Minimax description length for signal denoising and optimized representation

Nonlinear Modeling: Estimation and Prediction with Applications to GPS

“…The performance analysis of the regular lock discriminators and the proposed robust discriminators is conducted using real GPS data 2 . The data consists of the output of the analog-to-digital converter in a GPS receiver, which is the input fed to individual receiver channels for carrier and code stripping processes.…”

“…The second row shows the result of the geometric heat flow C t = KN ,(n = 0), which smoothes away not only fine features but some coarse features as well (the fins for example). The results of the flow, C t -cos' 2 (26)KN ,(71 = 2), are shown in the third row of Fig B.8. In this case, rectangular features are preserved for longer periods throughout the evolution.…”

“…Furthermore, it is not well understood how these curvaturebased filters are affected by different noise distributions and when this sort of problem may occur. Much like the anisotropic diffusion problem, the curve evolution technique has largely been addressed in the literature, outside [2,36], in a purely deterministic setting. In this part of our research effort, we provide a stochastic formulation of the geometric heat equation and use the resulting insights to develop a new class of curvature-based flows and anisotropic diffusion filters which preserve desired features in the shape of an object.…”

“…Partial support of this grant has also led to the publication of four journal papers [2,3,4,5] and three journal papers under review [6,7,8], as well as two invited book chapters [9,10] and several conference papers at ICASSP and ICIP [11,12,13,14] and invited national and international seminars, including an invitation for a one month visit in-the department of information sciences at University of Tokyo (Japan) (Nov. 1999), courtesy of the Japanese Society for Advancement of Science, and an invitation as principal guest speaker at a workshop on Mathematics in Imaging at University of Hong Kong (China) (Dec. 2000).…”

“…In this case, rectangular features are preserved for longer periods throughout the evolution. Finally, the flow, C t = sin 2 [A9)KN, {n = 4), is depicted in the. last row, preserving octagonal features as shown in the nose and the dorsal things.…”