Principles of Digital Wiener Filtering*

Robinson, Enders A.; Treitel, Sven

doi:10.1111/j.1365-2478.1967.tb01793.x

Cited by 152 publications

(57 citation statements)

References 9 publications

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“…In the preparation stage, local slope is calculated from the DEM by fitting a second-order polynomial surface (Hurst et al, 2012) with a window radius of 3 times the horizontal resolution of the DEM, selected because it is the minimum radius needed to calculate slope with this method. The DEM may be passed through a Wiener filter (Wiener, 1949;Robinson and Treitel, 1967) to reduce noise from lidar datasets and/or degraded by averaged subsampling before the determination of slope to match complementary datasets. The effect of enabling these optional treatments is further discussed in the results section.…”

Section: Preprocessing Topographic Datamentioning

confidence: 99%

Unsupervised detection of salt marsh platforms: a topographic method

2018

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Abstract. Salt marshes filter pollutants, protect coastlines against storm surges, and sequester carbon, yet are under threat from sea level rise and anthropogenic modification. The sustained existence of the salt marsh ecosystem depends on the topographic evolution of marsh platforms. Quantifying marsh platform topography is vital for improving the management of these valuable landscapes. The determination of platform boundaries currently relies on supervised classification methods requiring near-infrared data to detect vegetation, or demands labourintensive field surveys and digitisation. We propose a novel, unsupervised method to reproducibly isolate salt marsh scarps and platforms from a digital elevation model (DEM), referred to as Topographic Identification of Platforms (TIP). Field observations and numerical models show that salt marshes mature into subhorizontal platforms delineated by subvertical scarps. Based on this premise, we identify scarps as lines of local maxima on a slope raster, then fill landmasses from the scarps upward, thus isolating mature marsh platforms. We test the TIP method using lidar-derived DEMs from six salt marshes in England with varying tidal ranges and geometries, for which topographic platforms were manually isolated from tidal flats. Agreement between manual and unsupervised classification exceeds 94 % for DEM resolutions of 1 m, with all but one site maintaining an accuracy superior to 90 % for resolutions up to 3 m. For resolutions of 1 m, platforms detected with the TIP method are comparable in surface area to digitised platforms and have similar elevation distributions. We also find that our method allows for the accurate detection of local block failures as small as 3 times the DEM resolution. Detailed inspection reveals that although tidal creeks were digitised as part of the marsh platform, unsupervised classification categorises them as part of the tidal flat, causing an increase in false negatives and overall platform perimeter. This suggests our method may benefit from combination with existing creek detection algorithms. Fallen blocks and high tidal flat portions, associated with potential pioneer zones, can also lead to differences between our method and supervised mapping. Although pioneer zones prove difficult to classify using a topographic method, we suggest that these transition areas should be considered when analysing erosion and accretion processes, particularly in the case of incipient marsh platforms. Ultimately, we have shown that unsupervised classification of marsh platforms from high-resolution topography is possible and sufficient to monitor and analyse topographic evolution.

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Section: Preprocessing Topographic Datamentioning

confidence: 99%

Unsupervised detection of salt marsh platforms: a topographic method

2018

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“…In the preparation stage, local slope is calculated from the DEM by fitting a second order polynomial surface (Hurst et al, 2012) with a circular window radius equal to three times the horizontal resolution of the DEM. The DEM may be passed through a Wiener filter (Wiener, 1949;Robinson and Treitel, 1967) to reduce noise from lidar datasets and/or degraded by averaged subsampling 20 before the determination of slope to match complementary datasets. The effect of enabling these optional treatments is further discussed in the results section.…”

Section: Preprocessing Topographic Datamentioning

confidence: 99%

Unsupervised detection of salt marsh platforms: a topographic method

Goodwin¹,

Mudd²,

Clubb³

2017

Preprint

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Abstract.Salt marshes filter pollutants, protect coastlines against storm surges, and sequester carbon, yet are under threat from sea level rise and anthropogenic modification. The productivity and even survival of salt marsh vegetation depends on the topographic evolution of marsh platforms. Quantifying marsh platform topography is vital for improving the management of these valuable landscapes. Determining platform boundaries currently relies on supervised classification methods requiring near-infrared data 5 to detect vegetation, or demands labor-intensive field surveys and digitization. We propose a novel, unsupervised method to reproducibly isolate saltmarsh scarps and platforms from a DEM, referred to as Topographic Identification of Platforms (TIP).Field observations and numerical models show that saltmarshes mature into sub-horizontal platforms delineated by sub-vertical scarps: based on this premise, we identify scarps as lines of local maxima on a slope raster, then fill landmasses from the scarps upward, thus isolating mature marsh platforms. We test the TIP method using lidar-derived DEMs from six saltmarshes in 10England with varying tidal ranges and geometries, for which topographic platforms were manually distinguished from tidal flats. Agreement between manual and unsupervised classification exceeds 94% for DEM resolutions of 1 m, with all but one sites maintaining an accuracy superior to 90% for resolutions up to 3 m. For resolutions of 1 m, platforms detected with the TIP method are comparable in surface area to digitized platforms, and have similar elevation distributions. We also find that our method allows the accurate detection of local bloc failures as small as 3 times the DEM resolution. Detailed inspection 15 reveals that although tidal creeks were digitized as part of the marsh platform, unsupervised classification categorizes them as part of the tidal flat, causing an increase in false negatives and overall platform perimeter. This suggests our method would have increased accuracy if used in combination with existing creek detection algorithms. Fallen blocs and high tidal flat portions, associated with potential pioneer zones, may also be areas of discordance between our method and supervised mapping.Although pioneer zones prove difficult to classify using a topographic method, it also suggests that these transition areas 20 should be considered when analysing erosion and accretion processes, particularly in the case of incipient marsh platforms.Ultimately, we have shown that unsupervised classification of marsh platforms from high-resolution topography is possibleand sufficient to monitor and analyze topographic evolution.

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“…where the values of fs are the filter elements of the Wiener linear prediction filter which, formulated originally in terms of continuous time series (WIENER, 1949) and also adapted to discrete time series (LEVINSON, 1949), has been applied to geophysical problems involving digital data (e.g., ROBINSON and TREITEL, 1967). The filter coefficients can be determined by solving the following set of m+1 linear simultaneous equations derived using the least-squares criterion, which minimizes the mean square error between the desired output (z) and the actual output (y) The impulse responses of the maximum Pc5 powers in the morning and afternoon sectors for 1-3 and 3-6mHz bands are shown in Fig.…”

Section: Presentation Of the Datamentioning

confidence: 99%

A possible classification of Pc5 geomagnetic pulsations into two sub-groups(Pc5A and Pc5B) based on spectral structure.

Lam

1989

J. geomagn. geoelec

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Ground magnetic data recorded in the auroral zone station at Fort Churchill, Canada (FCC) during 1985 were used to study the spectral content of Pc5 magnetic pulsations. It was found that spectral peaks tend to group into two separate bands of 1-3mHz and 3-6mHz. The power in both bands appears to be linearly related to global planetary geomagnetic activity as represented by the Ap index. While pulsations in both bands show a 27-day recurrence tendency, only intense pulsations in the low frequency band (1-3mHz) seem to recur in the morning a few days after an initial enhancement. On the other hand, pulsations in the high frequency band (3-6mHz) always have low amplitudes in the afternoon. In general, the low frequency band activity is more intense than the high frequency band activity . It is suggested that Pc5 pulsations can be classified into two sub-groups, with pulsations in the low frequency band of 1-3mHz classified as Pc5A and those in the high frequency band of 3-6mHz classified as Pc5B. Probably, Pc5A is associated with the "ringing" of the large-scale three-dimensional magnetospheric and ionospheric current systems and Pc5B is due to field line resonance. This classification scheme would provide a convenient mean of expressing and recognizing the frequency content of Pc5 events.

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Principles of Digital Wiener Filtering*

Cited by 152 publications

References 9 publications

Unsupervised detection of salt marsh platforms: a topographic method

Unsupervised detection of salt marsh platforms: a topographic method

Unsupervised detection of salt marsh platforms: a topographic method

A possible classification of Pc5 geomagnetic pulsations into two sub-groups(Pc5A and Pc5B) based on spectral structure.

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