Novel A/D convertor with median filtering of programmable window length

Nonlinear digital filters play an important role in digital signal processing applications. In this brief, a novel architecture is proposed for the hardware implementation of fixed and runtime variable window length one-dimensional median filters. In the proposed architecture, the maximum working clock frequency is almost independent of the median filter window length, whereas the hardware complexity is proportional to the number of samples in the window. This feature enables the construction of filters with relatively large window lengths with negligible reduction in the maximum clock frequency, whereas in previous architectures, the maximum clock frequency significantly drops as the window length is increased. The benchmark results show the efficiency of the proposed architecture in comparison with state-of-the-art techniques.

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.

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.

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.

Weighted medians — positive Boolean functions conversion algorithms

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.

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).

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.

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.

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 the image handling process, effective interpretation or reconstruction of the original image is mandatory, since the post-processing of images relies upon this important pre-processing task. It is well recognised that the noise makes degradation in the quality of image, which in turn results poor interpretation of images. This paper targets to remove salt-and-pepper or fixed impulse noise from images by fusing two techniques, namely median and non-local means (MNLM) filtering, and exploits both filtering benefits altogether. In the first phase, median filtering has been applied along with new sorting algorithm instead of the conventional method of sorting in order to reduce computational and hardware complexity. Even though the non-linear median filter performs better for low-level noise density and best in edge preservation, it gives blurring effect in the case of high-level noise density. This paper tries to overcome this limitation by fusing NLM filter effectively during the second phase. This fusion approach has brought promising quantitative results such as higher PSNR (peak signal-to-noise ratio) and lower MSE (mean square error) when compared to other existing standard algorithms such as SMF (standard median filter) and NLM filtering approaches.

Medical images have noise, such as salt and pepper, speckle, and gaussian noise. So, getting the accuracy of magnetic resonance images is challenging always. The accuracy of brain images is essential for the clinical diagnosis process. The nonlinear method of median and morphological filters is used for enhancement, contrast adjustment, and histogram equalization for medical images and speech processing, to preserve them from noise and edge features. Because of its edge-preserving properties, this median spatial filter window is critically important and better for removing impulsive noise and speckle noise. Nine different shapes of windows and five different sizes of windows and five noise density injections are used for evaluating the performance of the median filter. The first person J.W.Tukey, did the smoothing process by median rank selection filter. The denoising using morphological process is also considered for analysis. These two nonlinear methods like median filtering and morphological methods are used for the restoration of noise from the original image. These two methods are applied in normal and seizure-affected images to calculate quality assessment metrics and also the performance evaluation metrics from magnetic resonance images. Any image needs to be denoised to get the accuracy, precision, and F-measure kind of common feature evaluation metrics. This paper evaluates two nonlinear filtering methods and their performance evaluated based on shapes and size of windows and for suppressing or de-noising to produce original noise-free images to assist clinically.