Fuzzy stack filters-their definitions, fundamental properties, and application in image processing

The signed binary number representation (SBNR) is used to reduce the number of PBF calculation stages in stack filters. The approach is based on the possibility of minimization of signed power-of-two terms in the SBNR representation of input data. A coder and a decoder for the mutual transformation of binary-weighted code and the minimal SBNR are proposed. An efficient algorithm and a processor structure for stack filtering based on the minimal SBNR are presented. The time complexity of the proposed filter is of order kT/sub PBF/, where k is the number of bits in the input signals and T/sub PBF/ is the delay in the incorporated circuit for the positive Boolean function (PBF). A stack filtering algorithm for the generalized nonadjacent form (GNAF) of signed digit number representation (SDNR) is also presented.

Selection probabilities, viz. rank and sample selection probabilities, quantify the impulse suppression, robustness, lowpass filtering ability, and detail preserving ability of stack filters. Closed-form expressions exist for computing selection probabilities from positive Boolean function describing the stack filter. We first present an analysis framework that interprets a Boolean vector to denote membership in a partition set. Using this framework a new algorithm to compute selection probabilities from positive Boolean functions is derived. Next a method to synthesize a stack filter from specified selection probabilities is presented. An underdetermined system of linear Diophantine equations is derived in the unknown elements of the C-matrix and the desired selection probabilities. This system of equations is solved to obtain the candidate solutions for the C-matrix. For each candidate C-matrix, an algorithm based on partition sets is used to derive one or more positive Boolean functions of the stack filter or show that none exists.

Weighted medians — positive Boolean functions conversion algorithms

Stack filters are a class of nonlinear filters for removing noise that is uncorrelated with signal. Their design is formulated as a high nonlinear optimization problem. An improved immune memory clonal selection algorithm (IMCSA) is suitable for designing stack filters. But as many algorithms for designing stack filters have to face that evaluation of each candidate solution is still takes the most computation complexity. By representing the positive Boolean functions (PBF) in objective function, a hybrid computation approach (software and hardware) for the calculation tasks has been proposed. Compared with available methods, the proposed method can improve the efficiencies of design stack filters and the design time is significantly reduced. The procedure of design and implementation for stack filters can be reached at the same time by the method

Rank order filters are nonlinear filters which choose an output based on the rank within a window of sample inputs determined by sorting the inputs. Rank order filters are a subset of the class of stack filters which are also nonlinear. A systematic method for applying block processing, which transforms single-input single-output structures to parallel-input parallel-output structures for non-recursive rank order and stack filters is presented. This method takes advantage of shared substructures within the block structure to efficiently generate a block filter whose complexity can be up to one-half the size of the original filter structure times the block size. This method can also be applied to two-dimensional non-recursive rank order filters.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents a new supervised classification technique for hyperspectral imagery, which consists of two algorithms, referred to as greedy modular eigenspace (GME) and positive Boolean function (PBF). The GME method is designed to extract features by a simple and efficient GME feature module. The GME makes use of the data correlation matrix to reorder spectral bands from which a group of feature eigenspaces can be generated to reduce dimensionality. It can be implemented as a feature extractor to generate a particular feature eigenspace for each of the material classes present in hyperspectral data. The residual reconstruction errors (RRE) are then calculated by projecting the samples into different individual GME-generated modular eigenspaces. The PBF is further developed for classification. It is a stack filter built by using the binary RRE as classifier parameters for supervised training. It implements the minimum classification error (MCE) as a criterion so as to improve classification performance. It utilizes the positive and negative sample learning ability of the MCE criteria to improve classification accuracy. The performance of the proposed method is evaluated by MODIS/ASTER airborne simulator (MASTER) images for land cover classification during the Pacrim II campaign. Experimental results demonstrate that the GME feature extractor suits the nonlinear PBF-based multi-class classifier well for classification preprocessing. The proposed approach is not only an effective method for land cover classification in earth remote sensing but also dramatically improves the eigen-decomposition computational complexity compared to the conventional principal components analysis (PCA).

The nonlinear digital filtering methods which are based on threshold decomposition and positive Boolean functions are becoming widely used. They are in use especially in image processing and biomedical signal processing, both of which usually involve large amounts of data. It is thus important to develop fast algorithms to realize weighted median weighted order statistics and more general stack filtering operations. The amounts of data are so large that fast algorithms are needed no matter how powerful the computers are that are available. In the following paper we introduce new algorithms for some of these problems and discuss the use of logical matrix algorithms for the solution of nonlinear digital filtering problems.

Cerebellar model articulation controller (CMAC) is a useful neural network learning technique. It was developed two decades ago but yet lacks an adequate learning algorithm, especially when it is used in a hybrid- type controller. This work is intended to introduce a simulation study for examining the performance of a hybrid-type control system based on the conventional learning algorithm of CMAC neural network. This study showed that the control system is unstable. Then a new adaptive learning algorithm of a CMAC based hybrid- type controller is proposed. The main features of the proposed learning algorithm, as well as the effects of the newly introduced parameters of this algorithm have been studied extensively via simulation case studies. The simulation results showed that the proposed learning algorithm is a robust in stabilizing the control system. Also, this proposed learning algorithm preserved all the known advantages of the CMAC neural network. Part II of this work is dedicated to validate the effectiveness of the proposed CMAC learning algorithm experimentally.

In this paper, an optimal multilevel stack filtering algorithm (the stack filters used at each level are designed to be optimal) is introduced. Optimal multilevel stack filter is capable of considering a larger window mask than an optimal stack filter. Multilevel unidirectional stack filters and multilevel bidirectional stack filters are studied in particular. Design of an optimal multilevel stack filter is similar to the design of an optimal stack filter where the compare-and- select algorithm can be used. However, the design procedure needs to be adapted to operation on more than one level. Several design examples are presented showing the good performance of the proposed method.

We present a simple efficient local unsupervised learning algorithm for online adaptive multichannel blind deconvolution and separation of i.i.d. sources. Under mild conditions, there exits a stable inverse system so that the source signals can be exactly recovered from their convolutive mixtures. Based on the existence of the inverse filter, we construct a two-stage neural network which consists of blind equalization and source separation. In the blind equalization stage, we employ anti-Hebbian learning in the temporal domain for decorrelation. For blind separation, we can apply any existing algorithms. Extensive computer simulations confirm the validity and high performance of our proposed learning algorithm.

In this paper multistage weighted order statistic (MWOS) filters are introduced. With the aid of threshold decomposition, it is shown that any MWOS filter in real domain corresponds to a multistage threshold logic gate, or a multilayer perceptron in binary domain, which can be viewed as another representation of a stack filter. The MWOS filter requires much fewer parameters to represent a stack filter than the truth table of the positive Boolean function. An adaptive filtering algorithm, named as constrained backpropagation (CBP) algorithm, is developed for finding the optimal MWOS filters under the mean absolute error (MAE) criterion. The CBP algorithm is the same as the backpropagation algorithm used in multilayer perceptrons except the positivity of the parameters of MWOS filters, equal to the stacking property of stack filters, is imposed. Simulation results on image restoration are provided to compare the performance of the adaptive MWOS filters and the adaptive stack filters.

The proposed systolic design for 2-D rank order filtering has a wide variety of applications in image processing. It derives its architecture mainly from a systolic design for 1-D rank order filtering proposed previously. The adopted systolic design, called the sample oriented rank order filter design, takes advantage of the evaluated rank values in the current window for the evaluation of the rank values in the next window without explicitly sorting the data in the window. This makes it possible to convert a 2-D windowed data sequence into a 1-D windowed data sequence with multiple data sample exchange at each window movement, and the 1-D systolic design is thus applicable. By cascading many such 1-D systolic arrays into a 2-D array, and supplied with simple parallel-in-serial-out (PISO) logic, this architecture can achieve the maximally available parallelism with nearly 100% efficiency if either the pipeline interleaving or processor sharing technique is used. The design does not require the preloading of the whole 2-D data array, and line scanned images can be processed with negligible time delay. >

Cerebellar model articulation controller (CMAC) is a useful neural network learning technique. It was developed two decades ago but yet lacks adequate learning algorithm especially when it is used in a hybrid-type controller. Part I of this work was devoted to introduce a new CMAC adaptive learning algorithm. Part II will be directed to experimental application of new learning algorithm of a CMAC based hybrid-type real time controller. The proposed controller is applied for the trajectory tracking of a piezoelectric actuated tool post. It has been proven that the piezoelectric actuated tool post has hysteretic behavior. Extensive experiments have been carried out on the experimental setup to evaluate the proposed adaptive learning algorithm of CMAC. Only few experiments and their results are being presented. In these experiments, the performance of the piezoelectric actuated tool post has been examined and evaluated using different types of control algorithms and applying external load disturbance. The control performance of the proposed controller is compared with those of conventional controllers (PI controller and the conventional CMAC based controller). The experimental results showed that performance of the hybrid-type controller using the proposed learning algorithm is stable and more effective than that of the conventional controllers. Testing and comparing the learning ability of the proposed learning algorithm with that of the conventional CMAC learning algorithm indicated the effectiveness of the learning ability of the proposed algorithm. Finally, the response using the proposed hybrid-type controller is slightly better than using the conventional PI controller under the effect of external load disturbance.

This paper introduces a novel multi-agent model for simulating water sharing scenarios under various irrigation policies, together with a novel self adaptive learning algorithm that achieves efficient resource allocation. The main contribution of this work lies in the fact that both the multi-agent model and the proposed learning algorithm operate under the lack of communication between the users of the resource, thus, no assumptions about the development of relations of trust between them are made. Moreover, the proposed learning algorithm uses only local information and operates in a decentralized manner, thus its implementation does not entail significant costs. The model was calibrated using data from a real world ecosystem and experimental results provided statistical and qualitative figures of merit for assessing typical irrigation policies. For all the irrigation policies examined, even if the users of the resource acted under profit maximization criteria, the proposed learning algorithm provided a means of achieving efficient resource allocation, despite the lack of communication. Thus, the proposed model and learning algorithm are valuable tools for assessing alternative irrigation policies and providing the best policy for any given scenario.

Q-Learning-based parameter control in differential evolution for structural optimization