The numerical solution of total variation minimization problems in image processing
- Montana State Univ., Bozeman, MT (United States)
Consider the minimization of penalized least squares functionals of the form: f(u) = 1/2 ({parallel}Au {minus} z{parallel}){sup 2} + {alpha}{integral}{sub {Omega}}{vert_bar}{del}u{vert_bar}dx. Here A is a bounded linear operator, z represents data, {parallel} {center_dot} {parallel} is a Hilbert space norm, {alpha} is a positive parameter, {integral}{sub {Omega}}{vert_bar}{del}u{vert_bar} dx represents the total variation (TV) of a function u {element_of} BV ({Omega}), the class of functions of bounded variation on a bounded region {Omega}, and {vert_bar} {center_dot} {vert_bar} denotes Euclidean norm. In image processing, u represents an image which is to be recovered from noisy data z. Certain {open_quotes}blurring processes{close_quotes} may be represented by the action of an operator A on the image u.
- Research Organization:
- Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)
- OSTI ID:
- 223841
- Report Number(s):
- CONF-9404305--Vol.1; ON: DE96005735
- Country of Publication:
- United States
- Language:
- English
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