LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

Anguelov, Roumen; Fabris‐Rotelli, Inger

doi:10.1109/tip.2010.2050639

Cited by 17 publications

(19 citation statements)

References 35 publications

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“…The consistency of signal decomposition by LULU operators enables a multiresolution analysis of a signal. The discrete pulse transform (DPT; Anguelov & Fabris‐Rotelli, ; Rohwer, , chapter 8) enables a decomposition of x in to constituent signals D n x , representing resolution component “n” with block pulses of width n :

D_{n} = C_{n - 1} x - C_{n} x, n \geq 1 .

…”

Section: Lulu Operatorsmentioning

confidence: 99%

Demonstrating the Use of a Class of Min‐Max Smoothers for D Region Event Detection in Narrow Band VLF Phase

Lotz

Clilverd

2019

Radio Science

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This paper describes the use of a class of nonlinear smoothers for the identification of interesting phenomena in narrow band very low frequency (VLF) transmission phase caused by perturbation events in the D region of the ionosphere. The LULU smoothers, named for their smoothing of upward (L) and downward (U) peaks in a signal, usually used for image processing tasks, are described, and examples are shown where these operators are used to automatically isolate and identify features in the phase of narrow band transmissions received at high and high‐middle latitudes (Antarctica and Marion Island, respectively). Identification of solar flare events, electromagnetic ion cyclotron wave precipitation, and substorm injection events are demonstrated, showing the potential for this technique to be used for space weather monitoring.

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D_{n} = C_{n - 1} x - C_{n} x, n \geq 1 .

…”

Section: Lulu Operatorsmentioning

confidence: 99%

Demonstrating the Use of a Class of Min‐Max Smoothers for D Region Event Detection in Narrow Band VLF Phase

Lotz

Clilverd

2019

Radio Science

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“…1D-LULU LULU filters the signal by performing a simple assessment method to remove the local peaks and valleys. For a particular bi-infinite sequence ξ = (ξ i ) iЄZ , the one dimensional LULU operators are defined as follows [9]: For more explanation about 2D processing using LULU operators, an example is shown as follows. We segment the neighbors of the pixel I(i,j) to four different parts as shown in (5) to (8) and Fig.…”

Section: Lulu Operatorsmentioning

confidence: 99%

“…LULU filters are being widely used in statistics as shown in [7] and recently it is implemented in object extraction of images by applying DPT method in [6], [8] and [9]. They are local, non-linear filters used for the elimination of salt and pepper noise.…”

Section: Lulu Operatorsmentioning

confidence: 99%

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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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“…In image processing, DPT is being used to separate the objects of the image by separating the pulses of different objects in the image. For applying DPT on images, we need to use LULU operators on multidimensional arrays and even with applying LULU operators, the essential property of DPT which is total variation preservation will get more highlighted [7]. Generally, DPT can plots the unlimited signals such as ȟ = (..., ȟ 1 , ȟ 0 , ȟ 1 , ȟ 2 , ...) onto an infinite vector DPT(ȟ) = (D 1 (ȟ),D 2 (ȟ), ...) (6) where D n (ȟ) refers to different pulses or different orders of LULU filters.…”

Section: The Discrete Pulse Transformmentioning

confidence: 99%

3-D content generation using optical passive reflective techniques

Rahmat

Malik

Kamel

2011

2011 IEEE 15th International Symposium on Consumer Electronics (ISCE)

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With the arrival of High Definition Television (HDTV), the TV technology is heading towards 3DTV. Evolution of 3DTV requires the facility of capturing and analyzing the multi-view images and compressing and transmitting massive volume of data through the communication channel. The most sever issue in 3D shape extraction is the roughness of the surfaces. Image focusing is a dominant method of reconstructing the 3D shapes of the surfaces. This paper review the different object oriented filtering methods in 3D content generation based on SFF (Shape from Focus) concept and compare between them. A new method in shape recovery based on Discrete Pulse Transform is also presented and analyzed.

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LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

Cited by 17 publications

References 35 publications

Demonstrating the Use of a Class of Min‐Max Smoothers for D Region Event Detection in Narrow Band VLF Phase

Demonstrating the Use of a Class of Min‐Max Smoothers for D Region Event Detection in Narrow Band VLF Phase

Comparison of LULU and Median Filter for Image Denoising

3-D content generation using optical passive reflective techniques

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