Comparative Analysis of Spectral Unmixing Algorithms Lidan Miao

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

Short Review First paper 1971 Not followed up… Adams 1985 After 2000 Use of spatial info. (AMEE) Focus on fast algorithms (b. PPI, Max. D, VCA) 1985 -2000 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

Unmixing System My Focus Data preprocessing Determine # of endmembers PCA, VD Dimensionality reduction PCA: maximum variance MNF: optimize SNR SVD: maximum power Endmember extraction Abundance estimation Performance evaluation 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 MVT Auto No No No Yes PPI Supervised No No Yes NFINDR Auto Yes No Yes MAXD Auto No No Yes No IEA Auto Yes No UFCLS Auto Yes No VCA Auto No No Yes c. ICA Auto Yes No No No AMEE Auto No Yes No ULCNN Auto Yes No

Abundance Estimation Algorithms Algorithm Impose ANC Impose ASC Iterative Use of spatial info ULS No No MLE No No NCLS Yes No SCLS No Yes No No FCLS Yes Yes No OSP No No Regularized estimator No No Yes No Relaxation No No Yes QP Yes Yes No LCNN Yes Yes 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 Ground truth Abundance Endmember map signatures Unmixing algorithm 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, 1997. Fig 2: Endmembers and abundance maps Fig 3: Hyperspectral scene and ground truth

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

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

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

Unmixing Synthetic Data (cont) • Quantitative comparison – Max. D performs the worst – When SNR>20 d. B, all methods present similar performance except Max. D – IEA is the best when SNR<20 d. B and the worst when SNR>20 d. B. – 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 Max. D

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, Max. D 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