The Discrete Pulse Transform

Rohwer, Carl; Laurie, Dirk

doi:10.1137/040620862

Cited by 13 publications

(20 citation statements)

References 8 publications

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“…As mentioned in [26], a decomposition by linear operators should typically recover the coordinates of any given linear combination of basis vectors, a property not at all applicable to the nonlinear case. A measure of the quality of any hierarchical decompositions is introduced in [26] in the following way:…”

Section: Consistent Hierarchical Decompositionmentioning

confidence: 99%

“…A measure of the quality of any hierarchical decompositions is introduced in [26] in the following way:…”

Section: Consistent Hierarchical Decompositionmentioning

confidence: 99%

“…The basics of the theory as well as the most significant results until 2005 are published in the monograph [29]. For more recent developments and applications see [2], [8], [14], [26], and [30].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Consistent Hierarchical Decompositionmentioning

confidence: 99%

“…A measure of the quality of any hierarchical decompositions is introduced in [26] in the following way:…”

Section: Consistent Hierarchical Decompositionmentioning

confidence: 99%

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LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

Anguelov

Fabris‐Rotelli

2010

IEEE Trans. on Image Process.

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“…For detailed discussion of properties of LULU operators, as well as their proofs, check references [5], [6].…”

Section: =[I(ij-1) I(ij) I(i+1j-1) I(i+1j)]mentioning

confidence: 99%

“…Initially LULU operators were evaluated for removal of impulse noise of sequences in [4]. LULU filters are computationally suitable and theoretically simpler contrast to the median filters which are fenally considered to be the "basic" smoothers [5], [6].…”

Section: Lulu Operatorsmentioning

confidence: 99%

Comparison of LULU and Median Filter for Image Denoising

Rahmat¹,

Malik²,

Kamel³

2013

IJCEE

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Abstract-This paper presents a comparison between LULU and Median filters for impulse noise in images. Noise removal from images is always a challenging area of research. Different methods are being used for different image noises such as Wiener filter for Gaussian noise, Frost filter for speckle noise and median filter for impulse noise. LULU filters are widely being used for impulse noise too. LULU filters are nonlinear rank selector operators which are computationally more competent and the performance of the operator is straightforward to describe. The comparison between Median and LULU filters, in this paper, is performed using two different image quality metrics which are RMSE and PSNR.Index Terms-LULU filters, impulse noise, RMSE, PSNR. I. INTRODUCTIONIn the field of image processing, there are so many issues and complexities for the recovery of original data from the noise corrupted data. In general, image noise is the variation of color or brightness intensity which can be caused by different sources. In general, image sensors degrade the quality of the images. Faulty devices, troubles with the data collection procedure, and interfering natural cause can all corrupt the data. Moreover, noise can be caused by compression and transmission errors. Thus, noise removal is required and is the first step before images are analyzed. It is necessary to apply an efficient noise reduction method to compensate for such data corruption [1], [2]. Even though there are so many different methodologies in this field for noise removal, image denoising is still a big issue. Some noise filters cause blurring of the images, because in reality the nature of the noise is unknown or only known to some extent.Impulse noise results due to the malfunctioning of the image sensors and the transmission channels. It can be identified by black and white points in the image. So far, there are so many different algorithms that had been proposed to filter this type of noise such as median, switching median, weighted median, adaptive median, rank conditioned median, separable median and contra harmonic mean filter. There are different names for impulse noise which are salt and pepper as well as shot noise.In this work, we address impulse noise. Generally, median filter is used for reducing impulse noise. We compared four different LULU filters with median filter. This comparison Manuscript received April 20, 2013; revised June 28, 2013 It is extensively applied in digital image processing due to its property of protecting edges as well as at the same time eliminating noise but it causes the image to blur. But still Median filter causes significantly a smaller amount of blurring than linear smooth filters of the same size. In general, all Median filters produce reasonable results for both bipolar and unipolar impulse noise. They are nonlinear, non-idempotent smoother which is computationally less efficient than LULU. A. 1D MedianIn one dimensional arrays, median filter is given by:The Fig. 2 illustrates the median operator in filtering a s...

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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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The Discrete Pulse Transform

Cited by 13 publications

References 8 publications

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

Comparison of LULU and Median Filter for Image Denoising

Fast meteor tracking in noisy video sequences

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