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https://github.com/etienne-monier/lib-unmixing

Python3 library for common unmixing functions
https://github.com/etienne-monier/lib-unmixing

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Python3 library for common unmixing functions

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# A Python3 library for basic unmixing functions



## Functions list



The three functions implemented in this library are:

- **[Vertex Component Analysis (VCA)](#vca-function)**. Related article is J. Nascimento and J. Dias, "Vertex Component Analysis: A fast algorithm to unmix hyperspectral data", IEEE Transactions on Geoscience and Remote Sensing, vol. 43, no. 4, pp. 898-910, 2005. 

- **[Simplex Identification via Split Augmented Lagrangian (SISAL)](#sisal-function)**. Related article is J. Bioucas-Dias, "A variable splitting augmented Lagrangian approach to linear spectral unmixing", in First IEEE GRSS Workshop on Hyperspectral Image and Signal Processing-WHISPERS'2009, Grenoble, France, 2009. 

- **[Sparse Unmixing via variable Splitting and Augmented Lagrangian methods(SUNSAL)](#sunsal-function)**. Related article is Bioucas-Dias, J. M., & Figueiredo, M. A., "Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing." in Workshop in Hyperspectral Image and Signal Processing: Evolution in Remote Sensing (WHISPERS), 2010  (pp. 1-4).



Matlab versions of these codes are available in the [Jose Bioucas Dias website](http://www.lx.it.pt/~bioucas/code.htm).



## VCA function



This function were translated by Adrien Lagrange ([view his github page](https://github.com/Laadr)).



### Usage



```

Ae, indice, Yp = vca(Y,R,verbose = True,snr_input = 0)

```



### Input variables



Y - matrix with dimensions L(channels) x N(pixels) each pixel is a linear mixture of R endmembers signatures Y = M x s, where 

- s = gamma x alpha

- gamma is a illumination perturbation factor and

- alpha are the abundance fractions of each endmember.

      

R - positive integer number of endmembers in the scene

    

### Output variables



Ae     - estimated mixing matrix (endmembers signatures)



indice - pixels that were chosen to be the most pure



Yp     - Data matrix Y projected.   

    

### Optional parameters

snr_input - (float) signal to noise ratio (dB)



v         - [True | False]

    

### Author, license and info



Author: Adrien Lagrange ([email protected])



This code is a translation of a matlab code provided by Jose Nascimento ([email protected]) and Jose Bioucas Dias ([email protected]) available at http://www.lx.it.pt/~bioucas/code.htm under the GNU General Public License 2.0.



Translation of last version at 22-February-2018 (Matlab version 2.1 (7-May-2004)).



## SISAL function



### Usage



```

M,Up,my,sing_values = sisal(Y,p,**kwargs)

```



### Description



Simplex identification via split augmented Lagrangian (SISAL) estimates the vertices  M={m_1,...m_p} of the (p-1)-dimensional simplex of minimum volume containing the vectors [y_1,...y_N], under the assumption that y_i belongs to a (p-1)  dimensional affine set.

    

For details see José M. Bioucas-Dias, "A variable splitting augmented lagrangian approach to linear spectral unmixing", First IEEE GRSS Workshop on Hyperspectral Image and Signal Processing - WHISPERS, 2009. ([http://arxiv.org/abs/0904.4635v1](http://arxiv.org/abs/0904.4635v1))



### Input

    

Y - matrix with dimension  L(channels) x N(pixels). Each pixel is a linear mixture of p endmembers signatures Y = M*x + noise.



p - number of independent columns of M. Therefore, M spans a (p-1)-dimensional affine set. p is the number of endmembers.

    

### Optional input

    

mm_iters - Maximum number of constrained quadratic programs. Default: 80

    

tau - Regularization parameter in the problem



```

             Q^* = arg min_Q  -\log abs(det(Q)) + tau*|| Q*yp ||_h

                   subject to np.ones((1,p))*Q=mq

             where mq = ones(1,N)*yp'inv(yp*yp) and ||x||_h is the "hinge" induced norm.

```

       Default: 1

    

mu - Augmented Lagrange regularization parameter. Default: 1

    

spherize - {True, False} Applies a spherization step to data such that the spherized data spans over the same range along any axis. Default: True

    

tolf - Tolerance for the termination test (relative variation of f(Q)). Default: 1e-2

    

M0 - Initial M, dimension L x p. Defaults is given by the VCA algorithm.

    

verbose - {0,1,2,3} 

- 0 - work silently

- 1 - display simplex volume

- 2 - display figures

- 3 - display SISAL information 

- 4 - display SISAL information and figures

Default: 1

    

### Output 

    

M - estimated endmember signature matrix L x p

    

Up - isometric matrix spanning the same subspace as M, imension is L x p

   

my - mean value of Y

    

sing_values - (p-1) eigenvalues of Cy = (y-my)*(y-my)/N. The dynamic range of these eigenvalues gives an idea of the  difficulty of the underlying problem

    

### Note 



The identified affine set is given by



```

{z\in R^p : z=Up(:,1:p-1)*a+my, a\in R^(p-1)}

```    

    

### Author, license and info



Author: Etienne Monier ([email protected])

    

This code is a translation of a matlab code provided by Jose Nascimento ([email protected]) and Jose Bioucas Dias ([email protected]) available at http://www.lx.it.pt/~bioucas/code.htm under the GNU General Public License 2.0.



Translation of last version at 20-April-2018 (Matlab version 2.1 (7-May-2004))



## SUNSAL function



### Usage

x = sunsal_v2(M,Y,**kwargs)

        

### Description 

        

SUNSAL (sparse unmixing via variable splitting and augmented Lagrangian methods) algorithm implementation. Accepted constraints are:

- 1. Positivity:  X >= 0

- 2. Addone:      np.sum(X,axis=0) = np.ones(N)

    

For details see J. Bioucas-Dias and M. Figueiredo, “Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing”, in 2nd  IEEE GRSS Workshop on Hyperspectral Image and Signal Processing-WHISPERS'2010, Raykjavik, Iceland, 2010.

    

### Input 

    

M - endmember signature matrix with dimensions L(channels) x p(endmembers)

    

Y - matrix with dimensions L(channels) x N(pixels). Each pixel is a linear mixture of p endmembers signatures

    

### Optional input 

    

al_iters - Minimum number of augmented Lagrangian iterations. Default: 100

    

lambda_p - regularization parameter. lambda is either a scalar or a vector with N components (one per column of x). Default: 0

    

positivity - {True, False} Enforces the positivity constraint. Default: False

    

addone - {True, False} Enforces the addone constraint. Default: False

    

tol - tolerance for the primal and  dual residuals. Default: 1e-4

    

verbose = {True, False}

- False - work silently

- True - display iteration info

Default: True

    

### Output 



X - estimated abundance matrix of size p x N

    

### Author, license and info



Author: Etienne Monier ([email protected])

    

This code is a translation of a matlab code provided by Jose Nascimento ([email protected]) and Jose Bioucas Dias ([email protected]) available at http://www.lx.it.pt/~bioucas/code.htm under the GNU General Public License 2.0.



Translation of last version at 20-April-2018 (Matlab version 2.1 (7-May-2004))



## Authors



Software translated from matlab to python by Etienne Monier ([email protected]), 2018.



Initial matlab author: Jose Bioucas-Dias, 2009



## License



This code is distributed under the terms of the GNU General Public License 2.0.