Multibeam Background Removal

This operator calculates a statistic from a window of pings around a current ping. The statistic captures the static background elements present in the data. With a Minimum SNR value as a threshold, the algorithm then subtracts that background statistic from the current ping, leaving the data without the static background.

The Multibeam Background Removal page specifies settings for the window, statsitic and threshold.

Echoview accepts a single operand of the following data types as input:

Notes:

Settings

The Multibeam Background Removal Variable Properties dialog box pages include (common) Variable Properties pages and these operator pages:

Operands page

(Multibeam) Background removal page

Setting

Description

Input data

Window size (pings)

The background statistic is calculated from a window of pings around the current ping. Window size is restricted to odd numbers.

Notes:

  • Calculations are faster for a smaller window radius.
  • Pings at the start or end of the variable have less pings from which to calculate a Window statistic.

Background object algorithm

Algorithm

Algorithms to characterize the background object. Algorithms include:

Note: The Mean algorithm is computationally the fastest. The Median and Nth percentile algorithms assess ordered lists and are computationally slower. For more information refer to Multibeam background removal algorithms.

Percentile

Specifies the Nth Percentile for the Percentile algorithm.

Threshold

Minimum SNR (dB)

Specifies the minimum signal to noise (background statistic in this operator) ratio. If the current sample Sv value divided by the background statistic is less than or equal to Minimum SNR value, the statistic is subtracted from the current ping.

The default value is 10 dB.

Algorithm

The Multibeam background removal operator uses a window around a ping to calculate a statistic representing the static background. A static background object could be rocks, man made artifacts, fixed but slowly moving vegetation, acoustic artifacts etc. When the ratio of the sample Sv value and the background statistic is less than or equal to Minimum SNR value, the background statistic is subtracted from the operand sample and output to the virtual variable.

Notes:

Algorithms

Multibeam samples

The diagram depicts samples, beams and pings in a multibeam echogram. The (same) sample in successive pings is shaded blue.

Given the equations for Sv and SNRdB:

Multibeam background removal fundamental equations

The Multibeam background removal operator assesses operand samples in a window of pings and outputs (to the virtual variable) sample values for the central ping of the window. The operator uses a sample statistic to represent the static background, where the static background is deemed to be unwanted "noise". The criteria to assess acceptable samples and unacceptable noise is given by:

SNR re-expressed

Using logarithm and exponent rules and working in the linear domain this expression becomes:

Multibeam background removal criteria in linear domain

If True then:

If criteria is true then

If False then:

If criteria is false then

Sv
=

the multibeam sample value in the dB domain.

sv
=

the multibeam sample value in the linear domain.

SNRdB
=

the Minimum SNR (dB) value specified on the Background Removal page of the Variable Properties dialog box

SampleLinear

 

 

=

an operand sample value, in the linear domain, of the central ping in the sliding ping window of the Multibeam background removal operator.

The ping window is specified as Window size on the Background Removal page of the Variable Properties dialog box

The operand sample value in the dB domain is called SvSample.

BackgroundStatisticLinear

 

=

the statistic value, in the linear domain, that represents the background. The statistic looks at a sample across a window of pings.

The ping window is specified as Window size on the Background Removal page of the Variable Properties dialog box

The statistic value in the dB domain is called SvBackgroundStatistic.

The following statistics are available:

Sv,I,J
=

the Multibeam background removal virtual variable sample J in ping I. Where I is the central ping in the sliding window in the operand.

SvSample,I,J
=

the operand sample J in ping I. Where I is the central ping in the sliding window in the operand.

Mean

SvBackgroundStatistic calculates the dB value of the mean statistic for sample Jfor the Multibeam background removal sliding windowas:

SvBackgroundStatistic = 10 log10 (mean_sv)

Multibeam background removal mean

Where:

Sv,I,J =

Operand sample value (dB) for sample J in ping I in the sliding window.

n
=

n is specified as Window size on the Background Removal page of the Variable Properties dialog box

Median

SvBackgroundStatistic calculatesthe dB value of median statistic for sample J for the Multibeam background removal sliding windowas:

SvBackgroundStatistic =   Wk       if N is odd

Where:

Wk = the value of sample k in the list W — (defined below)
k
= Floor N on 2*
N
=

the number of samples in the list W.

N is specified as Window size on the Background Removal page of the Variable Properties dialog box

W
=

the ordered list of operand sample values (dB) xi, j for all pings in the sliding window:

(W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

Nth Percentile

SvBackgroundStatistic calculates the dB value of the Nth Percentile score for sample J for the Multibeam background removal sliding window as:

SvBackgroundStatistic = Wk + (Wk+1 - Wk) (k' - k)

Where:

Wk = the value of sample k in the list W — (defined below)
k
= Floor k dash*
k'
= N x P/100
N
=

the number of samples in the list W.

N is specified as Window size on the Background Removal page of the Variable Properties dialog box

P
= the Percentile entered on the Background Removal page of the Variable Properties dialog box
W
=

the ordered list of sample values (dB) xi, j for all pings in the sliding window:

(W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1

Footnote:

*Floor function Floor x, gives the largest integer less than or equal to x.

See also

About virtual variables
Operator licensing in Echoview