Nonlinear Filtering
The earliest work in LIVE was focused on a new breed of image processing filters. As part of this work, researchers in LIVE developed the new theory of Order Statistic (OS) Filters, which provided the first mean-squared design methodology for filters in this class, which include the popular median filter. Much of the work in LIVE was devoted to exploring the relationship between OS filters, linear filters, robust statistics, and a plethora of applications, including edge detection, denoising, and image estimation. Some of the key papers follow:
A.C. Bovik, T.S. Huang and D.C. Munson, “A generalization of median filtering using linear combinations of order statistics,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-31, no. 6, pp. 1342-1350, December 1983.
A.C. Bovik, T.S. Huang and D.C. Munson, “Edge-sensitive image restoration using order- constrained least-squares methods,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-33, no. 4, pp. 1253-1263, October 1985.
A.C. Bovik and D.C. Munson, “Edge detection using median comparisons,” Computer Vision, Graphics, and Image Processing, vol. 33, pp. 377-389, March 1986.
A.C. Bovik, T.S. Huang and D.C. Munson, “Nonparametric tests for edge detection in noise,” Pattern Recognition, vol. 19, No. 3, pp. 209-219, 1986.
A.C. Bovik, T.S. Huang and D.C. Munson, “The effect of median filtering on edge estimation and detection,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. PAMI-9, no. 2, pp. 181-194, March 1987.
A.C. Bovik, “Streaking in median filtered images,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-35, no. 4, pp. 493-503, April 1987.
A. Restrepo and A.C. Bovik, “Adaptive trimmed mean filters for image restoration,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-36, no. 8, pp. 1326- 1337, August 1988.
H.G. Longbotham and A.C. Bovik, “Theory of order statistic filters and their relationship to linear FIR filters,” IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-37, no. 2, pp. 275-287, February 1989.
L. Naaman and A.C. Bovik, “Least-squares order statistic filters with coefficient censoring,” Signal Processing, vol. 18, no. 2, pp. 139-152, October 1989.
L. Naaman and A.C. Bovik, “Least-squares order statistic filters for signal restoration,” IEEE Transactions on Circuits and Systems, vol. CAS-38, no. 3, pp. 244-257, March 1991.
A. Restrepo and A.C. Bovik, “Locally monotonic regression,” IEEE Transactions on Signal Processing, vol. ASSP-41, no. 9, pp. 2796-2810, September 1993.
A. Restrepo and A.C. Bovik, “On the statistical optimality of locally monotonic regression,” IEEE Transactions on Signal Processing, vol. ASSP-42, no. 6, pp. 1548-1550, June 1994.
S.T. Acton and A.C. Bovik, “Nonlinear image estimation using piecewise and local image models,” IEEE Transactions on Image Processing, vol 7, no. 7, pp. 979-991, July 1998.