On generalized adaptive neural filter

Linear filters have historically been used in the past as the most useful tools for suppressing noise in signal processing. It has been shown that the optimal filter which minimizes the mean square error (MSE) between the filter output and the desired output is a linear filter provided that the noise is additive white Gaussian noise (AWGN). However, in most signal processing applications, the noise in the channel through which a signal is transmitted is not AWGN; it is not stationary, and it may have unknown characteristics. To overcome the shortcomings of linear filters, nonlinear filters ranging from the median filters to stack filters have been developed. They have been successfully used in a number of applications, such as enhancing the signal-to-noise ratio of the telecommunication receivers, modeling the human vocal tract to synthesize speech in speech processing, and separating out the maternal and fetal electrocardiogram signals to diagnose prenatal ailments. In particular, stack filters have been shown to provide robust noise suppression, and are easily implementable in hardware, but configuring an optimal stack filter remains a challenge. This dissertation takes on this challenge by extending stack filters to a new class of nonlinear adaptive filters called generalized adaptive neural filters (GANFs). The objective of this work is to investigate their performance in terms of the mean absolute error criterion, to evaluate and predict the generalization of various discriminant functions employed for GANFs, and to address issues regarding their applications and implementation. It is shown that GANFs not only extend the class of stack filters, but also have better performance in terms of suppressing non-additive white Gaussian noise. Several results are drawn from the theoretical and experimental work: stack filters can be adaptively configured by neural networks; GANFs encompass a large class of nonlinear sliding-window filters which include stack filters; the mean absolute error (MAE) of the optimal GANF is upper-bounded by that of the optimal stack filter; a suitable class of discriminant functions can be determined before a training scheme is executed; VC dimension (VCdim) theory can be applied to determine the number of training samples; the algorithm presented in configuring GANFs is effective and robust

The IPAC Image Subtraction and Discovery Pipeline for the intermediate Palomar Transient Factory

We describe the near real-time transient-source discovery engine for the intermediate Palomar Transient Factory (iPTF), currently in operations at the Infrared Processing and Analysis Center (IPAC), Caltech. We coin this system the IPAC/iPTF Discovery Engine (or IDE). We review the algorithms used for PSF-matching, image subtraction, detection, photometry, and machine-learned (ML) vetting of extracted transient candidates. We also review the performance of our ML classifier. For a limiting signal-to-noise ratio of 4 in relatively unconfused regions, "bogus" candidates from processing artifacts and imperfect image subtractions outnumber real transients by ~ 10:1. This can be considerably higher for image data with inaccurate astrometric and/or PSF-matching solutions. Despite this occasionally high contamination rate, the ML classifier is able to identify real transients with an efficiency (or completeness) of ~ 97% for a maximum tolerable false-positive rate of 1% when classifying raw candidates. All subtraction-image metrics, source features, ML probability-based real-bogus scores, contextual metadata from other surveys, and possible associations with known Solar System objects are stored in a relational database for retrieval by the various science working groups. We review our efforts in mitigating false-positives and our experience in optimizing the overall system in response to the multitude of science projects underway with iPTF.Comment: 66 pages, 21 figures, 7 tables, accepted by PAS

Long-term monitoring of geodynamic surface deformation using SAR interferometry

Thesis (Ph.D.) University of Alaska Fairbanks, 2014Synthetic Aperture Radar Interferometry (InSAR) is a powerful tool to measure surface deformation and is well suited for surveying active volcanoes using historical and existing satellites. However, the value and applicability of InSAR for geodynamic monitoring problems is limited by the influence of temporal decorrelation and electromagnetic path delay variations in the atmosphere, both of which reduce the sensitivity and accuracy of the technique. The aim of this PhD thesis research is: how to optimize the quantity and quality of deformation signals extracted from InSAR stacks that contain only a low number of images in order to facilitate volcano monitoring and the study of their geophysical signatures. In particular, the focus is on methods of mitigating atmospheric artifacts in interferograms by combining time-series InSAR techniques and external atmospheric delay maps derived by Numerical Weather Prediction (NWP) models. In the first chapter of the thesis, the potential of the NWP Weather Research & Forecasting (WRF) model for InSAR data correction has been studied extensively. Forecasted atmospheric delays derived from operational High Resolution Rapid Refresh for the Alaska region (HRRRAK) products have been compared to radiosonding measurements in the first chapter. The result suggests that the HRRR-AK operational products are a good data source for correcting atmospheric delays in spaceborne geodetic radar observations, if the geophysical signal to be observed is larger than 20 mm. In the second chapter, an advanced method for integrating NWP products into the time series InSAR workflow is developed. The efficiency of the algorithm is tested via simulated data experiments, which demonstrate the method outperforms other more conventional methods. In Chapter 3, a geophysical case study is performed by applying the developed algorithm to the active volcanoes of Unimak Island Alaska (Westdahl, Fisher and Shishaldin) for long term volcano deformation monitoring. The volcano source location at Westdahl is determined to be approx. 7 km below sea level and approx. 3.5 km north of the Westdahl peak. This study demonstrates that Fisher caldera has had continuous subsidence over more than 10 years and there is no evident deformation signal around Shishaldin peak.Chapter 1. Performance of the High Resolution Atmospheric Model HRRR-AK for Correcting Geodetic Observations from Spaceborne Radars -- Chapter 2. Robust atmospheric filtering of InSAR data based on numerical weather prediction models -- Chapter 3. Subtle motion long term monitoring of Unimak Island from 2003 to 2010 by advanced time series SAR interferometry -- Chapter 4. Conclusion and future work

Morphological filter mean-absolute-error representation theorems and their application to optimal morphological filter design

The present thesis derives error representations and develops design methodologies for optimal mean-absolute-error (MAE) morphological-based filters. Four related morphological-based filter-types are treated. Three are translation-invariant, monotonically increasing operators, and our analysis is based on the Matheron (1975) representation. In this class we analyze conventional binary, conventional gray-scale, and computational morphological filters. The fourth filter class examined is that of binary translation invariant operators. Our analysis is based on the Banon and Barrera (1991) representation and hit-or-miss operator of Serra (1982). A starting point will be the optimal morphological filter paradigm of Dougherty (1992a,b) whose analysis de scribes the optimal filter by a system of nonlinear inequalities with no known method of solution, and thus reduces filter design to minimal search strategies. Although the search analysis is definitive, practical filter design remained elu sive because the search space can be prohibitively large if it not mitigated in some way. The present thesis extends from Dougherty\u27s starting point in several ways. Central to the thesis is the MAE analysis for the various filter settings, where in each case, a theorem is derived that expresses overall filter MAE as a sum of MAE values of individual structuring-element filters and MAE of combinations of unions (maxima) of those elements. Recursive forms of the theorems can be employed in a computer algorithm to rapidly evaluate combinations of structuring elements and search for an optimal filter basis. Although the MAE theorems provide a rapid means for examining the filter design space, the combinatoric nature of this space is, in general, too large for a exhaustive search. Another key contribution of this thesis concerns mitigation of the computational burden via design constraints. The resulting constrained filter will be suboptimal, but, if the constraints are imposed in a suitable man ner, there is little loss of filter performance in return for design tractability. Three constraint approaches developed here are (1) limiting the number of terms in the filter expansion, (2) constraining the observation window, and (3) employing structuring element libraries from which to search for an optimal basis. Another contribution of this thesis concerns the application of optimal morphological filters to image restoration. Statistical and deterministic image and degradation models for binary and low-level gray images were developed here that relate to actual problems in the optical character recognition and electronic printing fields. In the filter design process, these models are employed to generate realizations, from which we extract single-erosion and single-hit-or-miss MAE statistics. These realization-based statistics are utilized in the search for the optimal combination of structuring elements

Design &implementation of complex-valued FIR digital filters with application to migration of seismic data

One-dimensional (I-D) and two-dimensional (2-D) frequency-space seismic migration FIR digital filter coefficients are of complex values when such filters require special space domain as well as wavenumber domain characteristics. In this thesis, such FIR digital filters are designed using Vector Space Projection Methods (VSPMs), which can satisfy the desired predefined filters' properties, for 2-D and three-dimensional (3-D) seismic data sets, respectively. More precisely, the pure and the relaxed projection algorithms, which are part of the VSPM theory, are derived. Simulation results show that the relaxed version of the pure algorithm can introduce significant savings in terms of the number of iterations required. Also, due to some undesirable background artifacts on migrated sections, a modified version of the pure algorithm was used to eliminate such effects. This modification has also led to a significant reduction in the number of computations when compared to both the pure and relaxed algorithms. We further propose a generalization of the l-D (real/complex-valued) pure algorithm to multi-dimensional (m-D) complex-valued FIR digital filters, where the resulting frequency responses possess an approximate equiripple nature. Superior designs are obtained when compared with other previously reported methods. In addition, we also propose a new scheme for implementing the predesigned 2-D migration FIR filters. This realization is based on Singular Value Decomposition (SVD). Unlike the existing realization methods which are used for this geophysical application, this cheap realization via SVD, compared with the true 2-D convolution, results in satisfactory wavenumber responses. Finally, an application to seismic migration of 2-D and 3-D synthetic sections is shown to confirm our theoretical conclusions. The proposed resulting migration FIR filters are applied also to the challenging SEGIEAGE Salt model data. The migrated section (image) outperformed images obtained using other FIR filters and with other standard migration techniques where difficult structures contained in such a challenging model are imaged clearly

SPIRE Point Source Catalog Explanatory Supplement

The Spectral and Photometric Imaging Receiver (SPIRE) was launched as one of the scientific instruments on board of the space observatory Herschel. The SPIRE photometer opened up an entirely new window in the Submillimeter domain for large scale mapping, that up to then was very difficult to observe. There are already several catalogs that were produced by individual Herschel science projects. Yet, we estimate that the objects of only a fraction of these maps will ever be systematically extracted and published by the science teams that originally proposed the observations. The SPIRE instrument performed its standard photometric observations in an optically very stable configuration, only moving the telescope across the sky, with variations in its configuration parameters limited to scan speed and sampling rate. This and the scarcity of features in the data that require special processing steps made this dataset very attractive for producing an expert reduced catalog of point sources that is being described in this document. The Catalog was extracted from a total of 6878 unmodified SPIRE scan map observations. The photometry was obtained by a systematic and homogeneous source extraction procedure, followed by a rigorous quality check that emphasized reliability over completeness. Having to exclude regions affected by strong Galactic emission, that pushed the limits of the four source extraction methods that were used, this catalog is aimed primarily at the extragalactic community. The result can serve as a pathfinder for ALMA and other Submillimeter and Far-Infrared facilities. 1,693,718 sources are included in the final catalog, splitting into 950688, 524734, 218296 objects for the 250\mu m, 350\mu m, and 500\mu m bands, respectively. The catalog comes with well characterized environments, reliability, completeness, and accuracies, that single programs typically cannot provide