title: Fast splitting alpha-rooting method of image enhancement: tensor representation.
abstract: In the tensor representation, a two-dimensional (2-D) image is represented uniquely by a set of one-dimensional (1-D) signals, so-called splitting-signals, that carry the spectral information of the image at frequency-points of specific sets that cover the whole domain of frequencies. The image enhancement is thus reduced to processing splitting-signals and such process requires a modification of only a few spectral components of the image, for each signal. For instance, the alpha-rooting method of image enhancement can be fulfilled through processing separately a maximum of 3N/2 splitting-signals of an image (N x N), where N is a power of two. In this paper, we propose a fast implementation of the a-rooting method by using one splitting-signal of the tensor representation with respect to the discrete Fourier transform (DFT). The implementation is described in the frequency and spatial domains. As a result, the proposed algorithms for image enhancement use two 1-D N-point DFTs instead of two 2-D N x N-point DFTs in the traditional method of alpha-rooting.
authors.affiliation: Department of Electrical and Computer Engineering, The University of Texas at San Antonio, San Antonio, TX 8249-0669, USA. arslan@lodestar.utsa.edu
authors.forename: Fatma Turkay
authors.initials: FT
authors.lastname: Arslan
authors.forename: Artyom M
authors.initials: AM
authors.lastname: Grigoryan
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D009716:Numerical Analysis, Computer-Assisted; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted