Weight Median Filter Using Neural Network for Reducing Impulse Noise

Noise is undesired information that affects an image. Noise appears in images from various sources. Noise reduction and noise removal is an important task in images processing. The weight median filters are extension of the median filter; it belongs to the broad class of nonlinear filters. Weight median filter is more effective form of image processing, it is the removing ability of impulsive noise. Impulsive noise is a kind of image corruption where each pixel value is replaced with an extremely large or small value that is not related to the surrounding pixel values by a probability. iv The design of weight coefficients of the weight median filter is considered as a difficult problem. The weight coefficients of the weight median filter learnt by the backpropagation with supervised multi-layer perceptron feed-forward networks and threshold decomposition has been presented in this thesis, which has been implemented using Turbo C++ language. Good results have been achieved by using program package. Results show that weight median filter based on threshold decomposition removes impulsive noise with an excellent image detail-preserving capability compared to nonlinear filter and linear filter. Restored images evaluation by using mean square error and speed. The package has been implemented using the MATLAB language. This study provides three types of filtering windows size, 3×3, 5×5 and 7×7 window size. The result shows that the mean square error of weight median filter based on threshold decomposition using 3×3 filtering window is less than 5×5, and 7×7 filtering window and the speed of weight median filter based on threshold decomposition using 3×3 is faster than 5×5, and 7×7 filtering window

Medical image enhancement using threshold decomposition driven adaptive morphological filter

One of the most common degradations in medical images is their poor contrast quality. This suggests the use of contrast enhancement methods as an attempt to modify the intensity distribution of the image. In this paper, a new edge detected morphological filter is proposed to sharpen digital medical images. This is done by detecting the positions of the edges and then applying a class of morphological filtering. Motivated by the success of threshold decomposition, gradientbased operators are used to detect the locations of the edges. A morphological filter is used to sharpen these detected edges. Experimental results demonstrate that the detected edge deblurring filter improved the visibility and perceptibility of various embedded structures in digital medical images. Moreover, the performance of the proposed filter is superior to that of other sharpener-type filters

Conditional vorticity budget of coherent and incoherent flow contributions in fully developed homogeneous isotropic turbulence

We investigate the conditional vorticity budget of fully developed three-dimensional homogeneous isotropic turbulence with respect to coherent and incoherent flow contributions. The Coherent Vorticity Extraction based on orthogonal wavelets allows to decompose the vorticity field into coherent and incoherent contributions, of which the latter are noise-like. The impact of the vortex structures observed in fully developed turbulence on statistical balance equations is quantified considering the conditional vorticity budget. The connection between the basic structures present in the flow and their statistical implications is thereby assessed. The results are compared to those obtained for large- and small-scale contributions using a Fourier decomposition, which reveals pronounced differences

Hierarchical stack filtering : a bitplane-based algorithm for massively parallel processors

With the development of novel parallel architectures for image processing, the implementation of well-known image operators needs to be reformulated to take advantage of the so-called massive parallelism. In this work, we propose a general algorithm that implements a large class of nonlinear filters, called stack filters, with a 2D-array processor. The proposed method consists of decomposing an image into bitplanes with the bitwise decomposition, and then process every bitplane hierarchically. The filtered image is reconstructed by simply stacking the filtered bitplanes according to their order of significance. Owing to its hierarchical structure, our algorithm allows us to trade-off between image quality and processing time, and to significantly reduce the computation time of low-entropy images. Also, experimental tests show that the processing time of our method is substantially lower than that of classical methods when using large structuring elements. All these features are of interest to a variety of real-time applications based on morphological operations such as video segmentation and video enhancement

Spectral Representations of One-Homogeneous Functionals

This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or $\ell^1$-norms. Those functionals serve as a substitute for a Hilbert space structure (and the related norm) in classical linear spectral transforms, e.g. Fourier and wavelet analysis. We discuss three meaningful definitions of spectral representations by scale space and variational methods and prove that (nonlinear) eigenfunctions of the regularization functionals are indeed atoms in the spectral representation. Moreover, we verify further useful properties related to orthogonality of the decomposition and the Parseval identity. The spectral transform is motivated by total variation and further developed to higher order variants. Moreover, we show that the approach can recover Fourier analysis as a special case using an appropriate $\ell^1$-type functional and discuss a coupled sparsity example

Probabilistic description of extreme events in intermittently unstable systems excited by correlated stochastic processes

In this work, we consider systems that are subjected to intermittent instabilities due to external stochastic excitation. These intermittent instabilities, though rare, have a large impact on the probabilistic response of the system and give rise to heavy-tailed probability distributions. By making appropriate assumptions on the form of these instabilities, which are valid for a broad range of systems, we formulate a method for the analytical approximation of the probability distribution function (pdf) of the system response (both the main probability mass and the heavy-tail structure). In particular, this method relies on conditioning the probability density of the response on the occurrence of an instability and the separate analysis of the two states of the system, the unstable and stable state. In the stable regime we employ steady state assumptions, which lead to the derivation of the conditional response pdf using standard methods for random dynamical systems. The unstable regime is inherently transient and in order to analyze this regime we characterize the statistics under the assumption of an exponential growth phase and a subsequent decay phase until the system is brought back to the stable attractor. The method we present allows us to capture the statistics associated with the dynamics that give rise to heavy-tails in the system response and the analytical approximations compare favorably with direct Monte Carlo simulations, which we illustrate for two prototype intermittent systems: an intermittently unstable mechanical oscillator excited by correlated multiplicative noise and a complex mode in a turbulent signal with fixed frequency, where multiplicative stochastic damping and additive noise model interactions between various modes.Comment: 29 pages, 15 figure