Mode estimation in high-dimensional spaces with flat-top kernels: Application to image denoising

Mode estimation is extensively studied in statistics. One of the most widely used methods of mode estimation is hill-climbing on a kernel density estimator with gradient ascent or a fixed-point approach. Within this framework, Gaussian kernels proves to be a natural and intuitive option for non-parametric density estimation. This paper shows that in the case of high-dimensional data, mode estimation can be improved by using differently shaped kernels, called flat-top kernels. The improvement are illustrated with an image denoising application, in which pictures are decomposed into small patches, i.e. groups of adjacent pixels, that are vectorized. Noise in the patches can be attenuated by substituting them with the closest mode in the observed distribution of patches. The quality of the denoised picture then depends on the accuracy of mode estimation in a high-dimensional space. Experiments conducted on usual benchmarks in the image processing community show that flat-top kernels outperform the Gaussian one.