Hyperspectral Data Processing: Algorithm Design and Analysis

3.5 Real Data-Based ROC Analysis

In real applications only a limited number of samples are available for data analysis, referred to as the power of the test. In this case, the data sample pool is generally not sufficiently large to constitute reliable statistics that can be used to characterize the LRT Λ(r) implemented by a detector. Under such a circumstance there is no effective means of producing Λ(r) and the ROC analysis must be carried out with data samples rather than statistics, p₀(r) and p₁(r).

3.5.1 How to Generate ROC Curves from Real Data

In what follows, we define

N = total number of data samples used for a particular detection method (technique)

N_signal = total number of data samples with presence of a signal (according to ground truth)

N_no-signal = total number of data samples with absence of a signal (according to ground truth)

N_D = total number of data samples with presence of a signal which is actually detected by the method

N_F = total number of data samples with absence of a signal, but claimed to have an signal detected by the method

N_M = total number of data samples with presence of a signal which is not detected by the method

N_TN = total number of data samples with presence of a signal and also claimed to have no signal detected by the method.

False alarm or false positive rate/probability is defined by

(3.10)

False negative or miss rate/probability:

(3.11) ...