SBNR processor for stack filters

A new fuzzy filter, called fuzzy stack filter (FSF), is proposed to extend the filtering capability of conventional stack filter (SF), which is based on the positive Boolean function (PBF) as its window operator. We fuzzify the onset and off-set of a given PBF to obtain two types of fuzzy PBFs. Then, we adopt the architecture of threshold decomposition to develop this new fuzzy filter with a fuzzy PBF as its window operator. Each fuzzy PBF is associated with a set of control parameters. Therefore, the original PBF can be estimated from above and below by two fuzzy PBFs with appropriate control parameters. Furthermore, we can apply the fuzzy modifiers to modify the fuzzy PBFs such that the PBFs can be completely estimated by the fuzzy PBFs. Hence, the stack filter is a special case of fuzzy stack filter. Since some control parameters are added in this new filter, the neural learning algorithms can be easily developed under the flexibility of the given control parameters. We first propose the fuzzy (m,n) rank-order filter to test our proposed learning algorithm. In this simple learning algorithm, we can remove the noise-corrupted images very well in contrast to the filtering behavior of rank-order filters. We believe that the results presented will lead to more fruitful research on more advanced and powerful learning algorithms dedicated to the appropriate applications.

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

In this paper, a classifier based on the positive Boolean function (PBF) is proposed for the supervised pattern classification. A PBF is exactly represented as one sum-of-product form without any negative components. The PBF possesses the well-known threshold decomposition and stacking properties. The classification errors can be calculated from the summation of the absolute errors incurred at each level. The optimal PBF are found and designed to be a classifier by minimizing the classification error rate along the training samples. The experimental results were given to show the validity of our proposed approaches.

New stack filter architectures are proposed. Known architectures are considered from new positions and combined to obtain new structures with suitable complexities and throughputs. It is shown that all stack filters can be used without changes when the input data is represented in one of the binary lexicographic codes. Stack filters are also proposed for the cases where the data are represented in multiple-value lexicographic codes. The class of pipeline-parallel structures for common stack filters is simple and modular in structure, and suitable for VLSI implementation. The time-area complexity of the proposed filters is O(k), where k is the number of bits in the input signals. >

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).

Median filtering with programmable window length is needed for environments with impulse noises of different lengths. The paper proposes a new architecture for an A/D convertor with median filtering of programmable window length. Both digital and analogue medians are available at the output. Previous architecture was implemented using a positive boolean function (PBF) circuit which requires a large area for large window length. In this architecture, the majority circuit, which has a smaller area and faster speed, is used to replace the PBF circuit. The throughput is independent of the window size and the hardware complexity is linearly dependent on the window size. The silicon area of this architecture is small and it is therefore suitable for monolithic implementation.

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.

Given a positive Boolean function fand a subset δ of its variables, we give a combinatorial condition characterizing the existence of a prime implicant Dˆof the Boolean dual f d of f having the property that every variable in δ appears in Dˆ We show that the recognition of this property is an NP-complete problem, suggesting an inherent computational difficulty of Boolean dualization, independently of the size of the dual function. Finally it is shown that if the cardinality of δ is bounded by a constant, then the above recognition problem is polynomial. In particular, it follows that the co-ocurrence graph of the dual of a positive Boolean function can be always generated in time polynomial in the size of the function.

Worst-case groundness analysis using positive Boolean functions

A hand-based personal authentication using a coarse-to-fine strategy

A novel approach to personal verification using the thermal images of palm-dorsa vein patterns is presented in this paper. The characteristics of the proposed method are that no prior knowledge about the objects is necessary and the parameters can be set automatically. In our work, an infrared (IR) camera is adopted as the input device to capture the thermal images of the palm-dorsa. In the proposed approach, two of the finger webs are automatically selected as the datum points to define the region of interest (ROI) on the thermal images. Within each ROI, feature points of the vein patterns (FPVPs) are extracted by modifying the basic tool of watershed transformation based on the properties of thermal images. According to the heat conduction law (the Fourier law), multiple features can be extracted from each FPVP for verification. Multiresolution representations of images with FPVPs are obtained using multiple multiresolution filters (MRFs) that extract the dominant points by filtering miscellaneous features for each FPVP. A hierarchical integrating function is then applied to integrate multiple features and multiresolution representations. The former is integrated by an inter-to-intra personal variation ratio and the latter is integrated by a positive Boolean function. We also introduce a logical and reasonable method to select a trained threshold for verification. Experiments were conducted using the thermal images of palm-dorsas and the results are satisfactory with an acceptable accuracy rate (FRR:2.3% and FAR:2.3%). The experimental results demonstrate that our proposed approach is valid and effective for vein-pattern verification.

In this paper it is shown how to calculate the joint distribution function of two different stack filters sharing the same arguments. The input signal is modeled as a sequence of independent, but not necessarily identical, random variables. Supposing that the input signal is filtered with stack filter, we apply the derived formula to find the joint distribution function of any two samples in the output signal. In the paper we first go through the derivation of the formula starting with real-valued stack filters and the definition of the joint distribution function of their outputs. After that we change into binary domain where the enumeration of the possible cases turns out to be quite a straightforward task. It also allows reasonably compact expression of the final formula. The joint distribution formula for stack filters has many possible applications. For example it allows the analytic computation of the autocorrelation functions of these filters. It may also be useful in system reliability studies where the failure of a system is derived as a function of its components states. Often this function can be composed of solely min- and max-operations, i.e., it possesses the weak superposition property called stack decomposition. The paper includes interesting examples where the joint distribution function is obtained in a particularly neat form. Also a special symmetry class of stack filters is characterized.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The static maximum relative error of the ADC for sensors is determined by the value of its least significant bit. During the input signal conversion in the ADC the information delay causes the dynamic error, which is added to the static error and actually reduces the effective number of bits. This decrease can be estimated by the effective number of bits, which illustrates the qualitative and quantitative assessment of the additional error. The article demonstrates that the effective bits rate is defined by the delay period of information in the ADC, as well as the sampling rate of the input signal. This, in turn, requires setting the spectrographic density (SD) for the converted signal, as well as an algorithm for selecting the sampling rate. It is recommended that the delay time of the ADC includes the delay in the analog storage and amplitude multiplexer, which are located at the ADC input and are directly involved in the conversion process. The article draws attention to the fact that the real sampling rate of analog signals, chosen from the point of view of the straight task of errors distribution in the automatic control system, significantly exceeds the sampling rate according to the sampling theorem. This requires the correction of the obtained results using the sampling theorem, in the direction of reduction of effective number of bits.