Hyperspectral Data Processing: Algorithm Design and Analysis

8.2 Successive N-FINDR (SC N-FINDR)

As noted in the s-SC IN-FINDR in Chapter 7, a major issue in its implementation is computational cost that is expected to be very high. In order to mitigate this problem, a sequential version of s-SC IN-FINDR developed in Section 7.2.3.3 can be derived by replacing simultaneous s endmembers carried out in step 5 of the s-SC IN-FINDR with successive p endmember replacements to achieve more computational efficiency at the expense of optimality. The resulting sequential version of p-SC IN-FINDR is referred to as SuCcessive N-FINDR (SC N-FINDR).

Successive N-FINDR (SC N-FINDR)

1. Preprocessing:

a. Let p be the number of endmembers required to generate.

b. Apply a DR transform such as MNF to reduce the data dimensionality from L to p–1, where L is the total number of spectral bands.

2. Initialization:

Let be a set of initial vectors randomly generated from the data.

3. For , find which yields the maximum volume of defined by (7.3) over all sample vectors r, while fixing other endmembers with and with . That is,

(8.1)

The major difference between ...