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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.

Data denoising can be achieved by approximating the data distribution and replacing each data item with an estimate of its closest mode. This idea has already been successfully applied to image denoising. The data then consists of pixel intensities or image patches, that is, vectorized groups of pixel intensities. The latter case raises the issue of mode estimation in a high-dimensional space, since patches can contain about 10 to more than 100 pixels. This paper shows that the widely used Gaussian kernel is outperformed by flat-top kernels that are specifically tailored in order to fight the curse of dimensionality.

In the field of medical image analysis, denoising is one of the most important preprocessing steps before medical analysis. The design of an efficient, robust, and computationally effective edge-preserving denoising algorithm is a widely studied, and yet unsolved problem. One of the most efficient edge-preserving denoising algorithms is the bilateral filter, which is an intuitive generalization of the local M-smoother. In this paper, we propose to modify both the bilateral filter and the local M-smoother to use patches of the image instead of single voxels in the denoising process. Using patches instead of single voxels in the filtering process is a way to adapt the filter to the textures, ramps, and edges of the image, and make the filter more discriminant. The filtering performances of the patch-based algorithms are evaluated on a benchmark and a CT phantom image and compared to the bilateral filter and local M-smoother., Anglais

The wavelet transform is a widely used pre-filtering step for subsequent R spike detection by thresholding of the coefficients. The time-frequency decomposition is indeed a powerful tool to analyze non-stationary signals. Still, current methods use consecutive wavelet scales in an a priori restricted range and may therefore lack adaptativity. This paper introduces a supervised learning algorithm which learns the optimal scales for each dataset using the annotations provided by physicians on a small training set. For each record, this method allows a specific set of non consecutive scales to be selected, based on the record’s characteristics. The selected scales are then used for the decomposition of the original long-term ECG signal recording and a hard thresholding rule is applied on the derivative of the wavelet coefficients to label the R spikes. This algorithm has been tested on the MIT-BIH arrhythmia database and obtains an average sensitivity rate of 99.7% and average positive predictivity rate of 99.7%.

Denoising is a key step in the processing of medical images. It aims at improving both the interpretability and visual aspect of the images. Yet, designing a robust and efficient denoising tool remains an unsolved challenge and a specific issue concerns the noise model. Many filters typically assume that noise is additive and Gaussian, with uniform variance. In contrast, noise in medical images often has more complex properties. This paper considers images with Poissonian noise and the patch-based bilateral filters, that is, filters that involve a tonal kernel and pair wise comparisons between shifted blocks of the images. The main aim is then to integrate two variance stabilizing transformations that allow the filters to work with Gaussianized noise. The performances of these filters are compared to those of the classical bilateral filter with the same transformations. The experiments include an artificial benchmark as well as a positron emission tomography image.

In the field of image analysis, denoising is an important preprocessing task. The design of an efficient, robust, and computationally effective edge preserving denoising algorithm is a widely studied, and yet unsolved problem. One of the most efficient edge-preserving denoising algorithms is the bilateral filter, which is an intuitive generalization of the local M-smoother. In this paper, we propose to modify both the bilateral filter and the local M-smoother to use patches of the image instead of single pixels in the denoising process. With this modification, the filtering effect becomes more sensitive to the different areas of the image and the filtering results improve. The denoising quality of these patch-based filters is evaluated on test images and compared to the classical bilateral filtering and local M-smoother.

Signal denoising proves to be important in many domains such as pattern recognition and image analysis. This paper investigates several refinements of adaptive local filters that rely on local mode finding. These spatial filters are anisotropic and offer the advantage of attenuating noise without smoothing salient signal features such as discontinuities or other sharp transitions. In particular, a bootstrapped procedure is developed and leads to an improvement of the denoising quality without increasing the computational complexity. Experiments with an artificial benchmark allow the quantification of the performance gain.