Parameter estimation of two-dimensional moving average random fields

Francos, J.M.; Friedlander, B.

doi:10.1109/78.705427

Cited by 18 publications

(7 citation statements)

References 17 publications

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“…To compute a value inside the volume, it is sufficient to identify the appropriate slices to which the point belongs at each level of this decomposition and then to compute the value of the residual texture inside the volume. For this purpose, modelling of residual texture as a 3Dl moving average field (Francos and Friedlander, 1998;Ojeda et al, 2010) is employed with calibrating the results to the observed statistics on the boundary of the borehole. Autocorrelations of this field are evaluated by its boundary values and are used for continuation of the field inside the volume.…”

Section: Description Of the Methodsmentioning

confidence: 99%

Pseudo-outcrop Visualization of Borehole Images and Core Scans

et al. 2017

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A pseudo-outcrop visualization is demonstrated for borehole and full-diameter rock core images to augment the ubiquitous unwrapped cylinder view and thereby to assist non-specialist interpreters. The pseudo-outcrop visualization is equivalent to a nonlinear projection of the image from borehole to earth frame of reference that creates a solid volume sliced longitudinally to reveal two or more faces in which the orientations of geological features indicate what is observed in the subsurface. A proxy for grain size is used to modulate the external dimensions of the plot to mimic profiles seen in real outcrops. The volume is created from a mixture of geological boundary elements and texture, the latter being the residue after the sum of boundary elements is subtracted from the original data. In the case of measurements from wireline microresistivity tools, whose circumferential coverage is substantially less

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Section: Description Of the Methodsmentioning

confidence: 99%

Pseudo-outcrop Visualization of Borehole Images and Core Scans

et al. 2017

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“…Once the phase parameters were estimated, the random amplitude of the polynomial phase signal is obtained by multiplying the observed signal by , where is the estimated phase. Since is a homogeneous random field, its parameters can be estimated using any standard algorithm (see, e.g., [14] for the case where is an autoregressive field and [16] for the case where is a moving-average field).…”

Section: A Estimation Procedures For a Nonzero Mean Amplitude Fieldmentioning

confidence: 99%

“…Thus, closed-form formulas for the CRB are obtained by substituting into the expression for the amplitude field covariance matrix, which is expressed in terms of the amplitude field parameters. As an example, the expression for the covariance matrix of a nonsymmetric half-plane 2-D moving average field is derived in [16].…”

Section: B Derivation Of the Crbmentioning

confidence: 99%

See 1 more Smart Citation

Parameter estimation of 2-D random amplitude polynomial-phase signals

Francos

Friedlander

1999

IEEE Trans. Signal Process.

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Phase information has fundamental importance in many two-dimensional (2-D) signal processing problems. In this paper, we consider 2-D signals with random amplitude and a continuous deterministic phase. The signal is represented by a random amplitude polynomial-phase model. A computationally efficient estimation algorithm for the signal parameters is presented. The algorithm is based on the properties of the mean phase differencing operator, which is introduced and analyzed. Assuming that the signal is observed in additive white Gaussian noise and that the amplitude field is Gaussian as well, we derive the Cramér-Rao lower bound (CRB) on the error variance in jointly estimating the model parameters. The performance of the algorithm in the presence of additive white Gaussian noise is illustrated by numerical examples and compared with the CRB.

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“…Many problems are related to not only the one dimensional (1-D) stochastic systems but also the two dimensional (2-D) stochastic systems since it is important for many engineering problems to study the stochastic 2-D systems, such as the signal processing, the image processing, the azimuth estimation of planar surface, the uniform texture processing, analysis of earthquake wave and the soil mechanics and so on [16][17][18][19][20][21][22][23][24][25][26][27][28]. For example, we have the 2-D Wold-like decomposition in the uniform texture processing [10].…”

Section: Introductionmentioning

confidence: 99%