Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of the class score function with respect to the input image. This gradient can be interpreted as a sensitivity map, and there are several techniques that elabo...

The problem of extracting a “signal” xn generated by a dynamical system from a times series yn = xn + en, where en is an observational error, is considered. It is shown that consistent signal extraction is impossible when the errors are distributed according to a density with unbounded support and the underlying dynamical system admits homoclinic pairs. It is also shown that consistent signal e...

Removing salt and pepper noise is an active research area in image processing. In this paper, a two-phase method is proposed for removing salt and pepper noise while preserving edges and fine details. In the first phase, noise candidate pixels are detected which are likely to be contaminated by noise. In the second phase, only noise candidate pixels are restored using adaptive median filter. In...

A method is proposed for suppressing Gaussian noise by extracting local singularities. The method is based on truncating Riemann series decomposition, whose components naturally characterize different orders of Hölder regularity. The approach yields a single-step filtering technique whose performance is comparable to three-step wavelet decomposition and thresholding techniques.

Reconciliation is the commonly used method for inferring the evolutionary scenario for a gene family. It consists in “embedding” an inferred gene tree into a known species tree, revealing the evolution of the gene family by duplications and losses. The main complaint about reconciliation is that the inferred evolutionary scenario is strongly dependant on the considered gene tree, as few misplac...

In this paper, a novel decision based median (DBM) filter for enhancing MR images has been proposed. The method is based on eliminating impulse noise from MR images. A median-based method to remove impulse noise from digital MR images has been developed. Each pixel is leveled from black to white like gray-level. The method is adjusted in order to decide whether the median operation can be appli...

Abstract Noise attenuation is a major seismic data processing concern. In seismic data, noise can appear as random, coherent and/or impulsive. Recently, many different techniques, ranging from relatively simple processes to extremely complex ones, have been used for noise attenuation. Image filtering techniques are relatively new methods in seismic exploration. We introduced the anisotropic non...