Y. Neuvo

Smoothed median filters with FIR substructures

In this paper we introduce a new generalized class of Median Filters (MF) which we call Smoothed Median Filters (SMF). The input signal x(n) is filtered with M linear phase FIR filters and the output of the SMF is the median of the outputs of the FIR filters. The statistical properties of the SMFs are analyzed for input signals with Gaussian, double exponential, and uniform density functions. It is shown that SMFs have essentially the same statistical properties and same type of root signals as the conventional MFs. SMFs preserve corner points and ramps and attenuate impulsive type noise components effectively. An interesting subclass of the SMFs requiring only two scaling multipliers and three data sorting operations irrespective of the filter length is introduced.

Optimal weighted order statistic filters under the mean absolute error criterion

Based on the relationship between weighted order statistic (WOS) filters and threshold logic, an algorithm is developed for determining optimal WOS filters under the mean absolute error (MAE) criterion. This algorithm requires much less computation than the adaptive stack filtering algorithm. In addition, experimental results in image restoration demonstrate that the WOS filters obtained by the proposed algorithm can even give better results than the adaptive stack filters.<<ETX>>

Scan rate conversions using weighted median filtering

A new concept based on the weighted median filter and an averaging substructure for scan rate conversion is introduced. The method can be used with motion information if it is available, or the weights can be fixed so that the interpolator gives a compromise between still image and motion reproduction. The weighted median interpolator gives a good image quality compared with commonly used interpolation methods. The algorithm is suitable for real-time implementations. It is also possible to use the proposed weighted median interpolation to produce high-quality still pictures, for example, from the VCR.<<ETX>>

3-dimensional median filters for image sequence processing

Two 3-D median-based filtering algorithms have been developed that preserve the motion in the image sequence while attenuating noise effectively. Some observations are made on the root signals in the binary domain based on the positive Boolean functions corresponding to the filters. From the Boolean expressions the output distribution functions are derived. The performance of both filters under various noise types is examined theoretically and experimentally. The structures are simulated on a video sequencer (DVSR 100) on real image sequences. Comparisons are made with other 2- and 3-D algorithms from the literature based on mean square error, mean absolute error, and subjective criteria.<<ETX>>

Adaptive neural filters

The authors introduce a new class of nonlinear filters called neural filters based on the threshold decomposition and neural networks. Neural filters can approximate both linear FIR filters and weighted order statistic (WOS) filters which include median, rank order, and weighted median filters. An adaptive algorithm is derived for determining optimal neural filters under the mean squared error (MSE) criterion. Experimental results demonstrate that if the input signal is corrupted by Gaussian noise adaptive neural filters converge to linear filters and if corrupted by impulsive noise, optimal neural filters become WOS filters.<<ETX>>

Sine wave responses of median type filters

The authors analyze the amplitude and phase responses of median type filters using sinusoidal input signals. The filter types studied are the standard median (SM) filters and FIR (finite impulse response) median hybrid (FMH) filters. The overall behavior of the sine wave response of the FMH filter is like that of a low-pass filter characterized roughly by the responses of the linear filters. The FMH filters were shown to provide a significantly better stopband attenuation than the SM filters. The results obtained by varying the input signal phase clearly indicate that, especially for the SM filters, an average response is not a sufficient characterization of the filters.<<ETX>>

Use of short floating-point formats in audio applications

Use of short floating-point formats that are shorter than the IEEE floating-point standard (ANSI/IEEE S+A 754-1985), 24+8-b, in digital audio applications is studied. The performance of these formats is analyzed in different parts of the digital audio signal processing chain and compared to the performance of widely used fixed-point formats. The statistics of practical audio signals and the characteristics of modern floating-point signal processors are considered in the analysis. >

Suppression and detection of impulse type interference using adaptive median hybrid filters

In this paper, we introduce a new type of nonlinear filters, the Adaptive Median Hybrid (AMH) filters, for the suppression and detection of short duration interferences. In the AMH filters, adaptive filter substructures are used to estimate the current signal value from the future and past signal values. The output of the overall filter is the median of the adaptive filter outputs and the current signal value. This kind of nonlinear filter structure is shown to adapt and preserve rapid changes in signal characteristics well. However, it filters out short duration interferences. By examining the difference between the original and filtered data, interferences can be detected. We introduce two types of AMH filters, the AMH filter with separate adaptive substructures (SAMH) and the AMH filter with coupled substructures (CAMH), which have different convergence properties and implementation. We use both synthetic and real data (speech and electroencephalogram (EEG)) to show the applicability of the proposed filters.

Optimal weighted order statistic filters under structural constraints

The authors present a procedure based on quadratic programming for finding the optimal weighted order statistic filter under the mean absolute error criterion satisfying imposed structural constraints. In this way, filters are obtained that simultaneously meet the desired detail preservation constraints and give a good noise attenuation. The algorithm is characterized by low computational complexity and simplicity in constraint formulation. The method is capable of handling large window size problems.<<ETX>>

Statistical properties of discrete morphological filters

The statistical properties of discrete morphological filters are analyzed by utilizing the connection between morphological and stack filters. Analytical expressions of the output distribution of basic morphological filters are derived. For one-dimensional filters closed form expressions are given.<<ETX>>