Projection-Based and Look Ahead Strategies for Atom Selection

In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of potential atoms in each iteration. The two new schemes lead to two new algorithms. For both the algorithms, in each iteration, the set of potential atoms is found using a standard matched filter. In case of the first scheme, we propose an orthogonal projection strategy that selects an atom from the set of potential atoms. Then, for the second scheme, we propose a look ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations. The use of look ahead strategy requires a higher computational resource. To achieve a trade-off between performance and complexity, we use the two new schemes in cascade and develop a third new algorithm. Through experimental evaluations, we compare the proposed algorithms with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201

A Robust Approach to Optimal Matched Filter Design in Ultrasonic Non-Destructive Evaluation (NDE)

The matched filter was demonstrated to be a powerful yet efficient technique to enhance defect detection and imaging in ultrasonic non-destructive evaluation (NDE) of coarse grain materials, provided that the filter was properly designed and optimized. In the literature, in order to accurately approximate the defect echoes, the design utilized the real excitation signals, which made it time consuming and less straightforward to implement in practice. In this paper, we present a more robust and flexible approach to optimal matched filter design using the simulated excitation signals, and the control parameters are chosen and optimized based on the real scenario of array transducer, transmitter-receiver system response, and the test sample, as a result, the filter response is optimized and depends on the material characteristics. Experiments on industrial samples are conducted and the results confirm the great benefits of the method

Compressed matched filter for non-Gaussian noise

We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic which can be easily communicated and/or stored for future inference. Such a statistic is usually unknown in the general non-Gaussian case. Instead, we propose a hybrid matched filter coupled with a randomized compressed sensing procedure, which together create a low dimensional statistic. We also derive a complementary algorithm for robust reconstruction given this statistic. Our recovery method is based on the fast iterative shrinkage and thresholding algorithm which is used for outlier rejection given the compressed data. We demonstrate the advantages of the proposed framework using synthetic simulations

Catalog Extraction in SZ Cluster Surveys: a matched filter approach

We present a method based on matched multifrequency filters for extracting cluster catalogs from Sunyaev-Zel'dovich (SZ) surveys. We evaluate its performance in terms of completeness, contamination rate and photometric recovery for three representative types of SZ survey: a high resolution single frequency radio survey (AMI), a high resolution ground-based multiband survey (SPT), and the Planck all-sky survey. These surveys are not purely flux limited, and they loose completeness significantly before their point-source detection thresholds. Contamination remains relatively low at <5% (less than 30%) for a detection threshold set at S/N=5 (S/N=3). We identify photometric recovery as an important source of catalog uncertainty: dispersion in recovered flux from multiband surveys is larger than the intrinsic scatter in the Y-M relation predicted from hydrodynamical simulations, while photometry in the single frequency survey is seriously compromised by confusion with primary cosmic microwave background anisotropy. The latter effect implies that follow-up observations in other wavebands (e.g., 90 GHz, X-ray) of single frequency surveys will be required. Cluster morphology can cause a bias in the recovered Y-M relation, but has little effect on the scatter; the bias would be removed during calibration of the relation. Point source confusion only slightly decreases multiband survey completeness; single frequency survey completeness could be significantly reduced by radio point source confusion, but this remains highly uncertain because we do not know the radio counts at the relevant flux levels.Comment: 14 pages, 13 figures, replaced to match version accepted for publication in A&

3D-Matched-Filter Galaxy Cluster Finder I: Selection Functions and CFHTLS Deep Clusters

We present an optimised galaxy cluster finder, 3D-Matched-Filter (3D-MF), which utilises galaxy cluster radial profiles, luminosity functions and redshift information to detect galaxy clusters in optical surveys. This method is an improvement over other matched-filter methods, most notably through implementing redshift slicing of the data to significantly reduce line-of-sight projections and related false positives. We apply our method to the Canada-France-Hawaii Telescope Legacy Survey (CFHTLS) Deep fields, finding ~170 galaxy clusters per square degree in the 0.2 <= z <= 1.0 redshift range. Future surveys such as LSST and JDEM can exploit 3D-MF's automated methodology to produce complete and reliable galaxy cluster catalogues. We determine the reliability and accuracy of the statistical approach of our method through a thorough analysis of mock data from the Millennium Simulation. We detect clusters with 100% completeness for M_200 >= 3.0x10^(14)M_sun, 88% completeness for M_200 >= 1.0x10^(14)M_sun, and 72% completeness well into the 10^(13)M_sun cluster mass range. We show a 36% multiple detection rate for cluster masses >= 1.5x10^(13)M_sun and a 16% false detection rate for galaxy clusters >~ 5x10^(13)M_sun, reporting that for clusters with masses <~ 5x10^(13)M_sun false detections may increase up to ~24%. Utilising these selection functions we conclude that our galaxy cluster catalogue is the most complete CFHTLS Deep cluster catalogue to date.Comment: 18 pages, 17 figures, 5 tables; v2: added Fig 5, minor edits to match version published in MNRA