2009
DOI: 10.1088/1742-2132/6/3/005
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A new stabilized least-squares imaging condition

Abstract: The classical deconvolution imaging condition consists of dividing the upgoing wave field by the downgoing wave field and summing over all frequencies and sources. The least-squares imaging condition consists of summing the cross-correlation of the upgoing and downgoing wave fields over all frequencies and sources, and dividing the result by the total energy of the downgoing wave field. This procedure is more stable than using the classical imaging condition, but it still requires stabilization in zones where … Show more

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Cited by 12 publications
(15 citation statements)
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“…Since the real point-spread function of the microscope setup was lacking, the convolution kernel was estimated by a general Gaussian function (the width of the Gaussian is empirically set to 2 pixels), which is a reasonable guess in the general case of isotropic blur. The actual deconvolution was done with a damped least squares method (see [27]).…”
Section: Methodsmentioning
confidence: 99%
“…Since the real point-spread function of the microscope setup was lacking, the convolution kernel was estimated by a general Gaussian function (the width of the Gaussian is empirically set to 2 pixels), which is a reasonable guess in the general case of isotropic blur. The actual deconvolution was done with a damped least squares method (see [27]).…”
Section: Methodsmentioning
confidence: 99%
“…However, this imaging condition becomes unstable for small values of the up-going wavefield. On the one hand, least-square imaging condition involving a division of the cross-correlation of the up-going and down-going wavefields by the autocorrelation of the up-going wavefields at each extrapolation depth [4,5,17,21,22] has been shown to be robust [21]:…”
Section: Imaging Conditionmentioning
confidence: 99%
“…Wavefield separation in 3D (e.g., [15][16][17][18][19][20]) is then applied to the modeled dual-sensor data to recover the up-going and down-going pressure fields. Subsequently, the separated wavefields are extrapolated upwards in small steps, and an imaging condition [5,6,17,21,22] is applied at every step in order to recover the modeled 3D sea surface. The depth positions of the maximum image values define the sea surface.…”
Section: Introductionmentioning
confidence: 99%
“…Alternatively, the least-squares imaging condition estimates the reflection coefficient by adding crosscorrelations of the upgoing and downgoing wavefields for all frequencies and sources available and dividing it by the total energy of the downgoing wavefield ͑Schle-icher et al, Vivas et al, 2009͒. Many authors ͑among them are Vivas et al, 2009, Chattopadhyay and McMechan, 2008 have shown that the least-squares imaging condition ͑also known as a source illumination map͒ is more robust and gives an improved image.…”
Section: Imaging Conditionmentioning
confidence: 99%
“…Many authors ͑among them are Vivas et al, 2009, Chattopadhyay and McMechan, 2008 have shown that the least-squares imaging condition ͑also known as a source illumination map͒ is more robust and gives an improved image. Nevertheless, unconditional division by the autocorrelation can cause instabilities.…”
Section: Imaging Conditionmentioning
confidence: 99%