On The Continuous Steering of the Scale of Tight Wavelet Frames

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation of steering steerable wavelets. The fundamental aspects of the construction are the same: an admissible collection of Fourier multipliers is used to extend a tight wavelet frame, and the "scale" of the wavelets is adapted by scaling the multipliers. As an application, the proposed wavelets can be used to improve the frequency localization. Importantly, the localized frequency bands specified by this construction can be scaled efficiently using matrix multiplication

Blind Curvelet based Denoising of Seismic Surveys in Coherent and Incoherent Noise Environments

The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a combination of the curvelet transform and a whitening filter along with procedure for noise variance estimation. The whitening filter is added to get the best performance of the curvelet transform under coherent and incoherent correlated noise cases, and furthermore, it simplifies the noise estimation method and makes it easy to use the standard threshold methodology without digging into the curvelet domain. The proposed method is tested on pseudo-synthetic data by adding noise to real noise-less data set of the Netherlands offshore F3 block and on the field data set from east Texas, USA, containing ground roll noise. Our experimental results show that the proposed algorithm can achieve the best results under all types of noises (incoherent or uncorrelated or random, and coherent noise)

Dual channel rank-based intensity weighting for quantitative co-localization of microscopy images

BACKGROUND: Accurate quantitative co-localization is a key parameter in the context of understanding the spatial co-ordination of molecules and therefore their function in cells. Existing co-localization algorithms consider either the presence of co-occurring pixels or correlations of intensity in regions of interest. Depending on the image source, and the algorithm selected, the co-localization coefficients determined can be highly variable, and often inaccurate. Furthermore, this choice of whether co-occurrence or correlation is the best approach for quantifying co-localization remains controversial. RESULTS: We have developed a novel algorithm to quantify co-localization that improves on and addresses the major shortcomings of existing co-localization measures. This algorithm uses a non-parametric ranking of pixel intensities in each channel, and the difference in ranks of co-localizing pixel positions in the two channels is used to weight the coefficient. This weighting is applied to co-occurring pixels thereby efficiently combining both co-occurrence and correlation. Tests with synthetic data sets show that the algorithm is sensitive to both co-occurrence and correlation at varying levels of intensity. Analysis of biological data sets demonstrate that this new algorithm offers high sensitivity, and that it is capable of detecting subtle changes in co-localization, exemplified by studies on a well characterized cargo protein that moves through the secretory pathway of cells. CONCLUSIONS: This algorithm provides a novel way to efficiently combine co-occurrence and correlation components in biological images, thereby generating an accurate measure of co-localization. This approach of rank weighting of intensities also eliminates the need for manual thresholding of the image, which is often a cause of error in co-localization quantification. We envisage that this tool will facilitate the quantitative analysis of a wide range of biological data sets, including high resolution confocal images, live cell time-lapse recordings, and high-throughput screening data sets

Properties of Umbral Dots from Stray Light Corrected Hinode Filtergrams

High resolution blue continuum filtergrams from Hinode are employed to study the umbral fine structure of a regular unipolar sunspot. The removal of scattered light from the images increases the rms contrast by a factor of 1.45 on average. Improvement in image contrast renders identification of short filamentary structures resembling penumbrae that are well separated from the umbra-penumbra boundary and comprise bright filaments/grains flanking dark filaments. Such fine structures were recently detected from ground based telescopes and have now been observed with Hinode. A multi-level tracking algorithm was used to identify umbral dots in both the uncorrected and corrected images and to track them in time. The distribution of the values describing the photometric and geometric properties of umbral dots are more easily affected by the presence of stray light while it is less severe in the case of kinematic properties. Statistically, umbral dots exhibit a peak intensity, effective diameter, lifetime, horizontal speed and a trajectory length of 0.29 I_QS, 272 km, 8.4 min, 0.45 km/s and 221 km respectively. The 2 hr 20 min time sequence depicts several locations where umbral dots tend to appear and disappear repeatedly with various time intervals. The correction for scattered light in the Hinode filtergrams facilitates photometry of umbral fine structure which can be related to results obtained from larger telescopes and numerical simulations.Comment: Accepted for publication in ApJ : 10 pages, 10 figures, 3 table

A hybrid approach to segmentation of medical images

The paper presents information theory based image segmentation algorithms. Both advantages and problems related to them are discussed. Then a segmentation framework based on combination of information theory and fuzzy logic is proposed