Discrete Pulse Transform of Images

Anguelov, Roumen; Fabris‐Rotelli, Inger

doi:10.1007/978-3-540-69905-7_1

Cited by 5 publications

(4 citation statements)

References 10 publications

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“…(9) where D n (j) is a sequence consisting of a wellseparated discrete block pulses with the support n (the set of non-zero values of a function is called the function's support). 8 As shown in equation (9), DPT of a sequence is a composition of DPT for different orders (pulses), and we shall calculate D 1 , D 2 , …, D n , one by one to be able to reconstruct the signal. D n is a sequence consisting of block pulses with the support n, for instance, it only compares the values of any position with n before and n after, and removes the pulses with width size n.…”

Section: D Dptmentioning

confidence: 99%

An overview of LULU operators and discrete pulse transform for image analysis

Rahmat

Malik

Faye

et al. 2013

The Imaging Science Journal

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This paper presents an overview of LULU operators and discrete pulse transform (DPT). Data extraction from signals and images is a popular area of research. Different methods are being used for data extraction such as different types of linear and nonlinear operators. LULU operator is one of the most important rank selector nonlinear filters used for data analysis which is widely being used for signal analysis, especially in impulse noise filtering. It is computationally more efficient and the behaviour of the operator is simple to describe. Based on the composition of different orders of LULU operators, DPT on multi-resolution is defined, which describes the sequences into pulses with different magnitudes. DPT allows a multi-resolution measure of roughness of images and sequences. It is a powerful technique for image analysis and can also be used for the estimation of standard deviation of a random distribution.

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Section: D Dptmentioning

confidence: 99%

An overview of LULU operators and discrete pulse transform for image analysis

Rahmat

Malik

Faye

et al. 2013

The Imaging Science Journal

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“…where the sets V ni = supp(φ ni ), i = 1, ..., γ − (n), are all the local minimum sets of f of size n and satisfy (2). Therefore…”

Section: The Lemmamentioning

confidence: 99%

“…This can be used for example in removing noise or extracting features of interest. See [12] for additional examples. Fig.…”

Section: Dpt Of Imagesmentioning

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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“…The aim of this work is to illustrate the use of a class of nonlinear smoothers to highlight features in narrowband VLF signal phase that are of interest to the VLF and broader space physics community. These "LULU" operators are a class of minimum-maximum smoothers designed by Rohwer (2005) that are mostly used in image processing applications (e.g., Anguelov & Fabris-Rotelli, 2008;2010;Jankowitz, 2007). To the best of our knowledge, these operators have not been used in geophysics applications before.…”

Section: Introductionmentioning

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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Discrete Pulse Transform of Images

Cited by 5 publications

References 10 publications

An overview of LULU operators and discrete pulse transform for image analysis

An overview of LULU operators and discrete pulse transform for image analysis

LULU Operators and Discrete Pulse Transform for Multidimensional Arrays

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

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