Hybrid Median Filter Research Articles

LMS order statistic filters adaptation by backpropagation

Abstract A novel class of nonlinear adaptive filters based on order statistics is presented. An LMS algorithm for their adaptation is proposed. This algorithm is essentially a backpropagation algorithm for the adaptation of coefficients that are used before data sorting. The nonlinear filters that can become adaptive by the techniques presented in this paper are the median hybrid filter, the general nonlinear filter structure, the L -filters and the Ll -filters.

Edge preserving filtering by combining nonlinear mean and median filters

A very general class of nonlinear filters, called mapping order-statistics filters (MOSFs), is introduced. A subclass of the MOSFs called L/sub p/-mean median filters (L/sub p/-MMFs) is discussed. The L/sub p/-MMF shows better properties in preserving edges and attenuating positive and negative impulse noise simultaneously than do the nonlinear mean filters. In the analysis of the deterministic properties of the L/sub p/-MMF, the concept of a monotonic trend region is introduced. A necessary condition for a signal to be a root signal is given. This necessary condition is also valid for the known finite-impulse-response median hybrid filter. >

Median filtering is appropriate to signals of saccadic eye movements

In this paper we show nonlinear standard and hybrid median filters are appropriate to the filtering of signals of saccadic eye movements. Although these filters effectively attenuate noise, they do not harm the parameters of saccades, particularly the maximum velocity which is an important indicator of certain diseases and disorders in man. The filters have been tested by simulation as well as actual eye movement signals recorded electro-oculographically and photoelectrically.

Far-infrared stack hybrid filters

We introduce a new class of linear-nonlinear combinational filters, called FIR stack hybrid (FSH) filters, which greatly enlarges the family of FIR median hybrid (FMH) filters. The optimal FSH filtering theory under the mean absolute error (MAE) criterion is studied. A general two-step method to synthesize optimal FSH filters is developed. In the first step, the probabilities needed in the optimal filter design are estimated based on images. In the second step, the linear program (LP) required to solve the best filter is avoided by using a good suboptimal algorithm that only needs data comparisons. A sufficient condition under which the suboptimal routine can result in optimal solutions is given, and this condition is shown to hold in most practical cases. To demonstrate the efficiency of the proposed approach, a group of FSH filters are synthesized for the standard image Bridge. The task is to restore the image from impulsive or Gaussian noise. By checking the sufficient condition, each filter is found to be optimal in the minimum MAE sense. Testing results of some synthesized filters show that the optimal FSH filters can do a much better job than the corresponding FMH filters in both noise environments.

Algorithms for real-time trend detection

In this paper, we develop FIR median hybrid (FMH) filter based algorithms for real-time trend detection. The algorithms are designed so that trends are gradually refined as data becomes available. Special attention is paid to the clear detection of sharp changes in trends. The algorithms are based on a new concept of five point median operations taken over the outputs of linear subfilters or some other auxiliary outputs. The noise attenuation and the edge preserving abilities of several FMH trend detection filters are analyzed. The results show clearly the usefulness of the FMH trend detection. Moreover, the in-place growing FMH filter based trend detector was found to have significant advantages over the FMH based methods. The trend filtering concept can also be successfully applied to the filtering of the beginning and end of a finite length data sequence.

Linear median hybrid filters

The authors introduce a general class of median-type filters which contain nonrecursive (finite impulse response) and/or recursive (infinite impulse response) substructures. The overall structure of the linear median hybrid (LMH) filters may be either nonrecursive or recursive. Altogether eight basic filter structures are introduced, and four of them are analyzed in more detail. General properties of the root signals, i.e. signals invariant to filtering, are discussed. Expressions characterizing the noise attenuating properties of some of the filters are derived, and a statistical analysis of the filters is performed. The LMH filters are simple structures enabling both analog and digital implementations and having properties not attainable with linear or median filters. By designing the linear substructures appropriately it is possible to tailor the root signals of the LMH filters to meet the time-domain specifications of a particular applications.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A signal processor for median-based algorithms

A sorter-based processor architecture is introduced for digital signal processing purposes. The processor has been optimized to implement sliding average-type linear structures and three- and five-sample sorting operations. The specialized processor can be used, for example, for the several variations of the finite-impulse-response (FIR) median hybrid (FMH) filters, as well as other types of ranked-order filters and running-sum averaging operations. FMH filters with averaging substructures and window lengths of up to 65 samples can be computed with sampling intervals of less than 20 clock cycles. The 12-bit microprogrammable core processor is designed as a full-custom very large scale integration (VLSI) circuit. Examples of filter implementations show that the sorter-based processor architecture is suitable for several kinds of digital signal processing tasks.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

FIR-median hybrid filters with predictive FIR substructures

A class of finite-impulse response (FIR) median hybrid (FMH) filters that contain linear FIR substructures to estimate the current signal value using forward and backward prediction is introduced. The output of the overall filter is the median of the predicted values and the actual signal value in the middle of the filter window. Predictors maximizing the signal-to-noise ratio on signal sections described by an lth-order polynominal are derived. The ramp enhancement filters are shown to attenuate the noise on a ramp signal better than the standard median (SM) filters. The new predictive FMH filters are shown to have root signals which do not exist for the SM filters, e.g. triangular waves. By combining the level and the ramp enhancement FMH filters, a filter is obtained which attenuates noise on constant and ramp signals. The noise attenuation on ramp signals is better than with the SM filter, and the predictive FMH filter has novel and meaningful root structures. The number of arithmetic operations needed to implement the predictive FMH filter grows linearly with the length of the filter. >

Filtering of nonstationary signals using predictor median hybrid structures

An approach to filtering of nonstationary signals that contain abrupt changes from one signal state to another is presented. Proposed nonlinear filters, the Predictor Median Hybrid (PMH) filters, contain substructures to estimate the current signal value using forward and backward prediction. The output of the overall filter is the median of the predicted values and the actual signal value. This kind of nonlinear filter structure is shown to have some interesting properties: (1) Due to the median operation, the filters do not disturb rapid changes from one stationary signal to another and yet they attenuate noise. (2) The predictive substructures can be chosen according to the application, thus greatly extending the class of signals where median type filters can be applied. (3) Due to the predictive nature of the substructures they adapt to the signal, thus simplifying the design of the filters. Two types of predictive substructures have been used: linear predictive substructures and curve fitting based predictors. The PMH filters with linear predictive substructures are shown to be especially useful for the restoration of deterministic and stochastic signals that contain impulse-like distortions. The curve fitting based substructures are shown to be useful for attenuation of Gaussian noise.

On root structures of median and median-type filters

In this correspondence, we analyze the root structures of the standard median (SM) filters, the recursive median (RM) filters, and the FIR median hybrid (FMH) filters. It is shown that these filters have many oscillatory infinitely long root signals. When a section of an oscillatory root is present in a signal, the filter's noise attenuation of the filter is not as good as predicted by statistical measures. We also suggest methods to prevent the possible harmful effect caused by the existence of these roots.

Median-type filters with adaptive substructures

In this paper, adaptive filter structures suitable for filtering signals with rapidly varying characteristics are presented. In the proposed Adaptive Median Hybrid (AMH) filters, adaptive filter substructures are used to estimate the current signal value from future signal values and from past input or output signal values. The output of the overall filter is the median of the adaptive filter outputs and the input signal value. Using computer simulations, the convergence properties of the filters in stationary and nonstationary signals have been analyzed. Due to the median operation, the AMH filters adapt and preserve abrupt changes in signal statistics substantially better than conventional adaptive filters.

Integrated FIR median hybrid filter

A low cost custom integrated circuit implementing the FIR Median Hybrid Filter is introduced. This novel concept combines linear FIR filters with nonlinear median filters. The method produces results that are essentially equivalent to median filtering. However, the VLSI implementation is orders of magnitude simpler. The IC is capable of working up to window lengths of 2049. The circuit architecture is microprocessor bus compatible with a high throughput.