Idempotent one-sided approximation of median smoothers

Rohwer, Carl

doi:10.1016/0021-9045(89)90017-8

Cited by 17 publications

(4 citation statements)

References 7 publications

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“…Figure 9 displays the EIMS values of the linear smoother MA 2 applied to the different nonlinear smoothers. The EIMS values of the compound LULU smoothers B 3 , B 4 signal recovery. Therefore, performance as measured by the two criteria has to be interpreted very carefully.…”

Section: Discussion Of the Simulation Resultsmentioning

confidence: 99%

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Performance of nonlinear smoothers in signal recovery

Conradie

Wet

Jankowitz

2009

Appl Stoch Models Bus & Ind

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Time series data can be decomposed as signal plus noise. A good smoother should be able to recover a smooth signal reasonably well from time series data. The performance of two classes of nonlinear smoothers in signal recovery is discussed in this paper. The first class is the well-known class of median smoothers. The other one is a relatively new class of smoothers based on extreme-order statistics, called lower-upper-lower-upper smoothers. Sinusoidal signals of different frequencies with contaminated normal noise and impulsive noise added were simulated. Members of the two classes of nonlinear smoothers were applied to remove the 'non-Gaussian' and impulsive noise. To this output linear smoothing was applied to remove the remaining Gaussian noise. By means of a simulation study, the success of the two classes of smoothers was investigated using as measures of success the least-squares regression of the smoothed sequence on the signal and the integrated mean square error. PERFORMANCE OF NONLINEAR SMOOTHERS IN SIGNAL RECOVERY 429 SIGNAL RECOVERYSignal recovery is the process by which a signal is recovered from a set of noisy time series data, generated at time t as data t = signal t +noise t

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Section: Discussion Of the Simulation Resultsmentioning

confidence: 99%

“…Median smoothers perform well when the noise is of an impulsive type. In the late 1980s a new class of nonlinear smoothers was introduced in the literature in [4]. These smoothers are based on the extreme-order statistics rather than on the central ones, and Rohwer named them as lower-upper-lower-upper (LULU) smoothers.…”

Section: Introductionmentioning

confidence: 99%

Performance of nonlinear smoothers in signal recovery

Conradie

Wet

Jankowitz

2009

Appl Stoch Models Bus & Ind

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“…Also, the LULU smoothers were shown to be consistent due to their idempotent and co‐idempotent properties. They regard the output signal of the smoother as a pure signal, thus resulting in the same output if the smoother is applied again (Rohwer ).…”

Section: Image Data Processingmentioning

confidence: 99%

Fast meteor tracking in noisy video sequences

Vítek

Nasyrova

2019

Astron Nachr

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Meteor recording, detection, and analysis is one of the traditional topics of astronomy. This paper deals with fast-tracking of faint meteors and meteor showers in video sequences with high frame rates. Since meteors are fast optical events, the utilization of cameras with high frame rates and short exposure times is the standard technique of meteor tracks capture. Low efficiency of such camera systems is typically compensated with image intensifiers, mostly based on the microchannel plate (MCP). In this work, we use image data captured with the meteor automatic imager and analyzer, double-station system dedicated for observing faint meteor showers.The system works with minimal human interaction, and it is necessary to automatically process (i.e., identify all meteor candidates) all captured data as fast as possible.Results show possible speed-up of the image processing method when fluctuations of MCP are reduced.

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“…It is, thus, natural to compare them to the median operator which is also a rank selector since it selects the middle element in the ranked window. It is given by (10) A comprehensive discussion can be found in [24], [27], and [29]. In [23], the total variation of the sequence is shown to decrease with each application of the median operator.…”

Section: Consistent Hierarchical Decompositionmentioning

confidence: 99%

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

Anguelov

Fabris‐Rotelli

2010

IEEE Trans. on Image Process.

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Abstract-The LULU operators for sequences, that is L n , U n and their compositions, are extended to multidimensional arrays in a way which preserves their essential properties, e.g., consistent separation, total variation and shape preservation. The power of the operators is demonstrated by deriving the discrete pulse transform (DPT), which is a hierarchical decomposition of the input array into pulses. Similar to its 1-D counterpart this transform satisfies a basic consistency property.

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Idempotent one-sided approximation of median smoothers

Cited by 17 publications

References 7 publications

Performance of nonlinear smoothers in signal recovery

Performance of nonlinear smoothers in signal recovery

Fast meteor tracking in noisy video sequences

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

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