GPU-CUDA

The unmixing of the hyperspectral imagery (HI) cube obtained from the images (of a certain area) formed by the spectral bands taken by the sensors is not done in the original HI because of its high quantity of data. In [1] the solution presented to reduce the data of HI (without losing much of the original spectral information) is band selection. The idea is to select a subset of spectral bands that sumarize most of the information in the HI. In the paper, two methods are presented, but our enfazis is the SVDSS which is a SVD (Singular Value Decomposition) based method. The SVDSS algorithm is presented below:

Algorithm: SVD Subset Selection:

1. Construct a matrix representation X of the hyperspectral image. Each column of X is constructed by stacking the columns of each single-band image.

2. Subtract the mean from each band.

3. Compute the SVD of X.

4. Compute the QR factorization with pivoting of the matrix V where V1 is formed by the first p right singular vectors of X. Save the pivot matrix P that results from this factorization.

5. Compute X1 = XP.

6. Take the first p columns of X1 as the selected bands.

My next approaches will be analizing the SVD method, and then the rest of the presented algorithm.

[1] M. Velez-Reyes, L. O. Jimenez, et. al. “Comparison of Matrix Factorization Algorithmes for Band Selection in Hyperspectral Imagery.” In Proceedings of SPIE: Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery VI, Vol. 4049, April 2000.

Remote Sensing : Understanding Hyperspectral Imaging

This is a presentation as part of my Research course.

In the paper “Algorithms for Non-negative Matrix Factorization” by D. D. Lee and H. Sebastian Seung, they analyzed two different multiplicative algorithms for NMF. The NMF (or PMF)

problem given by:

The two algorithms for NMF are based on iterative updates of W and V. To find an approximate factorization for this problem, they defined cost functions that quantify the quality of the approximation. Such a cost function can be constructed using some measure of distance between two non-negative matrices A and B. The first measure used is the square of the Euclidean distance between A and B.

The other one is referred to as “divergence” and not “distance” because it’s not symmetric as the first one.

Both measures are lower bounded by zero, and vanish if and only if A = B.

With this, they considered two alternative formulations of NMF as the following optimization problems:

Prob. 1: Minimize || V – WH ||² with respect to W and H, subject to the constraints W, H ≥ 0.

Prob. 2: Minimize D (V || WH) with respect to W and H, subject to the constraints W, H ≥ 0.

For solving problems 1 and 2, the following “multiplicative updating rules” are used:

Theorem 1 The Euclidean distance || V – WH ||² is nonincreasing under the update rules:

The Euclidean distance is invariant under these updates if and only if W and H are at a stationary point of the distance.

Theorem 2 The divergence D (V || WH) is nonincreasing under the update rules:

The divergence is invariant under these updates if and only if W and H are at a stationary point of the divergence.

Dr. Masalmah uses Theorem 1 to update the endmembers matrix in the Gauss-Seidel algorithm.

Once you open the solution on Visual Studio there are only few steps you need to succesfully run our application.  First off on line 76 and 77 you should see the following:

string input(”C:\\SourceData\\”);                                                                                                                        string endmemberFile(”C:\\SourceData\\”);

Input refers to where the hyperspectral image is located and endmemberFile refers to where the associated endmember file will be located.  Make sure you specify that the solution configuration

is set to release and hit run.

After the console screen appears, just choose which algorithm you wish to run (MAXL not implemented) and enter the name of the header of the image you wish to process along with the endmember file you wish to use ( do not forget to include the extensions of the files e.g. my_hyperpectral_image.hdr ).  Next select an appropriate size for the blocks of threads and finally enter a number of iterations.  After information about the header of the file being used is displayed the application will start processing the image.  After this process has finished the execution time (both the kernel execution time and complete execution including loading the image) is displayed.  Also where the results are stored are presented.  Next is a sample run from the application.