Abstract
We examine the so-called Discrete Orthonormal Stockwell Transform (DOST) and show that a number of quite simple modifications can be made to obtain various desired properties. For example, we introduce a real-valued Discrete Cosine-based DOST (DCST). The coefficients of the DOST and its variations are shown to exhibit a directed graph structure as opposed to the tree-like structure demonstrated by wavelet coefficients. Finally, we employ the DOST and DCST in a series of simple compression experiments and compare the results to those obtained with biorthogonal wavelets and the DCT.
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References
Brown, R.A., Lauzon, M.L., Frayne, R.: A general description of linear time-frequency transforms and formulation of a fast, invertible transform that samples the continuous s-transform spectrum nonredundantly. IEEE Transactions on Signal Processing 58(1), 281–290 (2010)
Drabycz, S., Stockwell, R.G., Mitchell, J.R.: Image texture characterization using the discrete orthonormal s-transform. Journal of Digital Imaging 22(6), 696–708 (2009)
Stockwell, R.G., Mansinha, L., Lowe, R.P.: Localization of complex spectrum: the S transform. IEEE Transactions on Signal Processing 144(4), 998–1001 (1996)
Stockwell, R.G.: A basis for efficient representation of the s-transform. Digital Signal Processing: A Review Journal 17(1), 371–393 (2007)
Wang, Y., Orchard, J.: Symmetric discrete orthonormal stockwell transform. Numerical Analysis and Applied Mathematics 1048, 585–588 (2008)
Wang, Y., Orchard, J.: On the use of the stockwell transform for image compression. Image Processing: Algorithms and Systems Vii 7245, 724504 (2009)
Wang, Y., Orchard, J.: Fast discrete orthonormal stockwell transform. Siam Journal on Scientific Computing 31(5), 4000–4012 (2009)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: From error visibility to structural similarity. IEEE Transactions on Image Processing 13, 600–612 (2004)
Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: The SSIM Index for Image Quality Assessment, https://ece.uwaterloo.ca/~z70wang/research/ssim/
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Ladan, J., Vrscay, E.R. (2013). The Discrete Orthonormal Stockwell Transform and Variations, with Applications to Image Compression. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2013. Lecture Notes in Computer Science, vol 7950. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39094-4_27
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DOI: https://doi.org/10.1007/978-3-642-39094-4_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39093-7
Online ISBN: 978-3-642-39094-4
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