title: Multiscale properties of weighted total variation flow with applications to denoising and registration.
abstract: Images consist of structures of varying scales: large scale structures such as flat regions, and small scale structures such as noise, textures, and rapidly oscillatory patterns. In the hierarchical (BV, L(2)) image decomposition, Tadmor, et al. (2004) start with extracting coarse scale structures from a given image, and successively extract finer structures from the residuals in each step of the iterative decomposition. We propose to begin instead by extracting the finest structures from the given image and then proceed to extract increasingly coarser structures. In most images, noise could be considered as a fine scale structure. Thus, starting the image decomposition with finer scales, rather than large scales, leads to fast denoising. We note that our approach turns out to be equivalent to the nonstationary regularization in Scherzer and Weickert (2000). The continuous limit of this procedure leads to a time-scaled version of total variation flow. Motivated by specific clinical applications, we introduce an image depending weight in the regularization functional, and study the corresponding weighted TV flow. We show that the edge-preserving property of the multiscale representation of an input image obtained with the weighted TV flow can be enhanced and localized by appropriate choice of the weight. We use this in developing an efficient and edge-preserving denoising algorithm with control on speed and localization properties. We examine analytical properties of the weighted TV flow that give precise information about the denoising speed and the rate of change of energy of the images. An additional contribution of the paper is to use the images obtained at different scales for robust multiscale registration. We show that the inherently multiscale nature of the weighted TV flow improved performance for registration of noisy cardiac MRI images, compared to other methods such as bilateral or Gaussian filtering. A clinical application of the multiscale registration algorithm is also demonstrated for aligning viability assessment magnetic resonance (MR) images from 8 patients with previous myocardial infarctions.
authors.affiliation: Department of Mathematics, University of Toronto, Toronto, ON M5S 1A1, Canada; The Fields Institute, 222 College Street, Toronto, ON M5T 3J1, Canada. Electronic address: prashantva@gmail.com.
authors.forename: Prashant
authors.initials: P
authors.lastname: Athavale
authors.affiliation: Schulich Heart Program and Physical Sciences Platform, Sunnybrook Research Institute, Toronto, ON M4N 3M5, Canada; Department of Medical Biophysics, University of Toronto, Toronto, ON M5G 2M9, Canada. Electronic address: robert.xu@sri.utoronto.ca.
authors.forename: Robert
authors.initials: R
authors.lastname: Xu
authors.affiliation: Schulich Heart Program and Physical Sciences Platform, Sunnybrook Research Institute, Toronto, ON M4N 3M5, Canada. Electronic address: perry.radau@gmail.com.
authors.forename: Perry
authors.initials: P
authors.lastname: Radau
authors.affiliation: Department of Mathematics, University of Toronto, Toronto, ON M5S 1A1, Canada; The Edward S. Rogers Sr. Department of Electrical & Computer Engineering, 10 King's College Road, Toronto, ON M5S 3G4, Canada; Institute of Biomaterials & Biomedical Engineering, University of Toronto, 164 College Street, Toronto, ON M5S 3G9, Canada. Electronic address: nachman@math.utoronto.ca.
authors.forename: Adrian
authors.initials: A
authors.lastname: Nachman
authors.affiliation: Schulich Heart Program and Physical Sciences Platform, Sunnybrook Research Institute, Toronto, ON M4N 3M5, Canada; Department of Medical Biophysics, University of Toronto, Toronto, ON M5G 2M9, Canada. Electronic address: gawright@sri.utoronto.ca.
authors.forename: Graham A
authors.initials: GA
authors.lastname: Wright
mesh_terms: D000465:Algorithms; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D009203:Myocardial Infarction / Q000473:pathology*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity
keywords: Fast denoising; Multiscale registration; Mutual information; Normalized gradient field; Total variation flow