Median filter

About: Median filter is a research topic. Over the lifetime, 12479 publications have been published within this topic receiving 178253 citations.

Generalized Hampel Filters

Abstract: The standard median filter based on a symmetric moving window has only one tuning parameter: the window width. Despite this limitation, this filter has proven extremely useful and has motivated a number of extensions: weighted median filters, recursive median filters, and various cascade structures. The Hampel filter is a member of the class of decsion filters that replaces the central value in the data window with the median if it lies far enough from the median to be deemed an outlier. This filter depends on both the window width and an additional tuning parameter t, reducing to the median filter when t=0, so it may be regarded as another median filter extension. This paper adopts this view, defining and exploring the class of generalized Hampel filters obtained by applying the median filter extensions listed above: weighted Hampel filters, recursive Hampel filters, and their cascades. An important concept introduced here is that of an implosion sequence, a signal for which generalized Hampel filter performance is independent of the threshold parameter t. These sequences are important because the added flexibility of the generalized Hampel filters offers no practical advantage for implosion sequences. Partial characterization results are presented for these sequences, as are useful relationships between root sequences for generalized Hampel filters and their median-based counterparts. To illustrate the performance of this filter class, two examples are considered: one is simulation-based, providing a basis for quantitative evaluation of signal recovery performance as a function of t, while the other is a sequence of monthly Italian industrial production index values that exhibits glaring outliers.

A New Adaptive Switching Median Filter

Abstract: A new Adaptive Switching Median (ASWM) filter for removing impulse noise from corrupted images is presented. The originality of ASWM is that no a priori Threshold is needed as in the case of a classical Switching Median filter. Instead, Threshold is computed locally from image pixels intensity values in a sliding window. Results show that ASWM provides better performance in terms of PSNR and MAE than many other median filter variants for random-valued impulse noise. In addition it can preserve more image details in a high noise environment.

Streaking in median filtered images

Abstract: This paper presents a probabilistic analysis of the streaking or blotching effect commonly observed in median filtered signals in both one and two dimensions. The effcts are identified as runs of equal or nearly equal values which create visual impressions that have no visual correlate. For one-dimensional discrete iid random signals with continuous input probability densities, the probability of a streak of length L occurring is computed and shown to be independent of the input probability distribution. Expressions for the first and second moments of the streak length are also derived, and certain asymptotic results are given. As the analysis and definition of the analogous effect in two dimensions is less tractable, the probability that medians taken from distinct overlapping windows will take the same value is derived for various filter geometries. The analytic results are supported by examples using both one- and two-dimensional signals.

Using stochastic computing to implement digital image processing algorithms

Abstract: As device scaling continues to nanoscale dimensions, circuit reliability will continue to become an ever greater problem. Stochastic computing, which performs computing with random bits (stochastic bits streams), can be used to enable reliable computation using those unreliable devices. However, one of the major issues of stochastic computing is that applications implemented with this technique are limited by the available computational elements. In this paper, first we will introduce and prove a stochastic absolute value function. Second, we will demonstrate a mathematical analysis of a stochastic tanh function, which is a key component used in a stochastic comparator. Third, we will present a quantitative analysis of a one-parameter linear gain function, and propose a new two-parameter version. The validity of the present stochastic computational elements is demonstrated through four basic digital image processing algorithms: edge detection, frame difference based image segmentation, median filter based noise reduction, and image contrast stretching. Our experimental results show that stochastic implementations tolerate more noise and consume less hardware than their conventional counterparts.

Simultaneous sources separation via multidirectional vector-median filtering

Abstract: Simultaneous source acquisition technology, also referred to as “blended acquisition,” involves recording two or more shots simultaneously. Despite the fact that the recorded data has crosstalk from different shots, conventional processing procedures can still produce acceptable images for interpretation. This is due to the power of the stacking process using blended data with its increased data redundancy and inherent time delays between various shots. It is still desirable to separate the blended data into single shot gathers and reduce the crosstalk noise to achieve the highest seismic image quality and for standard prestack processing, such as filtering, statics computation, and velocity analysis. This study introduced a new and simple multidirectional vector-median filter (MD-VMF) to separate the blended seismic shot gathers. This method extended the well-known conventional median filter from a scalar implementation to a vector version. More specifically, a vector median filter was applied in...