IGARSS 2011, Vancouver, Canada

HYPERSPECTRAL UNMIXING USING A NOVEL CONVERSION MODEL

Fereidoun A. Mianji, Member, IEEE, Shuang Zhou, Member, IEEE,

Ye Zhang, Member, IEEE

Presentation by: Shuang Zhou

School of Electronics and Information Technology

Harbin Institute of Technology, Harbin, China

Hyperspectral Unmixing Using a Novel Conversion Model

1. Introduction

2. Linear Mixture Model (LMM) and Mean-Based Algorithms for Unmixing

3. Structure of the Proposed Approach

4. Data and Experimental Design

5. Experiments with an Simulated Image made of Real Hyperspectral Data

6. Experiments with Real Hyperspectral Image with Implanted Mixed Pixels

7. Experiments with Real Hyperspectral image with Many Endmembers

8. Discussion and Conclusion on the Proposed Approach

1. Introduction

The precise information obtained by unmixing is very helpful in the other applications such as edge sharpening, area estimation, subpixel level target detection, etc.

Fig. 1.1. Spectral variability (a) and mixed-pixel interference (b).

1. Introduction

Continue

Unmixing generally refers to a process which includes two steps:

1) an endmember extraction algorithm (EEA) to define the pure (or purest) pixels in the scene as the endmembers;

2) an endmember abundance quantification algorithm (inversion step) to define the contribution of different endmembers in each pixel.

2. Linear Mixture Model (LMM) and Mean-Based Algorithms for Unmixing

There are two main models to deal with an unmixing problem:

1) the macroscopic mixture model which models a mixed pixel as a linear combination of materials with relative concentrations (LMM),

2) the intimate spectral mixture model which proposes a nonlinear mixing model of materials.

Two main constraints which are often imposed in constrained Linear Spectral Mixture Analysis(LSMA) are

a) abundance sum-to-one constraint (ASC) b) abundance nonnegativity constraint (ANC).

2. Linear Mixture Model (LMM) and Mean-Based Algorithms for Unmixing

Mean-Based Algorithms for Unmixing

Fully constrained least squares (FCLS) algorithm can efficiently meet both abundance constraints and is optimal in terms of least squares error (LSE).

FCLS assumes that the spectra for all endmembers in the scene are available and unique.

Therefore, it is optimized for ideal cases where the information of the pure pixels are a priori known, and where there is no spectral variability in the scene.

2. Linear Mixture Model (LMM) and Mean-Based Algorithms for Unmixing

Limitations of Mean-Based Algorithms

Two main obstacles for a successful LSMA-based method include:

1) the necessary a priori knowledge of the pure signatures of materials present in the image scene is usually not available.

2) these signatures rarely represent pure spectral signatures of all materials in the image scene in practical situations due to the endmember spectral variability.

The main resulting drawback with the mean-based unmixing algorithms is being limited to the mean spectra of each endmemeber. They ignore the statistics associated with the training samples.

3. Structure of the Proposed Approach

The rational behind the proposed method is exploiting the statistical variations of the training samples extracted from the scene rather than being only limited to their mean vectors.The central idea of the proposed method is converting the abundance quantification problem (inversion step) into a classification problem through assigning a set of artificial class labels to different possible abundances (0%-100%) of an endmember in a pixel.To realize the proposed method, an SVM approach is applied. Thus, the proposed method is referred to as unmixing-to-classification conversion model with SVM and is noted as uccm-SVM.

The well known one-against-all (OAA) strategy with parallel architecture is adopted in uccm-SVM for the multiendmember unmixing tasks.

3. Structure of the Proposed Approach

uccm-SVM

3. Structure of the Proposed Approach

uccm-SVM

Fig. 3.1. The layout and process flow of uccm-SVM designed for unmixing with a resolution of 1%.

Yes No

SVM training

SVM1: trained for 0% of “one”

SVM101: trained for 100% of “one”

SVM2: trained for 1% of “one”

1- Designating sample set i as “one” (initialize with i=1) 2- Making synthetic classes using remaining p-1 training sample sets (“rest”)

Quantification result for “one” in all pixels (fractional image)

…

p endmembers: p training sample sets including extracted pure pixel vectors Image Pixels

i>p ? Endmember fractions

rescaling to unity

Next i (endmember)

4. Data and Experimental Design

The hyperspectral data used to validate the proposed unmixing method include:

a) San Diego data for making a simulated image

b) Indian Pines data as real image with implanted compositions (mixed pixels)

c) The University of Pavia data set as a multiendmemebr real image.

5. Experiments with a Simulated Image Made of Real Hyperspectral Data

Using 30 randomly selected pixels from three classes of San Diego image, sand, concrete, and roof, we simulated a hyperspectral image.

We construct the background with sand and concrete and we use roof to implant the targets.

A: sandB: concreteC: roof

The simulated image is a 1530 pixel vectors (a 51 by 30 hyperspectral image)

Fig. 5.1. The simulated image constructed using samples from 3 classes of San Diego.

5. Experiments with a Simulated Image Made of Real Hyperspectral Data

Results

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 151 301 451 601 751 901 1051 1201 1351 1501

Pixel number

Abun

danc

e

Fig. 5.2 Unmixing result for roof by FCLS.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1 151 301 451 601 751 901 1051 1201 1351 1501

Pixel number

Abun

danc

e

Fig. 5.3. Unmixing result for roof by uccm-SVM.

We expect to see only 3 peaks, with the amplitue&width of 0.1&15, 0.2&10, and 0.3&5 starting in pixel locations in 300, 750, and 1200, respectively.

As can be seen, our method presents a much better result.

5. Experiments with a Simulated Image Made of Real Hyperspectral Data

Results

From the table below it is clear that the proposed method is superior to the FCLS algorithm.

Table 5.1 Comparison of uccm_SVM with FCLS in terms of average square error and computational time.

Technique Average square error (%) Proccessing time (s)

Sand Concrete Roof Training Test

FCLS 4.92 12.78 4.82 N/A 7.5

Uccm-SVM 1.19 1.29 0.0331 158.2 27.7

6. Experiments with Real Hyperspectral Image with Implanted Mixed Pixels

Regions of Interest covering corn-notill & soybean-notill (ROI1) and wheat & corn-min (ROI2) were selected.

Fig. 6.1 Two chosen ROIs on Indian Pine hyperspectral image for experiments.

6. Experiments with Real Hyperspectral Image with Implanted Mixed Pixels

Implanting the Border with Mixture of Neighboring Pixels

ROI1 is a 21 by 8 pixel area covering two landcovers, corn-notill and soybean-notill.

We implanted the pixels of the border line with a varying mixture of the two endmembers using the neighboring pixels.

To unmix the implanted pixel vectors, 21 different pixel vectors from the other areas of each landcover class were randomly chosen as the training samples.

Fig. 6.2. Implanting a varying mixture of neighboring pixel vectors in the border line between two adjacent landcover classes

6. Experiments with Real Hyperspectral Image with Implanted Mixed Pixels

Unmixing the Mixed Pixels Implanted in ROI1

Fig. 6.3. (from left to right) True abundance of corn-notill in the border line of ROI1, unmixing results by FCLS, and unmixing result by uccm-SVM.

Table 6.1. Comparison of uccm-SVM with FCLS in terms of average square error and computational time for Indian Pine ROI1.

Technique Average square error

(%)

Training time(s)

Test time (s)

FCLS 17.01 N/A 0.44

Uccm-SVM 3.16 85.5 0.39

7. Experiments with Real Hyperspectral image with Many Endmembers

1- Using all the labeled training and test samples, and a maximum likelihood classifier, we classified the image.

2- With a visual and spectral comparison to the result of some other techniques (e.g. SVM), we insured of the high accuracy of our classification result.

3- Then, we downsampled the image by a 3x3 mean filter to obtain an image (203x113) with a priori known compositions of endmembers.

4- We unmixed the downsampled image by FCLS and uccm-SVM with very low, low, and medium number of training samples (from pure samples of the downsampled image).

Fig. 7.1. The University of Pavia data set.

7. Experiments with Real Hyperspectral Image with Many Endmembers

Results

# Training samples Method

Average square errors (ASE) for classes and also average ASE (%) Time (s)

1 2 3 4 5 6 7 8 9 Ave.Train Test

2FCLS 10.43 8.51 4.04 6.93 1.17 6.01 2.17 3.10 7.75 5.57 - 223.4

uccm-SVM 6.55 13.29 4.45 6.77 0.95 6.15 2.15 2.45 0.69 4.84 0.45 15.5

10FCLS 8.80 8.24 3.27 5.13 0.91 6.43 2.41 2.81 4.74 4.75 - 239.8

uccm-SVM 5.15 6.60 1.61 6.07 0.82 5.00 1.84 1.89 1.22 3.35 6.9 94.3

100FCLS 8.47 8.23 2.41 50.1 0.87 6.73 2.23 2.78 3.32 4.45 - 186.3

uccm-SVM 3.89 3.78 1.23 4.12 0.98 3.45 1.16 1.44 1.09 2.35 511.1 985.2

ASE: uccm-SVM performs better than FCLS on majority of single classes and in ASE average over all sizes of training sets.

Computationally: uccm-SVM is faster than FCLS for low number of training samples and slower for higher numbers.

Table. 7.1. Average square error (ASE) for the obtained fractional images using FCLS and uccm-SVM for unmixing of The University of Pavia data set (downsampled).

8. Discussion and Conclusion on the Proposed Approach

A new learning-based unmixing technique through SVM is proposed in this paper. An unmixing-to-classification conversion model which transfers the unmixing task into a classification problem is the main premise of the method.

Abundance quantification for each endmember is performed in a one-against-rest framework using a number of artificially made classes.

Uccm-SVM considerably outperformed the mean-based technique, FCLS algorithm.

The next step would be improving the performance of the proposed method while reducing its computational burden for big sizes of training sets.

Thanks For Your Attention

Shuang ZhouSchool of Electronics and Information Technology

Harbin Institute of Technology, Harbin, China