Mathematical and computational modeling of genetic regulatory networks promises to uncover the fundamental principles governing biological systems in an integrarive and holistic manner. It also paves the way toward the development of systematic approaches for effective therapeutic intervention in disease. The central theme in this paper is the Boolean formalism as a building block for modeling complex, large-scale, and dynamical networks of genetic interactions. We discuss the goals of modeling genetic networks as well as the data requirements. The Boolean formalism is justified from several points of view. We then introduce Boolean networks and discuss their relationships to nonlinear digital filters. The role of Boolean networks in understanding cell differentiation and cellular functional states is discussed. The inference of Boolean networks from real gene expression data is considered from the viewpoints of computational learning theory and nonlinear signal processing, touching on computational complexity of learning and robustness. Then, a discussion of the need to handle uncertainty in a probabilistic framework is presented, leading to an introduction of probabilistic Boolean networks and their relationships to Markov chains. Methods for quantifying the influence of genes on other genes are presented. The general question of the potential effect of individual genes on the global dynamical network behavior is considered using stochastic perturbation analysis. This discussion then leads into the problem of target identification for therapeutic intervention via the development of several computational tools based on first-passage times in Markov chains. Examples from biology are presented throughout the paper. 1

Nonlinear filtering techniques based on the theory of robust estimation are introduced. Some deterministic and asymptotic properties are derived. The proposed denoising methods are optimal over the Huber-contaminated normal neighborhood and are highly resistant to outliers. Experimental results showing a much improved performance of the proposed filters in the presence of Gaussian and heavy-tailed noise are analyzed and illustrated.

Removing noise from the original signal is still a challenging problem for researchers. There have been several published algorithms and each approach has its assumptions, advantages, and limitations. This paper presents a review of some significant work in the area of image denoising. After a brief introduction, some popular approaches are classified into different groups and an overview of various algorithms and analysis is provided. Insights and potential future trends in the area of denoising are also discussed.

In this paper, a class of Weighted Vector Directional Filters (WVDFs) based on the selection of the output sample from the multichannel input set is analyzed and optimized. The WVDF output minimizes the sum of weighted angular distances to other input samples from the filtering window. Dependent on the weighting coefficients, the class of the WVDFs can be designed to perform a number of smoothing operations with different properties, which can be applied for specific filtering scenarios. In order to adapt the weighting coefficients to varying noise and image statistics, we introduce a methodology, which achieves an optimal trade-off between smoothing and detail preserving characteristics. The proposed angular optimization algorithms take advantage of adaptive stack filters design and weighted median filtering framework. The optimized WVDFs are able to remove image noise, while maintaining excellent signal-detail preservation capabilities and sufficient robustness for a variety of signal and noise statistics.

Earlier research has shown that the problem of optimal weighted median filtering with structural constraints can be formulated as a nonconvex nonlinear programming problem in general. However, its high computational complexity and poor performance due to its nonconvex nature prohibit it from practical applications. In this paper, we shall show that the design problem can be formulated as a convex quadratic programming problem. The new algorithm is very efficient in the sense of computational complexity. The algorithm is also efficient in the sense of its capability to approach the global minimum. Using the algorithm optimal 1-D weighted median filters preserving pulses of length 3, 4 and 5 are tabulated.

An image is often corrupted by noise in its acquisition and transmission. Image denoising is used to remove the additive noise while retaining as much as possible the important image features. The motivation is that as wavelet transform is good at energy compaction, the small coefficients are more likely due to noise and large coefficient due to important signal features [6]. The proposed technique is based upon the analysis of wavelet transform which uses a soft thresholding method for thresholding the small coefficients without affecting the significant features of the image. In the proposed work, image denoising is studied using various wavelets for different images with two different noises at various levels of decomposition and comparison is done between the e three methods of wavelet shrinkage techniques.

Noise present in the image hides necessary details. It compromises with level of quality of image. So, we need to remove the noise from images. Noise removal is one of the pre-processing tasks in several image processing techniques. Many researchers work on different types of filters used to remove different types of noises from images. There are some traditional filters, some filters derived from traditional filters and some filters are new innovations. In this paper, we make a survey on various denoising filters and conclude which works better among all.