Comparative Analysis of Spectral Unmixing Algorithms Lidan Miao Nov. 10, 2005

Short Review First paper 1971 Adams 1985 Not followed up… After 2000 Use of spatial info.(AMEE) Focus on fast algorithms (bPPI,MaxD,VCA) A number of algorithms were proposed with techniques such as maximum likelihood method orthogonal subspace projection, neural network (SVM, SOM) convex geometry based (PPI) maximum entropy, MAP, Application of ICA Fuzzy theory

My Focus Unmixing System Determine # of endmembers Dimensionality reduction Endmember extraction Abundance estimation Performance evaluation PCA, VD PCA:maximum variance MNF:optimize SNR SVD:maximum power Data preprocessing Fig.1: Block diagram of unmixing system

Problem Formulation Assume a linear mixture model –Observation vector: –Material signature matrix: –Abundance fractions: –Constraints: Given observation x, we need to solve both M and s. –It is a blind source separation problem

Endmember Detection Algorithms Algorithm Supervised Vs. auto Iterative Use of spatial info Assume pure pixel Dim. reduction MVTAutoNo Yes PPISupervisedNo Yes NFINDRAutoYesNoYes MAXDAutoNo YesNo IEAAutoYesNoYesNo UFCLSAutoYesNoYesNo VCAAutoNo Yes cICAAutoYesNo AMEEAutoNoYes No ULCNNAutoYesNoYesNo

Abundance Estimation Algorithms AlgorithmImpose ANCImpose ASCIterative Use of spatial info ULSNo MLENo NCLSYesNoYesNo SCLSNoYesNo FCLSYes No OSPNo Regularized estimator No YesNo RelaxationNo Yes QPYes No LCNNYes No

State of The Art AMEE ( Automated Morphological Endmember Extraction,2002 ) –Use both spatial and spectral information in a combined manner. –Morphological operation –Dilation and erosion have the effect of selecting the most pure and most mixed pixels. VCA ( Vertex component analysis,2004 ) –Convex geometry based, no spatial information is considered.

ULCNN Modified version of LCNN –Estimates material signature matrix from image instead of using learning algorithms. –Imposes ANC and ASC in a combined manner Algorithm description Problem –Estimated abundance might not be true abundance –Computational complexity

Performance Evaluation Based on real hyperspectral data –Compare with laboratory spectra (assume no degenerate case ) –Compare derived abundance maps with published results Based on synthetic data –Provides quantitative analysis –Generation of simulated scene is important issue. Selection of spectral signatures Generation of simulated scene Unmixing algorithm Ground truth Abundance map Endmember signatures Estimated abundance Extracted endmembers

Testing Data Synthetic data –Four material signatures selected from USGS spectral library. Real hyperspectral scene –Collected by the AVIRIS sensor over Cuprite, Nevada, Fig2: Endmembers and abundance mapsFig3: Hyperspectral scene and ground truth

Unmixing Synthetic Data Visual comparison (SNR = 20dB) Fig.4: PPI Fig.5: NFINDR

Unmixing Synthetic Data (cont) Fig.6: MaxD Fig.7: IEA

Unmixing Synthetic Data (cont) Fig.8: VCA Fig.9: ULCNN

Unmixing Synthetic Data (cont) Quantitative comparison –MaxD performs the worst –When SNR>20dB, all methods present similar performance except MaxD –IEA is the best when SNR<20dB and the worst when SNR>20dB. –ULCNN is slightly better than other methods when SNR is large.

Unmixing Real Data Fig.10: Abundance map and signatures using PPI

Unmixing Real Data (cont) Fig.11: Abundance map and signatures using NFINDR

Unmixing Real Data (cont) Fig.12: Abundance map and signatures using MaxD

Unmixing Real Data (cont) Fig.13: Abundance map and signatures using IEA

Unmixing Real Data (cont) Fig.14: Abundance map and signatures using VCA

Unmixing Real Data (cont) Fig.15: Abundance map and signatures using ULCNN

Conclusion and Future Work Comparison summary –Different algorithms generate similar results under high SNR. –Some algorithms use similar ideas (IEA vs. UFCLS, MaxD vs. PPI vs. VCA ). –AMEE is just a window-based pure pixel selection. (I expect that it can only work for large target, not subpixel) Problems of existing algorithms –Assumption of pure pixel –Computational burden Future work –Consider spatial information? –Data depletion –Improve ULCNN