAR since its beginnings for different purposes, new methods developed during the last decade have advanced the field significantly. Preprocessing of DS with spatio-temporal filtering allows today the use of DS in PS algorithms as if they were PS, thereby enlarging spatial coverage and stabilizing algorithms. This review explores the relations between different lines of research and discusses open questions regarding DS preprocessing for deformation analysis. The review is complemented with an experiment that demonstrates that significantly improved results can be achieved for preprocessed DS during parameter estimation if their statistical properties are used.on DInSAR is given in [2]). The initial approach consisted of using three images that were used to form interferograms and a DEM. The DEM served to calculate and remove the synthetic phase. Furthermore, phase unwrapping was applied to generate the DEM and to obtain the deformation field. An algorithm for phase unwrapping was developed somewhat earlier for DEM generation from InSAR data in [9]. During the following years, techniques for most of the basic challenges of InSAR were developed. Early work on phase statistics and the phenomenon of decorrelation can be found in [10][11][12][13][14][15]. Enhancement of signal quality by filtering was considered, e.g., in [16,17]. Investigations, where stacking of interferograms is used to mitigate atmospheric delay, are discussed in [18][19][20]. Theory and algorithms were based on DS until the existence of PS was observed in the late 1990s by Ferretti while working on DEM reconstruction from a stack of SAR images [21]. In the sequel, they developed the first Persistent Scatterer Interferometry (PSI) algorithm [22,23], which extended the applicability of InSAR to scenes where enough PS are found but large parts are strongly decorrelated and hence unwrapping on the full interferograms cannot succeed. For several years from this time on, DInSAR and PSI developed in parallel. The next big step for DInSAR was the small-baseline subset (SBAS) technique [24]. By considering a redundant graph of small baseline interferograms, the effects of decorrelation could be mitigated and the redundancy enhanced robustness of estimation. In this first version, only DS were considered (using boxcar multilooking), but the next step [25] was to include processing of PS: coherent targets in the full resolution interferograms were recognized as having small r...

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“…allow to reach an unique solution for any α and for any initial valueR 0 [49]. For the best of our knowledge, the literature has not provide a method for computing optimal value α.…”

Section: Sirv Casementioning

confidence: 99%

“…The existence of the estimator as a function of the parameter of regularisation is proven in [47,48]. An optimal parameter of regularisation is proposed in [49]. For the Huber's estimator, the existence has been proven in [49], but no criteria has been defined to estimate the optimal value.…”

Section: Introductionmentioning

confidence: 99%

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Robust adaptive detection of buried pipes using GPR

et al. 2017

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Detection of buried objects such as pipes using a Ground Penetrating Radar (GPR) is intricate for three main reasons. First, noise is important in the resulting image because of the presence of several rocks and/or layers in the ground, highly influencing the Probability of False Alarm (PFA) level. Also, wave speed and object responses are unknown in the ground and depend on the relative permittivity, which is not directly measurable. Finally, the depth of the pipes leads to strong attenuation of the echoed signal, leading to poor SNR scenarios. In this paper, we propose a detection method: (1) enhancing the signal of interest while reducing the noise and layer contributions, and (2) giving a local estimate of the relative permittivity. We derive an adaptive detector where the signal of interest is parametrised by the wave speed in the ground. For this detector, noise is assumed to follow a Spherically Invariant Random Vector (SIRV) distribution in order to obtain a robust detection. We use robust maximum likelihood-type covariance matrix estimators called M-estimators. To handle the significant amount of data, we consider regularised versions of said estimators. Simulation will allow to estimate the relation PFA-Threshold. Comparison is performed with standard GPR processing methods, showing the aptitude of the method in detecting pipes having low response levels with a reasonable PFA.

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Regularized <formula formulatype="inline"><tex Notation="TeX">$M$</tex> </formula>-Estimators of Scatter Matrix

Cited by 91 publications

References 34 publications

An Overview of Robust Subspace Recovery

An Overview of Robust Subspace Recovery

InSAR Deformation Analysis with Distributed Scatterers: A Review Complemented by New Advances

Robust adaptive detection of buried pipes using GPR

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