Implementation

A set of model-space coordinates must be pre-selected for input into LA according to the amplitude (squared) at all coordinate locations. Only coordinates with an amplitude greater than a supplied percentage of the maximum amplitude in the model space are kept. The amplitude range of model space is then quantized from the minimum threshold to the maximum (squared) value. Coordinates are repeatedly selected for input into LA according to the number of quantum levels associated with its amplitude.

Figure  shows graphically how the data input into LA is selected from a sampled 1D function. The continuous signal is assumed to be sampled only at the tick marks on the axis and therefore has 14 amplitude values. The heavy dark line above the axis represents a threshold of approximately 25% of the maximum amplitude, shown by the uppermost dashed line. The data values have been quantized into three levels above the threshold. The dots show how many times each coordinate is selected for input into LA. The coordinate set formed from the signal is therefore $\{4,5,5,6,6,10,11,11,11,12,12,12,13,13\}$.

 

data Figure 1 Dots represent coordinate selection as a function of squared signal amplitude for input into Lloyd's Algorithm.

Assuming that the linear operator chosen for the transform is appropriate, the model space should be mostly low amplitude or zero. Therefore, the pre-selection of coordinates for LA reduces the model space by several orders of magnitude. The selected model-space coordinates are input into LA whose output is a list of optimal locations that represent the energy in the model space of the transform. These are written out to a SEP77 file and a ASCII file formatted for input into Ricksep as a picks file.