Hyperspectral image processing constrained minimum variance (the LCMV) the line --- linearly constrained minimum variance

linearly constrained minimum variance linear constrained minimum variance (the LCMV)

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This article refers to the following documents. See you can also refer
1.Real-Time Detection and Processing algorithms for target ...
Link .
2.Chein the I-Chang-Hyperspectral the Data Exploitation_ Th
3. hyper-spectral target detection techniques of image processing (CEM algorithm)

A study on the orthogonal projection method Link .
This learning section linearly constrained minimum variance linear constrained minimum variance (the LCMV)

1.1 Algorithm summary

1. LCMV method requires only the signals of interest target
2. Using a sample covariance matrix minimize interference signals

1.2 Objectives and algorithm steps

1. Design of a FIR linear classifier
2. With a L W is the vector dimension to minimum output energy ( L is the number of channels of the image)
3. Of course, energy can not be infinitely small, to meet certain requirements

2 algorithm content

2.1 Symbol Description

FIR subject filter is a vector of dimension L: W (. 1 L dimension)
Of course, this W to meet certain conditions, ie:

where
T - K L dimension of the matrix (k targets of interest, L channel number)
C --1 * K dimension vector, vector constraint for each target of interest

2.2

In 1.2, we say that minimizing energy, then the energy function

(2) is a channel to each pixel component is multiplied by the weights, the use of weights to achieve the object of the compression is not the signal of interest.
Then, in order to prevent the number (or the impact of the number of samples N) is divided by N, the number of positive and negative effects to prevent, squared. Get the (3)

2.3

As a result, I put the original question of a constraint to minimize the problem. I.e., (4). Where all symbols are described, see 2.1

solution to give (. 5) W *
to this, the end of the algorithm LCMV.

3, CEM (LCMV special case)

In Section 2.3, (4) of T is the set target signal of interest, if we are interested in for a signal, LCMV degenerates only for CEM.