Hyperspectral Image Data

Transcription

1 CEE 615: Digital Image Processing Lab 11: Hyperspectral Noise p. 1 Hyperspectral Image Data Files needed for this exercise (all are standard ENVI files): Images: cup95eff.int &.hdr Spectral Library: jpl1.sli &.hdr Tasks: Use the MNF transform to a) remove residual noise from the spectral data and b) provide a convenient mechanism for selecting prototype spectra. The minimum (or maximum) noise fraction (MNF) transformation is used to isolate noise from signal in the data set. The MNF would be followed by an inverse transform to produce spectral images that are relatively noise free but retain most, if not all, of the spectral detail. 1,2 The resulting data will be particularly useful for direct comparison of the image spectra with library spectra. The MNF transform as modified from Green et al. (1988) and implemented in ENVI is essentially two cascaded Principal Component transformations. The first transformation, based on an estimated noise covariance matrix, decorrelates and rescales the noise in the data. This first step results in transformed data in which the noise has unit variance and no band-to-band correlations. The second step is a standard Principal Component transformation of the noise-whitened data. Further processing can take two forms: 1) Elimination of MNF component images with high noise content For the purposes of further spectral processing, the inherent dimensionality of the data is determined by examination of the final eigenvalues and the associated images. The data space can be divided into two parts: one part associated with large eigenvalues and coherent eigenimages, and a complementary part with near-unity eigenvalues and noise-dominated images. By using only the coherent portions, the noise is separated from the data, thus improving spectral processing results. 2) Isolation of spectral prototypes. The structure of the transformed data space is that of a central circular mass (noise) with multiple spikes or protrusions. Each spike represents a spectrally unique direction and typically relates to a particular type of material, and the tip of the spike represents the purest spectral representation of the material. These extrema are typically effective as "endmembers" for use with hyperspectral classification methods. Both the eigenvalues and the MNF images (eigenimages) are used to evaluate the dimensionality of the data. Eigenvalues for bands that contain information will be an order of magnitude larger than those that contain only noise. Since the noise variance was "whitened" by being normalized to a magnitude of 1.0, the break between signal and noise should occur for eigenvalues near 1.0. The signal-containing images will be spatially coherent, while the noise images will not contain any significant spatial information. 1 Green, A. A., Berman, M., Switzer, P, and Craig, M. D., 1988, A transformation for ordering multispectral data in terms of image quality with implications for noise removal. IEEE Transactions on Geoscience and Remote Sensing, 26(1): Boardman J. W., and Kruse, F. A., 1994, Automated spectral analysis: A geologic example using AVIRIS data, north Grapevine Mountains, Nevada: in Proceedings, Tenth Thematic Conference on Geologic Remote Sensing, Environmental Research Institute of Michigan, Ann Arbor, MI, p. I I-418.

2 CEE 615: Digital Image Processing Lab 11: Hyperspectral Noise p. 2 Original Image Dark (or flat field) Image Image Statistics Noise Statistics Homogeneous Image Area Noise Fraction Statistics Existing Statistics Estimated from the image MNF Transform MNF Component Images Eigenvalues Evaluation, Band reduction &/or filtering Reduced component, "noise-whitened" image set Inverse MNF Transform "noise-whitened" spectral image set Figure 1: Diagram of the general MNF procedure Forward MNF transform using noise statistics estimated from the image The optimal method for computing the image noise statistics is to use a dark current image collected at the time of the mission. In the absence of a dark current image one may estimate the noise using an ENVI utility to estimate noise statistics directly from the image data. This procedure assumes that each pixel contains both signal and noise, and that adjacent pixels contain the same signal but different noise. A "shift difference" is performed on the data by differencing adjacent pixels to the right and above each pixel and averaging the results to obtain the "noise" value to assign to the pixel being processed. The best noise estimate is gathered using the shift-difference statistics from a homogeneous area rather than from the whole image. ENVI allows you to select the subset for statistics extraction. We will perform the MNF transform, identify a subset of MNF images that contains more signal than noise. apply the inverse MNF transform to a reduced data set in order to produce a less noisy data set (with the same number of bands as the original data set) in the original spectral domain. Use the MNF image set to select candidate endmembers. Use the MNF inverse spectral data to compare with spectral library data.

3 CEE 615: Digital Image Processing Lab 11: Hyperspectral Noise p. 3 Create a reduced-noise subset using the MNF transform: 1. Load and display the cup95eff.int image. This is an AVIRIS hyperspectral image of an area near Cuprite, NV. The image has been atmospherically corrected using the ATREM atmospheric correction procedure 3,4 It was then "polished" to remove consistent noise and error features using the Empirical Flat Field Optimal Reflectance Transformation (EFFORT) procedure. 5 The reflectance values have been multiplied by 1000 in order to represent the spectra as integer values. 2. Select Transforms > MNF Rotation > Forward MNF > Estimate Noise Statistics From Data 3. Select the cup95eff.int image in the MNF Transform Input File and then select "OK". The "Forward MNF Transform Parameters" dialog appears. 4. In the "Forward MNF Transform Parameters" window, enter a filename in the "Enter Output Noise Stats Filename [.sta]" text box (e.g. cup95eff_mnf-noise.sta). 5. Enter a filename in the "Enter Output MNF Stats Filename [.sta]" text box (e.g. cup95eff_mnf.sta). Warning - Be sure that the MNF and noise statistics files have different names. Also, remember where you put these. You will need to access the Output MNF Stats file later. 6. Set the "Select Subset from Eigenvalues" toggle to No 7. Select "File" or "Memory" output. (e.g., cup95_mnf.img) Figure 2: MNF parameters window 8. Click "OK". When ENVI has finished processing, it loads the MNF bands into the Available Bands List and displays the MNF Eigenvalues Plot Window. 9. Examine the MNF Eigenvalues and note where the eigenvalues approach a value of 1.0. The MNF transform suppresses noise by normalizing the noise covariance matrix to a value of 1.0. Thus, one might expect the transition from signal to noise to occur when the eigenvalues of the MNF image set approach 1.0. Select the first MNF image and display as a gray scale image. 10. Select Tools >Animation and select all of the MNF bands. Step through the images and note the correspondence of the apparent image quality with the eigenvalue plot. Would using an eigenvalue of 1.0 delineate an effective boundary between signal and noise? 11. Display the 1 st three bands of the MNF image as a color image. Note that the image appears "flat", i.e., the topographic characteristics (shadows and illuminated areas) have been minimized and the color variations are prominent. 12. Select Transforms > MNF Rotation > Inverse MNF Transform 3 Gao, B.-C., & Davis, C. O. (1997). Development of a line-by-line-based atmosphere removal algorithm for airborne and spaceborne imaging spectrometers. SPIE Proceedings, Vol (pp ). 4 Gao, B.-C., Heidebrecht, K. B., & Goetz, A. F. H. (1993). Derivation of scaled surface reflectances from AVIRIS data. Remote Sensing of Environment, 44, Boardman, J. W., 1998, Post-ATREM polishing of AVIRIS apparent reflectance data using EFFORT: a lesson in accuracy versus precision, in Summaries of the Seventh JPL Airborne Earth Science Workshop, Vol. 1, p. 53.

4 CEE 615: Digital Image Processing Lab 11: Hyperspectral Noise p Choose the cup95eff_mnf.img image and select the first 13 bands of the MNF data set. This would be my choice for the transition from signal to noise in the image set. 14. Select "OK" 15. Choose the "cup95_mnf.sta" statistics file in the "Enter Forward MNF Stats Filename. 16. Name the output file (e.g., cup95_mnfinv-13.img) and select "OK". Compare the Filtered and original Images The point of MNF filtering in this exercise is to improve the comparison of the image spectra with laboratory spectra and, more generally, to improve the identification of target materials. One way to qualitatively evaluate the effect of the smoothing is to directly compare spectra from each image. 1. Display the original and the inverse of the MNF subset. (cup95eff.int; cup95eff_mnfinv.img). Use the same bands for the RGB display (R:2.101; G:2.2008; B:2.3402). 2. Link the displays, display the spectral profiles (Tools > Profiles > z-profiles) for both images, and compare the filtered and unfiltered spectra by moving the cursor around in either image. Look for smoother features in the MNFinv spectra. Ideally, the differences are due to a reduction of noise, and not a loss of spectral detail. 3. Compare multiple spectra for one mineral type. a. Pick an area that is predominantly one color. Examples are outlines in Figure 3. b. Move the cursor to one of the areas. c. In the spectral profile window, select Options > collect spectra. d. Move the cursor around within that area (most easily done with the arrow keys). Note that the MNFinv spectra are more stable than spectra for the original bands (Figure 4). e. Note also, the presence of specific absorption bands. These are molecular absorption features that are specific to each mineral type. They tend to be much more clearly defined in the noise-whitened image data. Figure 3: Uniform color areas. Figure 4: Spectra from original image (left), vs. spectra from the inverse MNF image (right).

5 CEE 615: Digital Image Processing Lab 11: Hyperspectral Noise p. 5 Examine MNF Scatter Plots A major use of the MNF data is to locate spectrally unique data. The MNF procedure is said to "whiten" noise, meaning that the noise is compressed to a unit variance in all bands. This tends to result in enhancing and isolating spectrally unique data. Use Tools > 2-D Scatter Plots in the Main Image window to examine the MNF images. 1. Examine the high variance (low band number) MNF bands. Notice the sharp protrusions in the low band number MNF scatter plots. These are spectrally distinct materials. 2. Examine at least one scatter plot of low variance (high band number) MNF bands (change the bands by selecting Options > Change Bands in the Scatter Plot window). a) MNF bands 1 & 2 b) MNF bands 15 & 16 Figure 5: 2-D scatterplots of MNF eigenimages Use Scatter Plots to Select Spectral Prototypes (endmembers) We will now investigate the possibility of selecting prototype pixels that represent the purest available examples of different minerals in the image using MNF images and the 2-D scatter plot tools. These prototypes, or "endmembers", will form the basis of a hyperspectral classification scheme. 1. Display the cup95eff_mnfinv image and use that to create a scatterplot of cup95eff_mnf bands 1 and 2. Note: Make sure that the 2-D scatterplot is created using the MNF inverse image. This is necessary in order to examine the spectra. 2. Create another scatterplot using MNF bands 15 & 16 (Figure 5b). Note the zero mean, the lack of any correlation between these two bands (spherical shape) and that the variance is O(1). 3. In the scatter plot, use the drawing function to select the outer portion of one of the more distinct protruding arms in the scatter plot and note the location in the image. Note: instead of selecting a cluster to obtain an average spectrum of mineral type, you are selecting the most extreme examples (red pixels in Figure 5). These should be representative of the "purest" examples of the mineral.

6 CEE 615: Digital Image Processing Lab 11: Hyperspectral Noise p Change the class color and select a set of pixels at the extreme end of each of the protruding arms. 5. Export all the classes that you have identified. Select Options > Export All in the Options pulldown menu of the scatter plot to export the identified pixels as ENVI Regions of Interest (ROIs). Optional: Continue the process, selecting other unique prototype ROIs using different combinations of the first several MNF bands. 6. Display the MNF inverse image and select Tools > Region of Interest > ROI Tool. (This may simply highlight the ROI window that you've already been working with.) 7. In the ROI Tool window, choose Select ALL and the Stats. 8. In the ROI Statistics Results window click on Select Plot > Mean for All ROIs. The plot should look something like that shown in the Figure on the right, with wavelength on the x-axis (not band numbers) and values in the 100s. 9. Right click in the ROI Statistics Results window and select Optiona > New Window with Plots. This makes it easier to enlarge the plot window and change the plot parameters. 10. Right Click in the plot window and select Plot Figure 6: Endmember spectra Key. 11. Close the 2-D scatter plot by selecting File > Cancel in the Scatter Plot window. Spectral Libraries / Reflectance Spectra The next task is to identify the minerals whose reflectance spectra most nearly resemble the image spectra. ENVI includes several spectral libraries. For the purposes of this exercise, you will use the JPL Spectral Library (Groves et al., 1992) and the USGS Spectral Library (Clarke et al., 1993). 1. Compare apparent reflectance spectra from the image to selected library reflectance spectra. a. Select Spectral > Spectral Libraries > Spectral Library Viewer from the ENVI main menu. b. In the Spectral Library Input File dialog, click Open > Spectral Library, select jpl_lib > jpl1.sli, and click OK and select any mineral from the library. This will cause the Spectral Library Plot to appear. c. The spectral library reflectance values range from The image reflectance is scaled from You cannot compare magnitude, but you can compare shape. d. Plot the following spectra by selecting the spectra names in the Spectral Library Viewer dialog (right click in the viewer box to display the names of the minerals): ALUNITE SO-4A BUDDINGTONITE FELDS TS-11A CALCITE C-3D KAOLINITE WELL ORDERED PS-1A LEPIDOLITE YELLOW PS-13A Select Options > Plot Key to display the labels for each spectrum.

7 CEE 615: Digital Image Processing Lab 11: Hyperspectral Noise p. 7 e. Customize the plot by selecting Edit > Plot Parameters from the plot window menu. In the Plot Parameters dialog, do the following: Select the X-Axis radio button, and adjust the Range to 2.00 to 2.5 change the Margin fields until the X margins are as desired. Select the Y-Axis radio button, and Change the Range to be from 0.4 to 0.9. (I also like to change the number of minor ticks to 4 in both the x- and y-axes, feeling that it makes the divisions easier to read.) Click Apply then Cancel in the Plot Parameters window. Blue is difficult to see against the black background. Change the display color to something that will be easily distinguishable. Select Edit > Data Parameters. Select the spectrum that appears in blue (Calcite in my example) and change the color. Click Apply then Cancel in the Data Parameters window. The final graph should look something like. Figure 7: Customized Plot Parameters f. Compare the prototype spectra to the mineral spectra. This will be easier to do in a separate window. In the Spectral Library Plots window, click on Options > New Window: blank. In the ROI Statistics window, click on the label of a mineral spectrum and dragging it to the new window. Next, drag the mineral spectrum that you wish to compare into the new window. Repeat for as many spectra as you wish to compare.