Cutting-edge Mathematical Tools in Processing and Analysis of Signals in Marine and Navy

Signal processing plays a pivotal role in information gathering and decision making. This paper presents and compares different signal processing techniques used in marine and navy applications, primarily based on using wavelets as kernel. The article covers Fourier transform, time frequency wavelet based techniques such as bandelets, contourlets, curvelets, edgelets, wedgelets, shapelets, and ridgelets. In the example section of the paper, several transform techniques are presented and commented on the harbour surveillance video stream example.

[1]  Kaoru Hirota,et al.  A Multidirectional Multiresolution Transform for Image Representation , 2007 .

[2]  A. Réfrégier Shapelets: I. a method for image analysis , 2001, astro-ph/0105178.

[3]  James L. Flanagan,et al.  Digital coding of speech in sub-bands , 1976, Bell Syst. Tech. J..

[4]  D. Walnut,et al.  Fundamental Papers in Wavelet Theory , 2006 .

[5]  Stéphane Mallat,et al.  Geometric Estimation with Orthogonal Bandlet Bases , 2007 .

[6]  Ronald E. Crochiere,et al.  A variable-band coding Scheme for speech encoding at 4.8 kb/s , 1977 .

[7]  Ramakant Nevatia,et al.  Detection of multiple, partially occluded humans in a single image by Bayesian combination of edgelet part detectors , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[8]  Jean-Michel Poggi,et al.  Wavelet Toolbox User s Guide , 1996 .

[9]  O. Rioul,et al.  Wavelets and signal processing , 1991, IEEE Signal Processing Magazine.

[10]  Jelena Kovacevic,et al.  Wavelets and Subband Coding , 2013, Prentice Hall Signal Processing Series.

[11]  M. Meneghetti,et al.  Reliable shapelet image analysis , 2006, astro-ph/0608369.

[12]  Ingrid Daubechies,et al.  Ten Lectures on Wavelets , 1992 .

[13]  Patrick Oonincx,et al.  Second generation wavelets and applications , 2005 .

[14]  Stéphane Mallat,et al.  Sparse geometric image representations with bandelets , 2005, IEEE Transactions on Image Processing.

[15]  Laurent Demanet,et al.  Fast Discrete Curvelet Transforms , 2006, Multiscale Model. Simul..

[16]  Kannan Ramchandran,et al.  Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms , 1993, IEEE Trans. Signal Process..

[17]  Wim Sweldens,et al.  The lifting scheme: a construction of second generation wavelets , 1998 .

[18]  D. Donoho Wedgelets: nearly minimax estimation of edges , 1999 .

[19]  A. Antoniou Digital Signal Processing: Signals, Systems, and Filters , 2005 .

[20]  B. Goulard,et al.  Sharpening enhancement of digitized mammograms with complex symmetric Daubechies wavelets , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.

[21]  Nick G. Kingsbury,et al.  The dual-tree complex wavelet transform: A new efficient tool for image restoration and enhancement , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[22]  Gene H. Golub,et al.  Matrix computations , 1983 .

[23]  S. Mallat A wavelet tour of signal processing , 1998 .

[24]  Langis Gagnon,et al.  Image enhancement with symmetric Daubechies wavelets , 1995, Optics + Photonics.

[25]  Dennis Gabor,et al.  Theory of communication , 1946 .

[26]  Martin Vetterli,et al.  Perfect reconstruction FIR filter banks: some properties and factorizations , 1989, IEEE Trans. Acoust. Speech Signal Process..

[27]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[28]  Richard Baraniuk,et al.  The Dual-tree Complex Wavelet Transform , 2007 .

[29]  Felix Friedrich,et al.  Beyond wavelets: New image representation paradigms , 2005 .

[30]  Truong Q. Nguyen,et al.  Wavelets and filter banks , 1996 .

[31]  Julian Magarey,et al.  Wavelet Transforms in Image Processing , 1998 .