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Several nonlinear multivariate image filtering methods based on order statistics theory are introduced. The techniques, which apply to noise-corrupted color images, were developed through the combination of several reduced ordering schemes with respect to noise attenuation, edge preservation and detail retention. They include an adaptive filter and an adaptive hybrid multivariate filter composed of the mean, marginal and identity filters.

An equation for the output moments of a weighted median filtered data is derived on the basis of solving a group of linear inequalities. The new equation provides an L-vector and M vector parameters, which enable the assessment of the noise reduction capability of a weighted median filter. The equation also facilitates the development of an optimality theory for weighted median filters.

Use of Fibonacci p-codes enables the development of an VLSI architecture and a parallel decomposition algorithm to determine the output of a nonlinear digital stack filter. A running stack filtering VLSI architecture and algorithm are derived for a subclass of positive Boolean functions.

In this paper, the complex matched median filter (MMF) is developed for QAM signal detection. It is shown that the MMF is robust against impulsive type noise. By combining the MMF and the linear matched filter (LMF), an extended class of matched filters is introduced. These filters combine the desirable properties of MMF and LMF and behave well in varying noise environments. Computer simulations demonstrate that the proposed detectors give a much smaller symbol error probability than the LMF when the noise has an impulsive component and produces only a slight performance degradation in the case of pure Gaussian noise.

The simple relationship between rank selection probabilities and quantities A(i) are derived using various types of output selection. The derivation yields a new fast method for the calculation of rank selection probabilities. Hence the concept of rank selection probabilities is applicable to stack filters. The output distributions for stack filters are determined easily if the probabilities are known.

In this paper, a multichannel edge enhancing filter (MEEF) based on the vector median is introduced for enhancing degraded edges in color images. An input multichannel signal is filtered with three subfilters, and the final output is determined by comparing the outputs of the subfilters and their vector median. Root signal and edge enhancement properties of the MEEF are examined in detail. In addition, we discuss line preservation and edge jitter resistance of the MEEF in noisy conditions. Finally, the MEEF is tested with: i) blurred edges caused by unfocusing or fast movement of camera, ii) serrated edges caused by interlaced scan, iii) false color edges caused by channel dispersion. The results show that the MEEF outperforms channelwise edge enhancing filtering in enhancing these degraded edges.

Novel multistage weighted-order statistic (MWOS) median filters are used to determine optimal nature under mean absolute error and MSE criteria. The MWOS filters help save computation time and memory due to their compact representation of stall filters. The filter design is based on the backpropagation algorithm.

A new type of nonlinear filters is presented. Neural filters unify linear and nonlinear filters such as finite impulse response, microstatic and stack filters. Neural filters use neural networks and the threshold decomposition architecture. Adaptive least mean absolute and least mean square error algotrithms are developed to derive optimal neural filters. Results show that adaptive neural filters are capable of eliminating noise such as Gaussian and impulsive noise.

Threshold decomposition and Bayes statistical decision theory are employed to develop nonadaptive and adaptive constrained least mean absolute algorithms for optimal stack filter estimation. Applicable in both real and binary domains, the algorithms are experimentally used in image processing problems and were shown to perform better than their optimal counterparts under the mean absolute error criterion.

A class of median type filters, called matched median filters, are defined for the estimation of the information which is carried by the amplitude of a noisy signal. These filters form the natural counterpart of linear matched filters in the class of median type filters and are maximum likelihood estimators if the noise is biexponential. Matched median filters are defined both for baseband and passband systems. Their statistical properties are analyzed and simulation results presented.

Abstract This article addresses under which conditions filtering can visibly improve the image quality. The key points are the following. First, we analyze filtering efficiency for 25 test images, from the color image database TID2008. This database allows assessing filter efficiency for images corrupted by different noise types for several levels of noise variance. Second, the limit of filtering efficiency is determined for independent and identically distributed (i.i.d.) additive noise and compared to the output mean square error of state-of-the-art filters. Third, component-wise and vector denoising is studied, where the latter approach is demonstrated to be more efficient. Fourth, using of modern visual quality metrics, we determine that for which levels of i.i.d. and spatially correlated noise the noise in original images or residual noise and distortions because of filtering in output images are practically invisible. We also demonstrate that it is possible to roughly estimate whether or not the visual quality can clearly be improved by filtering.

A class of parametric transforms that are based on unified representation of transform matrices in the form of sparse matrix products is described. Different families of transforms are defined within the introduced class. All transforms of one family can be computed with fast algorithms similar in structure to each other. In particular, the family of Haar-like transforms consists of discrete orthogonal transforms of arbitrary order such that they all may be computed with a fast algorithm that is in structure similar to classical fast Haar transform. A method for parameter selection is proposed that allows synthesizing specific transforms with matrices containing predefined row(s). The potential of the proposed class of Haar-like parametric transforms to improve the performance of fixed block transforms in image compression is investigated. With this purpose, two image compression schemes are proposed where a number of Haar-like transforms are synthesized each adapted to a certain set of blocks within an image.The nature of the proposed schemes is such that their performance (in terms of PSNR versus compression ratio) cannot be worse than a scheme based on classical discrete cosine transform (DCT). Simulations show that a significant performance improvement can be achieved for certain types of images such as medical X-ray images and compound images.

Abstract Background Microarray data normalization is an important step for obtaining data that are reliable and usable for subsequent analysis. One of the most commonly utilized normalization techniques is the locally weighted scatterplot smoothing (LOWESS) algorithm. However, a much overlooked concern with the LOWESS normalization strategy deals with choosing the appropriate parameters. Parameters are usually chosen arbitrarily, which may reduce the efficiency of the normalization and result in non-optimally normalized data. Thus, there is a need to explore LOWESS parameter selection in greater detail. Results and discussion In this work, we discuss how to choose parameters for the LOWESS method. Moreover, we present an optimization approach for obtaining the fraction of data points utilized in the local regression and analyze results for local print-tip normalization. The optimization procedure determines the bandwidth parameter for the local regression by minimizing a cost function that represents the mean-squared difference between the LOWESS estimates and the normalization reference level. We demonstrate the utility of the systematic parameter selection using two publicly available data sets. The first data set consists of three self versus self hybridizations, which allow for a quantitative study of the optimization method. The second data set contains a collection of DNA microarray data from a breast cancer study utilizing four breast cancer cell lines. Our results show that different parameter choices for the bandwidth window yield dramatically different calibration results in both studies. Conclusions Results derived from the self versus self experiment indicate that the proposed optimization approach is a plausible solution for estimating the LOWESS parameters, while results from the breast cancer experiment show that the optimization procedure is readily applicable to real-life microarray data normalization. In summary, the systematic approach to obtain critical parameters in the LOWESS technique is likely to produce data that optimally meets assumptions made in the data preprocessing step and thereby makes studies utilizing the LOWESS method unambiguous and easier to repeat.

The characteristics of impulse bursts in remote sensing images are analyzed and a model for this noise is proposed. The model also takes into consideration other noise types, for example, the multiplicative noise present in radar images. As a case study, soft morphological filters utilizing a training-based optimization scheme are used for the noise removal. Different approaches for the training are discussed. It is shown that these techniques can provide an effective removal of impulse bursts. At the same time, other noise types in images, for example, the multiplicative noise, can be suppressed without compromising good edge and detail preservation. Numerical simulation results, as well as examples of real remote sensing images, are presented.

The structure and biological behavior of a cell are determined by the pattern of gene expressions within that cell. The so-called gene prediction problem refers to finding rules, or sets of possible rules, on how certain genes expressions determine the expression level of a given target gene. In this paper, we investigate the gene prediction problem and propose the use of new predictors, selected according to the minimum description length (MDL) principle. We compare the use of Boolean predictors, ternary predictors and perceptron predictors. We resort to MDL as a tool for selecting the proper size of the prediction window. MDL is also well suited for comparing predictors having different complexities. We show that the best description can be achieved by the Boolean and ternary predictors, since they obtain better fitting of the data with a lower complexity of the model. To illustrate the comparison, both synthetic and experimental data are used.

The complexity of the consistency problem for several important classes of Boolean functions is analyzed. The classes of functions under investigation are those which are closed under function composition or superposition. Several of these so-called Post classes are considered within the context of machine learning with an application to breast cancer diagnosis. The considered Post classes furnish a user-selectable measure of reliability. It is shown that for realistic situations which may arise in practice, the consistency problem for these classes of functions is polynomial-time solvable. Index Terms--Computational complexity, computational learning theory, consistency problem, monotone Boolean function, Post class.

In this paper, we propose two scalable architectures (say, [Arc.sub.J] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]) that perform the discrete wavelet transform (DWT) of an [N.sub.o]-sample sequence in only [N.sub.o]/2 Clock cycles. Therefore, they are at least twice as fast as the other known architectures. Also, they have an [AT.sup.2] parameter that is approximately 1/2 that of already existing devices. This result has been achieved by means of a carefully balanced pipelining, and it has two 'faces.' First, [Arc.sub.J] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can be employed for performing two times faster processing than allowed by other architectures working at the same clock frequency (high-speed utilization). Second, they can be employed even using a two times lower clock frequency but reaching the same performance as other architectures. This second possibility allows for reducing the supply voltage and the power dissipation, respectively, by a factor of two and four with respect to other architectures (low-power utilization). As a final result, we show that a parallel architecture implementing an L-tap filter-based DWT with J decomposition levels [say, [Arc.sub.OPT] (J, L)] can be defined, aiming at having an excellent efficiency (say, eff[[Arc.sub.OPT] (J, L)]) for any value of J and L. For instance, the average value of eff[[Arc.sub.OPT] (J, L)] [computed in very wide set [Sigma]' of 'points' (J, L)] is 99.1%. The minimum value of eff[[Arc.sub.OPT](J, L)] in [Sigma]' is 93.8%, and, except for five 'points,' in all the others, eff[[Arc.sub.OPT] (J, L)] is not lower than 96.9%.

In many applications in communication, data retrieval and processing, digital system design, and related areas, incompletely specified switching (Boolean or multiple-valued) functions are encountered. A particular class of highly incompletely specified functions are the so-called index generation functions, which being defined on a small fraction of input combinations, often do not require all the variables to be represented. Reducing the variables of index generation functions is an important task, since they are used mainly in real-time applications and compactness of their representations influences performances of related systems. One approach towards reducing the number of variables in index generation functions are linear transformations meaning that initial variables are replaced by their linear combinations. A drawback is that finding an optimal transformation can be difficult. Therefore, in this paper, we first formulate the problem of finding a good linear transformation by using linear subspaces. This formulation serves as a basis to propose non-linear (polynomial) transformations to reduce the number of variables in index generation functions. [ABSTRACT FROM AUTHOR]

In this paper, we consider incompletely defined discrete functions, i.e., Boolean and multiple-valued functions, f : S → {0, 1, …, q - 1} where S ⊆ {0, 1, …, q - 1}n i.e., the function value is specified only on a certain subset S of the domain of the corresponding completely defined function. We assume the function to be sparse i.e. [ABSTRACT FROM AUTHOR]