IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. ?, NO. ?, 4 Operating System Memory Limitation 32-bit Microsoft Windows XP 2GB Windows Vista 32-bit Windows XP with 3 GB boot.ini switch 3GB 32-bit Windows Vista with increaseuserva set 32-bit LINUX 3GB 64-bit Windows XP, Linux, 4GB Apple Macintosh OS X or SunSolaris running 32-bit MATLAB c ○ 64-bit Windows XP, Windows Vista, 8GB Linux, or Solaris running 64-bit MATLAB c ○ TABLE I SUMMARY OF MEMORY LIMITATION DEPENDING ON OPERATING SYSTEM. B. Convex Hull Optimization (CHO) IV. PERFORMANCE AND ACCURACY OF CHO A. Synthetic data III. PERFORMANCE AND ACCURACY OF TO and the jobs could be submitted to a grid in order to speed up the calculation process. 2) Accuracy: Due to the stochastic nature of the BPSS algorithms, it is difficult to demonstrate that two algorithms are semantically identical. In order to check that no significant loss of accuracy has been induced by the TO and especially by the change from double to single precision, several tests have been performed with different random seeds χ$_{1}$ and χ$_{2}$ , used for the initialization step of the MCMC. The sources S$_{χ}$$_{1}$ and S$_{χ}$$_{2}$ estimated with and without TO have been compared. The average correlations between S$_{χ}$$_{1}$ and S$_{χ}$$_{2}$ without TO are 0 . 9816 ± 0 . 0315 and 0 . 9818 ± 0 . 0255 with TO. These correlations are due to the stochastic approach in the Bayesian framework. Correlation values are similar, indicating that the stochastic variance has not been affected by TO. The average cross-correlation between S$_{χ}$$_{1}$ and S$_{χ}$$_{2}$ with and without TO is 0 . 9760 ± 0 . 0388 . This value is similar to the correlation due to stochastic process, demonstrating that the TO version is equivalent to the original version of BPSS. No significant differences have been observed, confirming that the TO version is equivalent to the original version of BPSS. The impact of the convex hull pixel selection pre-processing step has been evaluated on two dataset: (i) synthetic data generated from linear mixtures of known materials and (ii) an OMEGA hyperspectral image of the south polar cap of Mars as an example from Planetology. Since the BPSS with TO has been shown to be semantically equivalent to the previous version, the TO approach is used in the rest of this article. The proposed pixel selection strategy is based on the convex hull of the data matrix projection into the subspace spanned by the principal components. The convex hull of a point set is the smallest convex set that includes all the points [31]. The pixels associated to the vertices of the convex hull are selected [32] and are expected, despite their limited number, to exhibit the main spectral features of the whole dataset. In terms of abundances, this sample of points should contain the pixels with the highest abundances of the components which contribute to the investigated hyperspectral image (i.e., the purest pixels or most extreme pixels). It can be used as a concise representation of the dataset which still features the strongest spectral signatures available in the original image. This strategy is also used as a first step in endmember extraction algorithms for dimension reduction and purest pixel determination [32]–[37]. Pixel selection has the advantage, to reduce the number of mixture spectra to unmix and to enforce the sparsity of the mixing coefficients to be estimated. Note that the spectral dimension of the selected spectra is not changed, only the spatial dimension is reduced since only few pixels are selected. The convex hull selection has been implemented after seven spectral components have been selected through PCA, which turned out to be a good compromise between resource consumption and accuracy. 1) Description: Several synthetic dataset have been gen- erated by mixing a known number of endmembers, with abundances simulated with uniform distribution. The generated dataset are of size 200 × 500 pixels, which is a spatial size similar to the one of a typical hyperspectral image. For the endmembers, the following spectra have been used: H$_{2}$O and CO$_{2}$ ice spectra [38], [39] and mineral spectra from the USGS Digital Spectral Library splib06a [40], resampled to match the 128 wavelengths of OMEGA C Channel [41]. To ensure the sum-to-one constraint on the R endmember abundances, a uniform distribution on the simplex has been used following a well established scheme [42]. Synthetic dataset have been generated with 3 , 5 and 10 endmembers. Based on this method, dataset for which the maximum abundance of each single endmember was limited to a certain value ( 100% , 80% and 60% ) have also been considered. This latter data, that are called “cutoff” in the sequel, allows one to test the method efficiency face to various conditions in terms of purity of the samples (in cases where pure – to a certain degree – components occur in the dataset or not). In addition, a 3 component asymmetric dataset has been investigated, with one of the the component abundance (albite) being limited to a cutoff of 35% and the abundances of the two others (ices) not being limited. Besides, dataset with some added OMEGA-like Gaussian noise, amplified or not, have been also generated and investigated. The noise estimation on the dark currents of the All the following runs are performed on a Quad-Core AMD Opteron(tm) Processor 8384 at 2 . 7 GHz with 2 Gb of memory. 1) Performance: Computation times between the previous version of BPSS and the TO version have been compared when processing a synthetic dataset of 1052 spectra of 128 bands and 3 sources. For a run attempting at estimating 3 sources, the computation time has decreased from 1106 s (previous version) to 724 s (TO version), i.e., by a factor of about 1 . 5 . In addition, the total memory consumption is nearly half for the TO version of the algorithm.