Much of the image processing and inverse problems literature is concerned with the introduction of novel algorithm. In comparison, relatively little work has concentrated on the analysis of performance bounds. We have produced some of the fundamental results regarding bounds on denoising, motion estimation, super-resolution, statistical resolution limits in optical imaging, and geometric reconstruction from shadows. One interesting question we answered was “What is the minimum detectable spacing between two point sources of light observed with a noisy imaging system at a given SNR?” The answer is a neat scaling law illustrated above.
Related Journal Publications
- P. Chatterjee and P. Milanfar, “ Is Denoising Dead?”, IEEE Trans. Image Processing vol. 19, no. 4, pp. 895-911, April 2010
- P. Chatterjee and P. Milanfar, “ Practical Bounds on Image Denoising: From Estimation to Information”, Accepted to IEEE Trans. on Image Processing
- M. Shahram, and P. Milanfar, “Statistical and Information-Theoretic Analysis of Resolution in Imaging”, IEEE Transactions on Information Theory, vol. 52, no. 8, pp. 3411-3427, August 2006.
- D. Robinson, and P. Milanfar, “Statistical Performance Analysis of Super-resolution”, IEEE Transactions on Image Processing, Vol. 15, no. 6, pp. 1413-1428, June 2006.
- M. Shahram, and P. Milanfar, “Local Detectors for High-Resolution Spectral Analysis: Algorithms and Performance”, Digital Signal Processing, vol. 15, pp. 305-316, 2005.
- M. Shahram, and P. Milanfar, “On the Resolvability of Sinusoids with Nearby Frequencies in the Presence of Noise”, IEEE Transactions on Signal Processing, vol. 53, no. 7, pp. 2579-2588, July 2005.
- D. Robinson, and P. Milanfar, “Fundamental Performance Limits in Image Registration”, IEEE Transactions on Image Processing, vol. 13, no. 9, pp. 1185-1199, September 2004.
- M. Shahram, and P. Milanfar, “Imaging Below the Diffraction Limit: A Statistical Analysis”, IEEE Transactions on Image Processing, vol. 13, no. 5, pp. 677-689, May 2004.
Related Conference Publications and Presentations
- M. Shahram, and P. Milanfar, “Improved Spectral Analysis of Nearby Tones Using Local Detectors” (Won best student paper award), Proceedings of the 2005 International Conference on Acoustic, Speech, and Signal Processing, Philadelphia, Pennsylvania, March 2005.
- D. Robinson, and P. Milanfar, “Statistical Performance Analysis of Superresolution Image Reconstruction”, Proceedings of the 38th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 2004.
- M. Shahram, P. Milanfar, “A Statistical Analysis of Achievable Resolution in Incoherent Imaging”, Proceedings of the SPIE Annual Meeting, San Diego, CA, August 2003.
- D. Robinson, P. Milanfar, “Fundamental Performance Limits in Image Registration”, Proceedings of the 2003 IEEE International Conference on Image Processing, Barcelona.
- D. Robinson, P. Milanfar, “Efficiency and Accuracy Tradeoffs in using Projections for Motion Estimation”, Proceedings of the 35th Asilomar Conference on Signals, Systems, and Computers, November 2001. (Won 3rd place in the best student paper competition)