Signal Enhancement Based on Hölder Regularity Analysis

International audienceWe present a approach for signal enhancement based on the analysis of the local Hölder regularity. The method does not make explicit assumptions on the type of noise or on the global smoothness of the original data, but rather supposes that signal enhancement is equivalent to increasing the Hölder regularity each point. Such a scheme is well adapted to the case where the signal to be recovered is itself very irregular, e.g. nowhere differentiable with rapidly varying local regularity. In particular, we show an application to SAR image denoting where this technique yields good results compared to other algorithms

Nonmonotone Barzilai-Borwein Gradient Algorithm for ℓ1\ell_1-Regularized Nonsmooth Minimization in Compressive Sensing

This paper is devoted to minimizing the sum of a smooth function and a nonsmooth $\ell_1$-regularized term. This problem as a special cases includes the $\ell_1$-regularized convex minimization problem in signal processing, compressive sensing, machine learning, data mining, etc. However, the non-differentiability of the $\ell_1$-norm causes more challenging especially in large problems encountered in many practical applications. This paper proposes, analyzes, and tests a Barzilai-Borwein gradient algorithm. At each iteration, the generated search direction enjoys descent property and can be easily derived by minimizing a local approximal quadratic model and simultaneously taking the favorable structure of the $\ell_1$-norm. Moreover, a nonmonotone line search technique is incorporated to find a suitable stepsize along this direction. The algorithm is easily performed, where the values of the objective function and the gradient of the smooth term are required at per-iteration. Under some conditions, the proposed algorithm is shown to be globally convergent. The limited experiments by using some nonconvex unconstrained problems from CUTEr library with additive $\ell_1$-regularization illustrate that the proposed algorithm performs quite well. Extensive experiments for $\ell_1$-regularized least squares problems in compressive sensing verify that our algorithm compares favorably with several state-of-the-art algorithms which are specifically designed in recent years.Comment: 20 page

Phenotype Recognition with Combined Features and Random Subspace Classifier Ensemble

<p>Abstract</p> <p>Background</p> <p>Automated, image based high-content screening is a fundamental tool for discovery in biological science. Modern robotic fluorescence microscopes are able to capture thousands of images from massively parallel experiments such as RNA interference (RNAi) or small-molecule screens. As such, efficient computational methods are required for automatic cellular phenotype identification capable of dealing with large image data sets. In this paper we investigated an efficient method for the extraction of quantitative features from images by combining second order statistics, or Haralick features, with curvelet transform. A random subspace based classifier ensemble with multiple layer perceptron (MLP) as the base classifier was then exploited for classification. Haralick features estimate image properties related to second-order statistics based on the grey level co-occurrence matrix (GLCM), which has been extensively used for various image processing applications. The curvelet transform has a more sparse representation of the image than wavelet, thus offering a description with higher time frequency resolution and high degree of directionality and anisotropy, which is particularly appropriate for many images rich with edges and curves. A combined feature description from Haralick feature and curvelet transform can further increase the accuracy of classification by taking their complementary information. We then investigate the applicability of the random subspace (RS) ensemble method for phenotype classification based on microscopy images. A base classifier is trained with a RS sampled subset of the original feature set and the ensemble assigns a class label by majority voting.</p> <p>Results</p> <p>Experimental results on the phenotype recognition from three benchmarking image sets including HeLa, CHO and RNAi show the effectiveness of the proposed approach. The combined feature is better than any individual one in the classification accuracy. The ensemble model produces better classification performance compared to the component neural networks trained. For the three images sets HeLa, CHO and RNAi, the Random Subspace Ensembles offers the classification rates 91.20%, 98.86% and 91.03% respectively, which compares sharply with the published result 84%, 93% and 82% from a multi-purpose image classifier WND-CHARM which applied wavelet transforms and other feature extraction methods. We investigated the problem of estimation of ensemble parameters and found that satisfactory performance improvement could be brought by a relative medium dimensionality of feature subsets and small ensemble size.</p> <p>Conclusions</p> <p>The characteristics of curvelet transform of being multiscale and multidirectional suit the description of microscopy images very well. It is empirically demonstrated that the curvelet-based feature is clearly preferred to wavelet-based feature for bioimage descriptions. The random subspace ensemble of MLPs is much better than a number of commonly applied multi-class classifiers in the investigated application of phenotype recognition.</p

Accelerated CMR using zonal, parallel and prior knowledge driven imaging methods

Accelerated imaging is highly relevant for many CMR applications as competing constraints with respect to spatiotemporal resolution and tolerable scan times are frequently posed. Three approaches, all involving data undersampling to increase scan efficiencies, are discussed in this review. Zonal imaging can be considered a niche but nevertheless has found application in coronary imaging and CMR flow measurements. Current work on parallel-transmit systems is expected to revive the interest in zonal imaging techniques. The second and main approach to speeding up CMR sequences has been parallel imaging. A wide range of CMR applications has benefited from parallel imaging with reduction factors of two to three routinely applied for functional assessment, perfusion, viability and coronary imaging. Large coil arrays, as are becoming increasingly available, are expected to support reduction factors greater than three to four in particular in combination with 3D imaging protocols. Despite these prospects, theoretical work has indicated fundamental limits of coil encoding at clinically available magnetic field strengths. In that respect, alternative approaches exploiting prior knowledge about the object being imaged as such or jointly with parallel imaging have attracted considerable attention. Five to eight-fold scan accelerations in cine and dynamic CMR applications have been reported and image quality has been found to be favorable relative to using parallel imaging alone

Renormalizing Experiments for Nonlinear Functionals

this paper, we discuss the extent to which this situation continues to hold for nonlinear functionals T . We exhibit several nonlinear functional

The flow structure in the wake of a fractal fence and the absence of an "inertial regime"

Recent theoretical work has highlighted the importance of multi-scale forcing of the flow for altering the nature of turbulence energy transfer and dissipation. In particular, fractal types of forcing have been studied. This is potentially of real significance in environmental fluid mechanics where multi-scale forcing is perhaps more common than the excitation of a specific mode. In this paper we report the first results studying the detail of the wake structure behind fences in a boundary layer where, for a constant porosity, we vary the average spacing of the struts and also introduce fractal fences. As expected, to first order, and in the far-wake region, in particular, the response of the fences is governed by their porosity. However, we show that there are some significant differences in the detail of the turbulent structure between the fractal and non-fractal fences and that these override differences in porosity. In the near wake, the structure of the fence dominates porosity effects and a modified wake interaction length seems to have potential for collapsing the data. With regards to the intermittency of the velocities, the fractal fences behave more similarly to homogeneous, isotropic turbulence. In addition, there is a high amount of dissipation for the fractal fences over scales that, based on the energy spectrum, should be dominated by inter-scale transfers. This latter result is consistent with numerical simulations of flow forced at multiple scales and shows that what appears to be an “inertial regime” cannot be as production and dissipation are both high