A training framework for stack and Boolean filtering-fast optimal design procedures and robustness case study

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.

Optimal multistage (MS) stack filtering under the mean absolute error (MAE) criterion is discussed, with image restoration in mind. Using the recently developed techniques, the optimal MS stack filters are designed efficiently. Compared to single-stage (SS) stack filtering, an MS filter provides an additional design flexibility by choosing the window masks at different stages to provide a good compromise between the noise removal and the image-detail preservation. To achieve a comparable performance, MS filters can select considerably smaller window masks. The relationship between the filtering complexity/memory requirement and the window size suggests that the MS stack filtering is much faster and requires much less memory than SS stack filtering. Results of image recovery experiments are reported. >

A deterministic algorithm is proposed to design the optimal stack filter. The proposed algorithm can generate the optimal stack filter in one second for a window size of 9 and it can still generate the optimal stack filter for a window size of 21 although it takes about 4 hours. Experimental results reveal the feasibility and efficiency of the proposed algorithm in finding the optimal stack filter.

Nonlinear signal processing elements are increasingly needed in current signal processing systems. Stack filters form a large class of nonlinear filters, which have found a range of applications, giving excellent results in the area of noise filtering. Naturally, the development of fast procedures for the optimization of stack filters is one of the major aims in the research in the field. The objective of the optimization method presented in this paper is to find the stack filter producing optimal noise attenuation and satisfying given constraints. The constraints may limit the search into a set of stack filters with some common statistical description or they may describe certain structures which must be preserved or deleted.

The stack filter is the largest class of nonlinear digital filters, including weighted median filters and morphology filters. The design of the stack filter is reduced to the problem of determination of the Boolean function defining its filter and is divided into design methods of estimation type using a training signal, and design methods maximizing the noise elimination capability under the constraint of preserving a specific configuration. With a view to expanding the class of stack filters, the authors have proposed the fuzzy stack filter, a stack filter defined by the fuzzy Boolean function. Also, for the fuzzy weighted median filter, as the most fundamental fuzzy stack filter, a design method based on the estimation standpoint is provided. In this paper, a new fuzzy stack filter preserving a specific structure is explained. The noise elimination characteristics of the fuzzy stack filter preserving a specific structure and the preservation characteristics of the specific structure under the effect of the noise are clarified. Further, a procedure is presented for deriving a filter suitable for restoration of the degraded images in a wide range without departing from the standpoint of a design method preserving the specific structure (for which empirical information on the signal to be processed cannot be obtained). The effectiveness of the filter obtained by this procedure is presented. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 83(2): 11–21, 2000

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>

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.

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

Two interpolative BTC (block truncation coding) image coding schemes with optimal stack filters (in the minimum MAE sense) as the interpolator are suggested. Compared to the standard BTC, the new schemes yield >25% and >37.5% reductions in bit rate, respectively, with little performance degradation. Compared to a previous interpolative BTC coding method, the quality of coded images has been greatly improved with the new schemes (at the same or even a lower rate).

The authors derive efficient parallel algorithms on a VLSI array for several signal and image processing tasks. The parallel architecture has n/sup 2/ memory modules storing the input data which is accessed by n PEs. They consider several signal processing tasks such as k selection, median filtering, labeling 0/1 image, etc. For these problems, linear speedup is obtained, compared to a single-processor system. For the k selection problem they also provide an efficient parallel solution using log transformation on the data. The expected time of this method is O(n) with a small constant factor. The proposed array is suitable for general-purpose signal processing and can be implemented in VLSI using a limited chip set.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A new nonlinear filter known as the generalised adaptive neural filter (GANF) is introduced. It is extended from the generalised stack filter and can be adapted by various neural networks. It is also shown that there always exists a GANF that can achieve an absolute error less than or equal to that of a stack filter with the same window width. Experimental results are presented to demonstrate the effectiveness of GANF for suppressing noise.

Implementing remote, real-time spectroscopic monitoring of radiochemical processing streams in hot cell environments requires efficiency and simplicity. The success of optical spectroscopy for the quantification of species in chemical systems highly depends on representative training sets and suitable validation sets. Selecting a training set (i.e., calibration standards) to build multivariate regression models is both time- and resource-consuming using standard one-factor-at-a-time approaches. This study describes the use of experimental design to generate spectral training sets and a validation set for the quantification of sodium nitrate (0-1 M) and nitric acid (0.1-10 M) using the near-infrared water band centered at 1440 nm. Partial least squares regression models were built from training sets generated by both D- and I-optimal experimental designs and a one-factor-at-a-time approach. The prediction performance of each model was evaluated by comparing the bias and standard error of prediction for statistical significance. D- and I-optimal designs reduced the number of samples required to build regression models compared with one-factor-at-a-time while also improving performance. Models must be confirmed against a validation sample set when minimizing the number of samples in the training set. The D-optimal design performed the best when considering both performance and efficiency by improving predictive capability and reducing number of samples in the training set by 64% compared with the one-factor-at-a-time approach. The experimental design approach objectively selects calibration and validation spectral data sets based on statistical criterion to optimize performance and minimize resources.

The theory of optimum nonlinear filters outlined in this paper is based on the consideration of a sequence of classes of nonlinear filters, designated as 𝔑1, 𝔑2, 𝔑3, …, such that each class in the sequence includes all the preceding classes and, furthermore, the class of linear filters is a subclass of every class in the sequence. A filter of class 𝔑m is described in terms of a characteristic function which involves m age variables and m values of the input time-function. The input-output relationship for a filter of class 𝔑m has the form of an m-fold integral of the characteristic function with respect to the m age variables. It is shown that the characteristic function of the optimum filter (in the least squares sense) within the class 𝔑m satisfies a linear integral equation of 2mth order. The optimization of filters of class 𝔑1 is treated in detail, and methods of approximate realization of such filters in the form of nonlinear delay line filters and power series filters are indicated. The results are extended to the case of nonstationary time series.

This paper considers the nonlinear system filtering with packet dropouts. We assume that the packet arrived rate is known in advance but the sequence of packet dropouts is unknown. At first, we use the probability-weighted method to achieve a pseudo measurement sequence, and every pseudo measurement is the weighted value of the measurements acquired at the current time step and the prior time step. Some classical nonlinear filtering methods can be used via the pseudo measurement sequence and the dynamic equation of the system, and then the pseudo measurement unscented Kalman filter (PM_UKF) and the pseudo measurement particle filter (PM_PF) are given. This pseudo measurement sequence can be also used in the linear system, and its time complexity is lower than that of Sun's optimal filter at this time. Simulation results show the effectiveness of the proposed algorithms.

The role of pertinently diversified and balanced training as well as testing data sets in achieving the true performance of classifiers in predicting the antifreeze proteins