Applicability of compressive sensing on three-dimensional terahertz imagery for in-depth object defect detection and recognition using a dedicated semisupervised image processing methodology

Abstract. The quality control of composite multilayered materials and structures using nondestructive tests is of high interest for numerous applications in the aerospace and aeronautics industry. One of the established nondestructive methods uses microwaves to reveal defects inside a three-dimensional (3-D) object. Recently, there has been a tendency to extrapolate this method to higher frequencies (going to the subterahertz spectrum) which could lead to higher resolutions in the obtained 3-D images. Working at higher frequencies reveals challenges to deal with the increased data rate and to efficiently and effectively process and evaluate the obtained 3-D imagery for defect detection and recognition. To deal with these two challenges, we combine compressive sensing (for data rate reduction) with a dedicated image processing methodology for a fast, accurate, and robust quality evaluation of the object under test. We describe in detail the used methodology and evaluate the obtained results using subterahertz data acquired of two calibration samples with a frequency modulated continuous wave system. The applicability of compressive sensing within this context is discussed as well as the quality of the image processing methodology dealing with the reconstructed images.

[1]  Seymour Shlien,et al.  A Method for Computing the Partial Singular Value Decomposition , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Richard Bamler,et al.  Super-Resolution Power and Robustness of Compressive Sensing for Spectral Estimation With Application to Spaceborne Tomographic SAR , 2012, IEEE Transactions on Geoscience and Remote Sensing.

[3]  I. Daubechies,et al.  An iterative thresholding algorithm for linear inverse problems with a sparsity constraint , 2003, math/0307152.

[4]  John Morton,et al.  The impact resistance of composite materials — a review , 1991 .

[5]  A. Kak,et al.  Simultaneous Algebraic Reconstruction Technique (SART): A Superior Implementation of the Art Algorithm , 1984, Ultrasonic imaging.

[6]  Loris Nanni,et al.  Particle swarm optimization for prototype reduction , 2009, Neurocomputing.

[7]  H.B. Wallace,et al.  Standoff Detection of Weapons and Contraband in the 100 GHz to 1 THz Region , 2007, IEEE Transactions on Antennas and Propagation.

[8]  Justin P. Haldar,et al.  Compressed-Sensing MRI With Random Encoding , 2011, IEEE Transactions on Medical Imaging.

[9]  Stefano Serra Capizzano,et al.  Multigrid Methods for Multilevel Circulant Matrices , 2004, SIAM J. Sci. Comput..

[10]  D. M. Titterington,et al.  Joint discriminative-generative modelling based on statistical tests for classification , 2010, Pattern Recognit. Lett..

[11]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[12]  Lucila Ohno-Machado,et al.  Logistic regression and artificial neural network classification models: a methodology review , 2002, J. Biomed. Informatics.

[13]  Don J. Roth,et al.  Signal Processing Approaches for Terahertz Data Obtained from Inspection of the Shuttle External Tank Thermal Protection System Foam , 2007 .

[14]  Gilda Schirinzi,et al.  Three-Dimensional SAR Focusing From Multipass Signals Using Compressive Sampling , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[15]  Alexander A. Nepomnyashchy,et al.  Advances in Sensing with Security Applications , 2006 .

[16]  Addisson Salazar,et al.  Learning material defect patterns by separating mixtures of independent component analyzers from NDT sonic signals , 2010 .

[17]  Hiroshi Murase,et al.  Learning and recognition of 3D objects from appearance , 1993, [1993] Proceedings IEEE Workshop on Qualitative Vision.

[18]  Ram M. Narayanan,et al.  Compressive radar imaging using white stochastic waveforms , 2010, 2010 International Waveform Diversity and Design Conference.

[19]  Yoav Freund,et al.  A decision-theoretic generalization of on-line learning and an application to boosting , 1995, EuroCOLT.

[20]  Bruce A. Draper,et al.  Using the low-resolution properties of correlated images to improve the computational efficiency of eigenspace decomposition , 2006, IEEE Transactions on Image Processing.

[21]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[22]  Mike E. Davies,et al.  In greedy PURSUIT of new directions: (Nearly) Orthogonal Matching Pursuit by directional optimisation , 2007, 2007 15th European Signal Processing Conference.

[23]  Peter C. Doerschuk,et al.  Maximum-likelihood methods in cryo-EM. Part I: theoretical basis and overview of existing approaches , 2010 .

[24]  Joachim H. G. Ender,et al.  On compressive sensing applied to radar , 2010, Signal Process..

[25]  Stan Matwin,et al.  Addressing the Curse of Imbalanced Training Sets: One-Sided Selection , 1997, ICML.

[26]  Xinyu Zhang,et al.  An improved compressive sensing reconstruction algorithm using linear/non-linear mapping , 2011, 2011 Information Theory and Applications Workshop.

[27]  H. Quast,et al.  Towards real-time active THz range imaging for security applications , 2009, 2009 International Conference on Electromagnetics in Advanced Applications.

[28]  R Appleby,et al.  Passive millimetre–wave imaging and how it differs from terahertz imaging , 2004, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[29]  T. Goyette,et al.  High Resolution Imaging using 325 GHz and 1 . 5 THz Transceivers , 2004 .

[30]  Deanna Needell,et al.  CoSaMP: Iterative signal recovery from incomplete and inaccurate samples , 2008, ArXiv.

[31]  Emmanuel J. Candès,et al.  Decoding by linear programming , 2005, IEEE Transactions on Information Theory.

[32]  Zhu Han,et al.  Sampling rate reduction for 60 GHz UWB communication using compressive sensing , 2009, 2009 Conference Record of the Forty-Third Asilomar Conference on Signals, Systems and Computers.

[33]  Shengli Zhou,et al.  Application of compressive sensing to sparse channel estimation , 2010, IEEE Communications Magazine.

[34]  N. Karpowicz,et al.  Damage and defect inspection with terahertz waves , 2006 .

[35]  Hartmut G. Roskos,et al.  Continuous-wave terahertz imaging with a hybrid system , 2007 .

[36]  M. Vandewal,et al.  Development and optimization of THz NDT on aeronautics composite multilayered structures , 2012, Defense + Commercial Sensing.

[37]  A. H. Andersen.  Algebraic reconstruction in CT from limited views. , 1989, IEEE transactions on medical imaging.

[38]  Moeness G. Amin,et al.  Partially sparse reconstruction of behind-the-wall scenes , 2012, Defense + Commercial Sensing.

[39]  I. Johnstone,et al.  Wavelet Shrinkage: Asymptopia? , 1995 .

[40]  N. Llombart,et al.  Penetrating 3-D Imaging at 4- and 25-m Range Using a Submillimeter-Wave Radar , 2008, IEEE Transactions on Microwave Theory and Techniques.

[41]  Matthias Franz,et al.  Reducing non-linear artifacts of multi-material objects in industrial 3D computed tomography , 2008 .

[42]  Patrick J. Flynn,et al.  Eigenshapes for 3D object recognition in range data , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[43]  M H S Siqueira,et al.  The use of ultrasonic guided waves and wavelets analysis in pipe inspection. , 2004, Ultrasonics.

[44]  D. Ruta,et al.  An Overview of Classifier Fusion Methods , 2000 .

[45]  Jorge S. Marques,et al.  Robust Deformable Model for Segmenting the Left Ventricle in 3D Volumes of Ultrasound Data , 2012, ICPRAM.

[46]  Peter H. Siegel,et al.  Fast high-resolution terahertz radar imaging at 25 meters , 2010, Defense + Commercial Sensing.

[47]  Adam Krzyżak,et al.  Methods of combining multiple classifiers and their applications to handwriting recognition , 1992, IEEE Trans. Syst. Man Cybern..

[48]  Chin-Hui Lee,et al.  A maximum-likelihood approach to stochastic matching for robust speech recognition , 1996, IEEE Trans. Speech Audio Process..

[49]  D. Donoho,et al.  Sparse MRI: The application of compressed sensing for rapid MR imaging , 2007, Magnetic resonance in medicine.

[50]  Rick Chartrand,et al.  Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data , 2009, 2009 IEEE International Symposium on Biomedical Imaging: From Nano to Macro.

[51]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[52]  Arttu Luukanen,et al.  Terahertz active direct detection imagers , 2004, SPIE Defense + Commercial Sensing.

[53]  T. Tanabe,et al.  Sub-terahertz imaging of defects in building blocks , 2009 .

[54]  R. M. Willett,et al.  Compressed sensing for practical optical imaging systems: A tutorial , 2011, IEEE Photonics Conference 2012.

[55]  Richard O. Duda,et al.  Pattern classification and scene analysis , 1974, A Wiley-Interscience publication.

[56]  Thomas E. Hall,et al.  Active millimeter-wave standoff and portal imaging techniques for personnel screening , 2009, 2009 IEEE Conference on Technologies for Homeland Security.

[57]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[58]  Wei-Chang Zhong.  The Magnetic Dipole Theory for Non—Destructive Testing in China , 2008 .

[59]  D. Ruderman.  The statistics of natural images , 1994 .

[60]  B. Boro Djordjevic.  NONDESTRUCTIVE TEST TECHNOLOGY FOR THE COMPOSITES Keynote lecture , 2009 .

[61]  R. Cartwright.  Problems and solutions for estimating indel rates and length distributions. , 2009, Molecular biology and evolution.

[62]  Michael S. Shur,et al.  Detection of space shuttle insulation foam defects by using a 0.2 THz Gunn diode oscillator and pyroelectric detector , 2004 .

[63]  Ralf Henneberger,et al.  Fast Active THz Cameras with Ranging Capabilities , 2009 .

[64]  Xuejun Liu,et al.  Microarray Data Analysis using Probabilistic Methods , 2006 .

[65]  J S Osberg,et al.  Kappa coefficient calculation using multiple ratings per subject: a special communication. , 1989, Physical therapy.