Home > Research > Nonparametric Kernel Regression

Classical parametric signal processing methods rely on a specific model of the signal of interest and seek to compute the parameters of this model in the presence of noise. A generative model based upon the estimated parameters is then produced as the best estimate of the underlying signal.

In contrast to the parametric methods, nonparametric methods rely on the data itself to dictate the structure of the model, in which case this implicit model is referred to as a regression function. We have developed a framework where problems such as image fusion, denoising, and deblurring can be solved in a unified setting using data-adaptive kernel regression methods.

Related Journal Publications

1. H. Takeda, S. Farsiu, P. Milanfar, “Deblurring Using Regularized Locally-Adaptive Kernel Regression”, accepted for publication in IEEE Transactions on Image Processing, Jan 2008
   See also: Regularized Kernel Regression-based Deblurring Toolbox for MATLAB
2. H. Takeda, S. Farsiu, and P. Milanfar, “Kernel Regression for Image Processing and Reconstruction”, IEEE Trans. on Image Processing, vol. 16, no. 2, pp. 349-366, February 2007.
   See also: Kernel Regression-Based Image Processing ToolBox for MATLAB and Kernel Regression for Image Processing and Reconstruction—example results

Related Conference Publications and Presentations

1. P. Chatterjee, and P. Milanfar, “A Generalization of Non-Local Means via Kernel Regression ”, Proc. of the SPIE Conf. on Computational Imaging, San Jose, January 2008.
2. H. Takeda, S. Farsiu, and P. Milanfar, “Higher Order Bilateral Filters and Their Properties”, Proc. of the SPIE Conf. on Computational Imaging, San Jose, January 2007.
3. H. Takeda, S. Farsiu, and P. Milanfar, “Regularized Kernel Regression for Image Deblurring”, Proceedings of the 40th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 2006.
4. H. Takeda, S. Farsiu, P. Milanfar, “Robust Kernel Regression for Restoration and Reconstruction of Images from Sparse, Noisy Data”, to appear in Proc. of the International Conference on Image Processing, Atlanta, GA, October 2006.
5. H. Takeda, S. Farsiu, J. Christou, P. Milanfar, “Super-Drizzle: Applications of Adaptive Kernel Regression in Astronomical Imaging”, Advanced Maui Optical and Space Surveillance (AMOS) Technologies Conference, September 2006.
6. H. Takeda, S. Farsiu, and P. Milanfar, “Image Denoising by Adaptive Kernel Regression”, Proceedings of the 39th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, November 2005.