Time Frequency Analysis

Combines Fourier and wavelet analysis to provide a complete Fourier domain around each sample in a signal or image. We are using the Stockwell transform to remove artifacts and describe texture in medical images.

The Fourier transform (FT) forms the cornerstone of magnetic resonance (MR) imaging. However, the FT is not appropriate for signals whose frequency content change with time. Since patient motion and physiological fluctuations can cause time-varying noise and artifacts, a time-frequency representation is more suitable MR signal processing.


Time domain signal containing two sine functions and two bursts of noise	Frequency domain of the signal generated from the Fourier Transform	Time-Frequency domain of the signal generated from the S-Transform

The Stockwell transform ( ST) combines the time–frequency representation of the Gabor Transform with the multi-scaling feature of the Wavelet Transform. It provides a unique time–frequency representation of a signal by adapting the FT to analyze the localized signal, using frequency-dependent time-scaling windows. The interpretation in a time–frequency domain becomes much easier and the multi-resolution analysis allows the ST to detect subtle Fourier spectral changes over time. In addition, the Fourier and Stockwell spectra are intimately related; they can be readily converted from one to the other. This close connection suggests the possibility of pre-processing image data in the Stockwell domain for Fourier-based imaging modalities (in particular, MRI and CT). Thus, the properties of the ST make it a potentially valuable processing tool for medical imaging.

Projects at the centre related to time-frequency analysis include texture analysis in both multiple sclerosis and cancer patients, the development of new transforms, the formulation of an efficient (fast) ST and development of a general theoretical framework to describe time-frequency transforms and analysis.

Patents

Local Multi-Scale Fourier Analysis for MRI. Mitchell JR, Fong C, Zhu H, Goodyear BG, Brown R. US patent #6,850,062 (issued Feb 1 2005).

Papers

Texture Quantification of Medical Images Using a Novel Complex Space-Frequency Transform. Drabycz S, Mitchell JR. The 22^nd International Congress on Computer Assisted Radiology and Surgery, Barcelona Spain, (2008).
Reduced memory requirements for the S-transform. Bjarnason TA, Drabycz S, Mitchell JR, Proceedings of the 20th Canadian Conference on Electrical and Computer Engineering (CCECE). Vancouver, 20; 275-7 (2007).
A new method to collapse the S-transform into local spectra by integrating in squares. Drabycz S, Bjarnason TA, Mitchell JR. Proceedings of the 20th Canadian Conference on Electrical and Computer Engineering (CCECE). Vancouver, 20; 271-4 (2007).

A Novel MRI Texture Analysis of Demyelination and Inflammation in Relapsing-remitting Experimental Allergic Encephalomyelitis. Zhang Y, Wells J, Buist R, Peeling J, Yong VW, Mitchell JR. Medical Image Computing and Computer-Assisted Intervention (MICCAI), Lecture Notes in Computer Science 760-767 (2006).
Texture Analysis for Non-Invasive Identification of Brain Tumor Genotype from MRI. Brown RA, Zlatescu MC, Cairncross JG, Mitchell JR. Proceedings of the Fifth IASTED International Conference on Visualization, Imaging, and Image Processing (VIIP). Benidorm, Spain. ACTA Press, #480-116 pg. 459-464 (2005).
Distributed Vector Processing of a New Local Multi-Scale Fourier Transform For Medical Imaging Applications. Brown RA, Zhu H, Mitchell JR. IEEE Transactions on Medical Imaging, 24(5):689-91 (2005).
3D MRI Progressive Imaging: Data- and Transform-Space Strategies. Brown RA, Baeza I, Mitchell JR, Villanueva RJ, Zhu H, Villanueva-Oller J, Law AG. CCCT in-press.
3D Progressive Imaging with Feature Selection. Brown RA, Zhu H, Mitchell JR, Law AG. Proceedings of the 2004 International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences (METMBS). Valafar FH, Arabnia HR, He M, Sinha U (Eds); CSREA Press, ISBN 1-932415-43-2, 216-219 (2004).
A New Local Multiscale Fourier Analysis for Medical Imaging. Zhu H, Goodyear BG, Lauzon ML, Brown RA, Mayer G, Law AG, Mansinha L, Mitchell JR. Medical Physics, 30:1134-1141 (2003).

Invited Talks

"Applications of time frequency analysis in medicine and geiophysics." Adler DH, Bjarnason TA, Drabycz S, Mitchell JR. ISAAC Workshop on Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis, Toronto, ON. December 11-15, 2006. (Podcast)
Time/frequency analysis of medical images. Mitchell JR, Brown RA, Drabycz S. Pacific Institute for the Mathematical Sciences Workshop on Time-Frequency Analysis and Non-Stationary Filtering, Banff, Alberta, Canada (2005).
Texture Analysis for Non-Invasive Identification of Brain Tumor Genotype from MRI. Brown RA, Zlatescu MC, Cairncross JG, Mitchell JR. Universidad Politécnica de Valencia, Valencia, Spain (2005).

Abstracts

Developing a Method for Detecting MGMT Promoter Methylation in Glioblastoma Multiforme by Multiscale Texture Image Analysis Based on the Stockwell Transform. Drabycz S, Roldan G, de Robles P, Adler DH, Magliocco A, Cairncross G, Mitchell JR. The 13^th Biennial Canadian Neuro Oncology Meeting, Banff AB, (2008).
Coarseness of MRI Texture in Acute Lesions Relates to Subsequent Recovery Activity in Multiple Sclerosis. Zhang Y, Zhu H, Mitchell JR, Metz LM. The 16^th International Society for MR in Medicine, Toronto, (2008).
A Novel Pixel-by-pixel Texture Analysis Technique Improves Frequency Resolution of Local MS Spectra. Drabycz S, Mitchell JR. The 16^th International Society for MR in Medicine, Toronto, (2008).

A 2D local frequency analysis approach using the S-transform. Drabycz S and Mitchell JR. Poster presentation by S Drabycz at CAIMS/MITACS Joint Annual Conference, Toronto, Ontario (2006).
Time/frequency analysis in magnetic resonance imaging. Drabycz S, Mitchell JR. Oral presentation at the Applied Mathematics Graduate Student Conference, Simon Fraser University, Vancouver, BC, Canada (2006).
Progressive Imaging: A Transform Space Approach. Brown RA, Baeza I, Zhu H, Villanueva RJ, Mitchell JR, Law AG. Poster at the Society for Industrial and Applied Mathematics Conference, Salt Lake City, Utah (2004).

Keywords

Stockwell transform; wavelets; short-time Fourier transform; Gabor transform; Magnetic resonance imaging

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