Some recent methods, like the Empirical Mode De-composition (EMD), propose to decompose a signal accordingly to its contained information. Even though its adaptability seems useful for many applications, the main issue with this approach is its lack of theory. This paper presents a new approach to build adaptive wavelets. The main idea is to extract the different modes of a signal by designing an appropriate wavelet filter bank. This construction leads us to a new wavelet transform, called the empirical wavelet transform. Many experiments are presented showing the usefulness of this method compared to the classic EMD.

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In this paper, we present an algorithm to automatically detect meaningful modes in a histogram. The proposed method is based on the behavior of local minima in a scale-space representation. We show that the detection of such meaningful modes is equivalent in a two classes clustering problem on the length of minima scale-space curves. The algorithm is easy to implement, fast and does not require any parameter. We present several results on histogram and spectrum segmentation, grayscale image segmentation and color image reduction.

Carboranethiol molecules self-assemble into upright molecular monolayers on Au{111} with aligned dipoles in two dimensions. The positions and offsets of each molecule's geometric apex and local dipole moment are measured and correlated with sub-Ångström precision. Juxtaposing simultaneously acquired images, we observe monodirectional offsets between the molecular apexes and dipole extrema. We determine dipole orientations using efficient new image analysis techniques and find aligned dipoles to be highly defect tolerant, crossing molecular domain boundaries and substrate step edges. The alignment observed, consistent with Monte Carlo simulations, forms through favorable intermolecular dipoleÀdipole interactions.

The non-uniformity is a time-dependent noise caused by the lack of sensor equalization. We present here the detailed algorithm and online demo of the non-uniformity correction method by midway infrared equalization. This method was designed to suit infrared images. Nevertheless, it can be applied to images produced for example by scanners, or by push-broom satellites. This single image method works on static images, is fully automatic, has no user parameter, and requires no registration. It needs no camera motion compensation, no closed aperture sensor equalization and is able to correct for a fully non-linear non-uniformity. Source Code The source code, version 2.0, is available from the article web page 1. The documentation is included in the archive. Basic compilation and usage instructions are included in the README.txt file. The source code for the contrast adjustment preprocessing is available from the same location with its own documentation (see [10]). The demo permits to try the proposed method on several well chosen test images, and on any uploaded image. To improve visibility (without changing the algorithm) the input image can be preprocessed using the "Simplest Color Balance" algorithm [10]. The s1 parameter is the percentage of pixels saturated to black and s2 the percentage saturated to white. If both s1 = s2 = 0 the image is simply stretched to [0, 255] by an affine contrast change (causing no loss of information) before applying the denoising algorithm. The output image is re-stretched to [0, 255] by an affine contrast change. The outputs are 1) the processed image and 2) the optimal scale parameter s found by the algorithm.

We map buried hydrogen-bonding networks within self-assembled monolayers of 3-mercapto-N-nonylpropionamide on Au{111}. The contributing interactions include the buried S-Au bonds at the substrate surface and the buried plane of linear networks of hydrogen bonds. Both are simultaneously mapped with submolecular resolution, in addition to the exposed interface, to determine the orientations of molecular segments and directional bonding. Two-dimensional mode-decomposition techniques are used to elucidate the directionality of these networks. We find that amide-based hydrogen bonds cross molecular domain boundaries and areas of local disorder.

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β-Amyloid aggregates in the brain play critical roles in Alzheimer's disease, a chronic neurodegenerative condition. Amyloid-associated metal ions, particularly zinc and copper ions, have been implicated in disease pathogenesis. Despite the importance of such ions, the binding sites on the β-amyloid peptide remain poorly understood. In this study, we use scanning tunneling microscopy, circular dichroism, and surface-enhanced Raman spectroscopy to probe the interactions between Cu ions and a key β-amyloid peptide fragment, consisting of the first 16 amino acids, and define the copper-peptide binding site. We observe that in the presence of Cu, this peptide fragment forms β-sheets, not seen without the metal ion. By imaging with scanning tunneling microscopy, we are able to identify the binding site, which involves two histidine residues, His13 and His14. We conclude that the binding of copper to these residues creates an interstrand histidine brace, which enables the formation of β-sheets.