Abstract:
A method is disclosed herein for compressing spectral data corresponding to an image comprising a plurality of pixels. The method includes the step of creating a set of potential endmembers. A first plurality of the potential endmembers are identified as a first set of endmembers based upon their respective correlations with a first spectral signature of a first of the plurality of pixels. The first pixel is then represented as a combination of the first set of endmembers. Processing of the image preferably continues by identifying a second plurality of the potential endmembers as a second set of endmembers based upon their respective correlations with a second spectral signature of a second of the plurality of pixels. The second pixel is then represented as a combination of the second set of endmembers.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
   This application is a continuation application of U.S. patent application Ser. No. 09/704,338 entitled ADAPTIVE HYPERSPECTRAL DATA COMPRESSION, filed Nov. 1, 2000 now U.S. Pat. No. 6,804,400, which is incorporated herein by reference in its entirety. 

   FIELD OF THE INVENTION 
   The present invention relates to the field of data compression, and more particularly to a method and system for adaptively compressing and decompressing hyperspectral image and other data. 
   BACKGROUND OF THE INVENTION 
   It has recently become possible to commercially obtain satellite and aerial images of terrain of interest from a number of sources. For example, certain large farms currently use satellite images provided by Landsat, the system of land-observing satellites operated by the federal government. Landsat satellites orbit the earth at approximately 900 km., and provide images in which each pixel represents a square area of between 1 m 2  and 1E6 m 2  (a pixel area of 100 m 2  is common for systems designed for land-use purposes). Visible, near-infrared, shortwave infrared, thermal infrared sensors deployed on such satellites can detect, among other things, the spectral reflectance, temperature, and other physical characteristics of specified terrestrial areas. 
   The sensors used in generating the images used for many commercial purposes are typically characterized as either “multispectral” or “hyperspectral”. Multispectral sensors collect images of a terrain or landscape and provide a handful of wide spectral bands of imagery. These bands encompass the visible, short wave infrared, and, in some cases, thermal infrared portion of the electromagnetic spectrum. Similarly, hyperspectral sensors typically provide hundreds of narrow spectral bands of hyperspectral imagery spanning the visible, near-infrared, and shortwave infrared portion of the electromagnetic spectrum. Such sensors can produce enormous amounts of information needing to be transmitted on a limited bandwidth cross-link or down-link channel. For example, the Earth Observing System (“EOS”), which is currently scheduled to begin operation by 2001, will carry a high-resolution hyperspectral imager (the “Hyperion”) capable of resolving  220  spectral bands. The Hyperion is expected to produce a maximum output data rate of at least several hundred Mbit/s. 
   Such high data rates not only increase the complexity of required communications infrastructure, but may also strain the capacity of ground data storage and processing facilities. It will of course be appreciated that data compression of some type would at least partially alleviate these difficulties. 
   Many image compression algorithms have been designed and implemented over the years in order to address the storage and transmission needs of monochromatic and multispectral imaging sensors. Most of these algorithms have focused on the spatial character of the imagery and limitations in the human visual system. Hyperspectral imagery shares certain characteristics with monochromatic and multispectral imagery, but also possesses certain other characteristics providing additional opportunities for compression of the constituent spectral data. For example, it is well recognized that hyperspectral imagery typically exhibits high levels of spectral correlation. Like other imagery, hyperspectral imagery also exhibits some level of spatial correlation, but such correlation is often less than that inherent in other types of images. The data redundancy resulting from spectral and spatial correlation has been exploited by certain algorithms to provide relatively high compression ratios with insubstantial loss of information content. Such algorithms have been based upon vector quantization, use of the discrete cosine transform followed by trellis coded modulation, spectral re-ordering and linear prediction, and spectral signature matching. 
   However, existing data compression algorithms may fail to consider all parameters of an image potentially relevant to optimizing compression ratios. For example, such algorithms are not known to utilize image noise statistics for the purpose of ensuring that any compression loss be related substantially to image noise rather than to scene information. 
   SUMMARY OF THE INVENTION 
   In summary, the present invention pertains to a method of compressing spectral data corresponding to an image comprising a plurality of pixels. The method includes the step of creating a set of potential endmembers. A first plurality of the potential endmembers are identified as a first set of endmembers based upon their respective correlations with a first spectral signature of a first of the plurality of pixels. The first pixel is then represented as a combination of the first set of endmembers. Processing of the image preferably continues by identifying a second plurality of the potential endmembers as a second set of endmembers based upon their respective correlations with a second spectral signature of a second of the plurality of pixels. The second pixel is then represented as a combination of the second set of endmembers. 
   In another aspect, the present invention relates to a compression system for compressing spectral data corresponding to an image comprising a plurality of pixels. The compression system includes a database including a set of potential endmembers. An adaptive linear unmixing module operates to identify a first plurality of the potential endmembers as a first set of endmembers based upon correlation of the first plurality of potential endmembers with a first spectral signature of a first of the plurality of pixels. The compression system further includes an encoder for representing the first pixel as a combination of the first set of endmembers. 
   The present invention also pertains to a method for reconstructing an image comprising a plurality of pixels from a compressed data stream. In an initial step of this method a set of endmembers are extracted from the data stream. Information identifying a first plurality of the endmembers corresponding to a first pixel of said plurality of pixels is also extracted from the data stream. A first plurality of endmember coefficients, each of such endmember coefficients corresponding to one of the first plurality of endmembers, is also extracted from the data stream. Each of the first plurality of endmembers is multiplied by a corresponding one of the first plurality of endmember coefficients to produce a first plurality of intermediate products. The method further includes the step of combining the first plurality of intermediate products. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the accompanying drawings: 
       FIG. 1  is a high-level block diagram of an imaging system for producing spectral images disposed to be adaptively compressed by an encoder in accordance with the teachings of the present invention. 
       FIG. 2  is a generalized block diagram representation of the functional blocks of an encoder used in adaptively compressing hyperspectral image data in accordance with the present invention. 
       FIG. 3  is a flow chart of an image noise calculation process performed by an image noise calculator included within the encoder of  FIG. 2 . 
       FIGS. 4A and 4B  collectively comprise a flow chart of an endmember selection process carried out by an image endmember identifier included within the encoder of  FIG. 2 . 
       FIG. 5  is a high-level flow chart of a linear unmixing process performed by the adaptive linear unmixing module within the encoder of  FIG. 2 . 
       FIGS. 6A and 6B  are flow charts of a preferred implementation of the adaptive linear unmixing process generally described with reference to  FIG. 5 . 
       FIG. 7  is a block diagram of an image reconstruction module within a ground station or other facility disposed to reconstruct an image using a compressed image data file transmitted by the imaging system of  FIG. 1 . 
       FIGS. 8A-8B  are a computer program listing of a MATLAB routine which implements the adaptive hyperspectral data compression process of the present invention. 
       FIGS. 9A-9C  are a computer program listing of a MATLAB routine which implements the adaptive hyperspectral data compression process of the present invention. 
       FIG. 10  is a computer program listing of a MATLAB routine which implements the adaptive hyperspectral data compression process of the present invention. 
       FIG. 11  is a computer program listing of a MATLAB routine which implements the adaptive hyperspectral data compression process of the present invention. 
       FIGS. 12A-12B  are a computer program listing of a MATLAB routine which implements the adaptive hyperspectral data compression process of the present invention. 
       FIG. 13  is a computer program listing of a MATLAB routine which implements the adaptive hyperspectral data compression process of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   System Overview 
     FIG. 1  is a high level block diagram of an imaging system  10  for producing spectral images disposed to be adaptively compressed by an encoder  14  in accordance with the teachings of the present invention. The encoder  14  forms part of a codec, e.g., a coder-decoder pair. In an exemplary embodiment, the imaging system  10  and encoder  14  are used in a spacecraft or satellite, while a complementary decoder is disposed within a terrestrial ground station or other receiving system. The encoder  14  is operative to adaptively compress images obtained using data collected by an instrument  20 . 
   The instrument  20  may be realized using any of various types of instrument systems which provide signals indicative of spectral reflectance, such as multi-band digital imaging cameras, color television cameras, multi-band infrared scanners, visible light microscopes, spectroradiometers and the like. Although in the preferred embodiment of  FIG. 1  the instrument  20  is disposed to measure spectral reflectance, in alternate implementations other spectral characteristics (e.g. spectral emission) may be measured and processed in accordance with the present invention. Signals are provided by the instrument  20  to a digitizer  24 , which produces a set of image pixels defining the optical characteristics of the object or terrain of interest. 
   As is indicated by  FIG. 1 , a set of image pixels from the digitizer  24  is provided to an input interface  28 . The hyperspectral image data  26  received through the input interface  28  is provided to the encoder  14 , a computer system capable of appropriate processing, such as image processing. In the alternative, discrete logic devices, specially designed integrated circuits, and commercially available processors can also be used to implement the systems and methods consistent with this invention. 
   The image data  26  in a single image pixel provided to the encoder  14  by the digitizer  24  consists of N data samples (typically between 10 and 200) which collectively form a hyperspectral “signature” of the image pixel. Each data sample corresponds to the reflectance or ratio of emission of photons from the object as compared to the photons illuminating the surface or terrain of interest at some spectral wavelength. As is described hereinafter, the encoder  14  then operates to adaptively compress the received hyperspectral image data  26  and to provide the resultant compressed image data to a transmitter (not shown) aboard the spacecraft or satellite. 
   Adaptive Hyperspectral Data Compression 
     FIG. 2  is a generalized block diagram representation of the functional blocks of the encoder  14  used in adaptively compressing the hyperspectral image data  26  in accordance with the present invention. In a preferred implementation, each such functional block of the encoder  14  is implemented as a software routine disposed to execute on a computer system of the type described above. Referring to  FIG. 2 , an image noise calculator  100  determines certain noise statistics for each band of the received hyperspectral image data  26  and uses such statistics to calculate an overall image noise level. The encoder  14  further includes an image endmember identifier  104  for deriving a set of spectral endmembers from the received hyperspectral data for storage in a spectral library  110 . A linear unmixing module  120  is operative to represent each image pixel using a linear combination of endmembers from the spectral library  110 . As is described further below, the processing carried out by the linear unmixing module  120  takes advantage of the spectral and spatial correlation present in hyperspectral imagery to decorrelate the image using linear regression. The linear unmixing module  120  also uses the image noise level provided by the image noise calculator  100  in determining the number of endmembers selected to represent each pixel, thereby effecting adaptive data compression on a pixel-by-pixel basis. Once a particular set of endmembers and associated coefficients been selected to represent each image pixel, the entire image is encoded by an encoding module  130  and the resultant compressed image data provided to a transmitter (not shown). 
   Image Noise Calculation 
     FIG. 3  is a flow chart of an image noise calculation process performed by the image noise calculator  100 . This noise calculation process is initiated by estimating the noise variance in each of the N spectral bands of the image to be compressed (step  150 ). Such estimation is preferably effected using an automated technique which contemplates determining separate linear regression coefficients for distinct blocks of pixels. See, for example, “Reliably Estimating the Noise in AVIRIS Hyperspectral Images,” by Roger, R. E. and Arnold, J. F., Int. J. Remote Sensing, 1966, Vol. 17, No. 10, 1951-1962. First, the entire image is divided into small, rectangular, continuous, non-overlapping blocks of pixels of length L, where L is typically between 8 and 16 (step  160 ). Within each such pixel block, the value of each pixel is estimated in each of the N spectral bands using a set of four linear regression coefficients derived using a least squares fitting process (step  170 ). Specifically, two of such coefficients correspond to the values of the subject pixel in the bands adjacent the band of interest, one coefficient corresponds to the value of the pixel in an adjacent spatial location in the band of interest, and one coefficient corresponds to a bias term. During the fitting process, which is preferably conducted separately for each of the N spectral bands, a residual difference between each pixel value in a given band and its predicted value in such band is computed and is assumed to be noise energy introduced by the imaging chain. The fitting process is performed by selecting the four linear regression coefficients associated with a pixel value such that the sum of the squares of the residuals for each pixel block is minimized (step  180 ). 
   Once the fitting process has been completed for all pixel blocks, the variance in each of the N spectral bands of the image is computed for each block using the applicable residuals (step  190 ). Next, the variances for each block in a given spectral band are aggregated to produce an estimate of the noise variance within such band (step  200 ). An image variance is then computed for each of the N spectral bands using the hyperspectral image data  26  in order to yield an estimate of the signal power in each such band (step  210 ). 
   A signal to noise ratio (SNR) for each spectral band is then computed by dividing the image variance by the noise variance (step  220 ). Any spectral band having a SNR less than a predefined threshold (e.g., 10) is excluded from the hyperspectral image data  26  provided to the adaptive linear unmixing module  120 . Removal of such “noisy” bands prevents image noise from corrupting the unmixing process described below (step  230 ). In addition, an RMS image noise value is computed by determining the square root of the mean of the noise variance across all N spectral bands (step  240 ). This RMS image noise value may be considered to be one standard deviation (i.e., one “sigma level”) of the noise energy associated with the image. Assuming a Gaussian noise distribution, more than 99% of the image pixels would be expected to be characterized by noise levels not exceeding three sigma levels. As is described further below, in a preferred implementation the adaptive linear unmixing module  120  operates to select endmembers for a given image pixel until the residual difference between the actual value of such image pixel and its estimated value using a linear combination of such endmembers drops below a predefined target value (e.g., 1, 2 or 3 sigma levels). 
   Endmember Selection 
   As mentioned above, the image endmember identifier  104  functions to derive a set of spectral endmembers from the received hyperspectral image data  26 . Although a preferred embodiment of the invention contemplates use of the image endmember identifier  104  to derive endmembers from the received hyperspectral image data  26 , endmembers may alternately be physically derived directly from the scene. Such direct physical derivation may be conventionally effected using field spectrometers, by recourse to a material database, or by using other imagery of the scene. In alternate embodiments, endmembers may be derived from the spectra of individual or multiple pixels using automated, semi-automated, or manual techniques. 
     FIGS. 4A and 4B  collectively comprise a flow chart of an endmember selection process carried out by the image endmember identifier  104 . The selection process begins with computation of an image covariance matrix: 
                   ∑   ij     ⁢           ⁢     =       1     Npix   -   1       ⁢       ∑     k   =   1     Npix     ⁢           ⁢       (       d     k   ,   i       -     μ   i       )     ⁢     (       d     k   ,   j       -     μ   j       )                     (   1   )               
where d k,i  represents the value of the kth pixel in the ith spectral band, μ i  represents the mean of the ith spectral band, and Npix represents the number of pixels in the image (step  250 ). Next, the image covariance matrix is transformed into a set of constituent principal components (step  260 ). In a preferred implementation, this transform is effected through an eigenvector or principal component decomposition of the image covariance matrix defined by Equation (1). Specifically, the eigenvalues of the image covariance matrix are computed and sorted in decreasing order, which allows the associated principal components to also be arranged in decreasing order (step  270 ). It has been found that the first few principal components will contain the bulk of the variance from the image covariance matrix. In a preferred implementation a predetermined number (e.g., 5) of the most significant principal components are retained (step  274 ), which substantially reduces the dimensionality of the hyperspectral image data  26  without appreciable loss of scene information.
 
   It is observed that the hyperspectral image data  26  may be represented using this set of most significant principal components. In particular, the dot product of each pixel within the hyperspectral image data  26  with the eigenvector corresponding to a given principal component represents the contribution of such principal component to such pixel. This allows the hyperspectral image data  26  (as represented by its most significant principal components) to be partitioned into K small blocks of pixels where each such block represents a potential class (step  280 ). As is described below, similar ones of these potential classes are then merged using the Bhattacharyya distance, and the remaining classes consolidated into a predefined number of image endmembers through an iterative unmixing process. 
   Referring again to  FIG. 4A , the mean and covariance of each of the K blocks of pixels is computed (step  290 ) in order to define a set of K potential classes. Next, the Bhattacharyya distance (B) between each of these K potential classes is computed based on their respective means (μ n ) and covariances (Σ n ) as follows (step  300 ): 
                 B   =         1   4     ⁢       (       μ   1     -     μ   2       )     T     ⁢       (       ∑   1     ⁢           ⁢     +     ∑   2         ⁢           )       -   1       ⁢     (       μ   1     -     μ   2       )       +       1   2     ⁢     ln   ⁡     (                ∑   1     ⁢     +           ⁢     ∑   2         2                     ∑   1     ⁢           ⁢     ∑   2       ⁢                    )                   (   2   )               
Those of the potential K classes separated by less than a predefined distance B are then merged, thereby resulting in a smaller set of J classes (step  310 ). Consistent with the invention, the dependence of the Bhattacharyya on covariance tends to prevent classes representing a mixture of scene materials from being merged into other classes. This is desirable since each endmember should preferably represent the spectral signature of only a single material present in the scene defined by the hyperspectral image data  26 .
 
   Once the set of J classes have been established, the mean of each is computed (step  320 ). An unmixing process is then initiated to reduce the set of J classes to a desired number M (e.g., 30) of endmembers (step  330 ). This unmixing process begins by selecting the mean of the one of the J classes having the largest number of members (i.e., image pixels) as the first endmember (step  340 ). The remaining M-1 endmembers are then iteratively selected from the means of the remaining J-1 classes using the first endmember (and each subsequently selected endmember) in the following manner. In a first iteration, a first set of RMS residuals are computed by determining the magnitude of the vector difference between the first endmember and the mean of each of the remaining J-1 classes (step  350 ). Each of the RMS residuals within this first set is then weighted by multiplying each such residual by the number of members in the associated one of the remaining J-1 classes, thereby generating a first set of weighted RMS residuals (step  360 ). The mean of the one of the remaining J-1 classes associated with the largest weighted RMS residuals is then chosen as the second endmember (step  370 ), which concludes the first iteration. 
   During the second and each subsequent iteration, the previously selected endmembers are added in order to create an endmember set vector (step  380 ). A set of RMS residuals are computed by determining the magnitude of the vector difference between the endmember set vector and the mean of each of the remaining classes (step  390 ). Each of these RMS residuals is then weighted by multiplying each such residual by the number of members in the associated one of the remaining classes, thereby generating a set of weighted RMS residuals (step  400 ). The mean of the class associated with the largest weighted RMS residual is selected as the next endmember (step  410 ), which concludes the iteration. This iterative process is repeated until M endmembers have been selected and stored within the endmember spectral library  110  (step  420 ). 
   Adaptive Linear Unmixing 
     FIG. 5  is a high-level flow chart of a linear unmixing process performed by the adaptive linear unmixing module  120 . Consistent with the invention, the linear unmixing module  120  functions to create a representation of each pixel spectra within the hyperspectral image data  26  using a linear combination of endmembers from the spectral library  110 . In a preferred embodiment this process is effected using a technique termed the Residual Correlation Method (RCM). The RCM contemplates finding an iterative solution to a set of linear mixing equations that model each pixel spectra as a linear combination of a set of endmembers. The linear mixing equations are based upon a Linear Mixing Model, which posits that the measured spectrum (i.e., the hyperspectral image data  26 ) is composed of the sum of individual reflectance spectra corresponding to particular materials (i.e., endmembers). Each endmember is weighted by the fractional area that the corresponding material occupies within the image field of view: 
                   R   meas     =       ∑     n   =   1     N     ⁢           ⁢       f   n     ⁢     R   n                 (   3   )               
where R meas  is the measured spectrum as defined by the hyperspectral image data  26 , and the R n  are the component endmembers. The sum of the fractional weighting coefficients is unity; that is, the area covered by all of the materials in the scene must be equivalent to the total field of view.
 
                     ∑     n   =   1     N     ⁢           ⁢     f   n       =   1           (   4   )               
The difference between the spectrum for a given image pixel approximated by the right side of Equation (3) and the measured spectrum for such pixel (R meas ) defined by the hyperspectral image data  26  is referred to as the residual spectrum. The RCM proceeds on a pixel-by-pixel basis until a set of endmembers has been selected to collectively represent each image pixel defined by the hyperspectral image data  26 .
 
   Referring to  FIG. 5 , processing of a given image pixel (P) in accordance with the RCM is initiated by selecting from the spectral library  110  the endmember (E 1 ) most highly correlated with the spectra of the pixel P (step  450 ). The residual spectrum (R 1 ) between endmember E 1  and pixel P is then computed (step  460 ). In addition, a residual spectrum (R 1 ′) is also computed between endmember E 1  and each of the other M-1 endmembers within the spectral library  110  (step  470 ). The correlation between R 1  and each of the other residual spectra R 1 ′ is then evaluated, and a corresponding correlation coefficient assigned to each of the M-1 residual spectra R 1 ′ (step  480 ). The endmember associated with the spectra R 1 ′ having the largest correlation coefficient is selected as the second endmember (E 2 ) to be used in representing pixel P (step  490 ). This process (i.e., steps  450  through  490 ) is repeated until a set of endmembers have been selected for pixel P to be approximated sufficiently accurately by such set. Specifically, processing with respect to pixel P terminates when the residual difference between the value of R meas  for pixel P and its estimated value using a linear combination of the previously selected endmembers (E 1 , E 2 , . . . ) drops below a predefined target value related to the RMS image noise level (e.g., 1, 2 or 3 sigma levels) (step  500 ). Steps  450  through  500  are then repeated for each pixel defined by the hyperspectral image data  26  (step  510 ). 
     FIG. 6A  is a top-level flow diagram, and  FIG. 6B  a more detailed flow chart, of a preferred implementation of the adaptive linear unmixing process described with reference to  FIG. 5 . The implementation of  FIGS. 6A and 6B  is enhanced in several respects relative to the unmixing process of  FIG. 5 . For example, although the sum of the weighting coefficients f n  are constrained by equation (4) to be unity, the implementation of  FIGS. 6A and 6B  further requires that none of the weighting coefficients f n  be less than zero (since each coefficient is representative of a non-negative physical area within the image field of view). In addition, the implementation of  FIGS. 6A and 6B  utilizes a correlation process not entirely predicated on a least squares fit to select the first endmember (E 1 ). As is described below, use of this approach may require that certain endmembers selected during prior iterations be replaced during subsequent iterations. 
   The most significant functional blocks comprising the implementation of the adaptive linear unmixing process of  FIGS. 6A and 6B  are described below. 
   Initialize 
   The initialize function  516  instantiates the arrays utilized during execution of the Residual Correlation Method using the hyperspectral image data  26 , reads in the complete set of potential endmember spectra from the endmember spectral library  110 , and selects for processing an image pixel within the hyperspectral image data  26 . 
   ComputeLMM; DemixEMS 
   The ComputeLMM function  518  performs an inversion of the equations defined by the Linear Mixing Model (i.e., steps  450  to  500  of  FIG. 5 ) during the first iteration of the adaptive linear unmixing module  120 . Following selection of the initial endmember E 1  (step  450 ), during each subsequent iteration the DemixEMS function  519  adjusts the weighting coefficient f n  associated with all endmembers selected during previous iterations. The ComputeLMM function  518  and the DemixEMS function  519  each (i) operate upon the set of potential endmember spectra from the endmember spectral library  110  and the hyperspectral image data  26 , and (ii) output the weighting coefficient(s) f n  of the endmember(s) which have been selected to represent the image pixel being processed. 
   Compute Residuals 
   The Compute Residuals function  520  operates upon the hyperspectral image data  26  and each selected endmember in order to compute the residual spectrum Rn (step  460 ) and the residual spectra Rn′ (step  470 ). 
   AddEndMember 
   The AddEndMember function  522  computes the correlation between a given residual spectrum Rn and each associated residual spectra Rn′. The potential endmember spectrum associated with the residual spectrum Rn′ most highly correlated with the residual spectrum Rn is selected as the next endmember used in representing the pixel being processed. 
   ReplaceEndMember 
   The ReplaceEndMember function  524  operates to replace a previously selected endmember with another potential endmember spectrum from the database  110  if the weighting coefficient f n  associated with such spectrum would be larger than the coefficient f n  associated with the previously selected endmember. 
   CheckNegEMS; RemoveEndMember 
   The CheckNegEMS function  526  checks to ensure that none of the weighting coefficients f n  for the previously selected endmembers have been computed to be a negative fraction. In the event of computation of such a negative fraction, the associated endmember is removed from the set of previously selected endmembers. 
   CheckDone 
   The CheckDone function  530  determines when a sufficient number of endmembers have been selected to represent the pixel P being processed with a predetermined accuracy. Specifically, a sufficient number of pixels are deemed to have been selected when either (i) when the residual difference between pixel P and its estimated value using a linear combination of the previously selected endmembers (E 1 , E 2 , . . . ) drops below a predefined target value related to the RMS image noise level (e.g., 1, 2 or 3 sigma levels), or (ii) if all the potential endmember spectra within the library  110  have been evaluated and such residual difference remains above such predefined target value. 
   StopTrash 
   The StopTrash function  534  operates to cause the adaptive linear unmixing process of  FIGS. 6A and 6B  to terminate under certain conditions. In particular, the StopTrash function  534  monitors whether a potential endmember spectrum from the library  110  is alternately added to, and removed from, the set of selected endmembers during successive processing iterations. In such event the StopTrash function  534  terminates the linear unmixing process by posting a “Done” flag following completion of a specified number of iterations. 
   Encoding 
   Once the adaptive linear unmixing module  120  has identified a unique set of endmembers for each image pixel, the entire image is encoded by the encoding module  130 . In a preferred embodiment the module  120  creates a file having a header specifying (i) image dimensions (length, width, number of spectral bands N), (ii) number of endmembers M, (iii) the shape of each such endmember, and (iv) gain and bias terms for each endmember. With respect to each pixel, the file preferably includes (i) flags indicative of which endmembers are used to represent each such pixel, and (ii) the coefficients associated with the endmembers for each such pixel. If the adaptive linear unmixing module is unable to identify a set of endmembers capable of approximating a given image pixel within the residual bound specified in step  500 , then the pixel is not compressed. It is observed that the specified residual bound (e.g., 1, 2 or 3 sigma levels) will typically affect the image compression ratio ultimately achieved in a couple of respects. First, more endmembers are generally required to satisfy a smaller residual bound, thereby resulting in a reduction in the compression ratio. Secondly, a very small residual bound (e.g., 1 sigma level) could be expected to preclude many image pixels from being approximated by a set of endmembers within such a bound, thereby further reducing the compression ratio. 
   Image Reconstruction 
     FIG. 7  is a block diagram of an image reconstruction module  550  within a ground station or other facility disposed to reconstruct an image using a compressed image data file transmitted by the imaging system  10 . In a preferred embodiment, each functional block of the reconstruction module is implemented as a software routine disposed to execute on a computer system of a type typically utilized for image processing applications. The reconstruction module includes a demultiplexer  560 , which is provided with the compressed image data file by a ground station receiver (not shown). The demultiplexer produces (i) a signal  570  representing the image dimensions (number of pixels in length and width, and number of spectral bands N), and (ii) a signal  580  representing the number of endmembers M, the shape of each endmember, and gain and bias terms for each endmember. In addition, the demultiplexer generates a signal  590  indicative of (i) which endmembers are used to represent each such pixel, and (ii) the coefficients associated with the endmembers for each such pixel. 
   In a preferred implementation the module  550  reconstructs images on a pixel-by-pixel basis. In particular, a multiplier  600  multiplies each of the endmembers used to represent a given image pixel by a corresponding endmember coefficient to produce a set of intermediate products. These intermediate products are combined within an accumulator  610  in order to provide a reconstructed representation of the image pixel. This process is then repeated for each pixel defined by the compressed image data file. 
   Exemplary Software Implementation 
     FIGS. 8A and 8B  are a computer program listing of a top-level MATLAB routine  700  implementing the adaptive hyperspectral data compression process described above with reference to  FIGS. 3-6 . Referring to  FIG. 8A , a code segment  710  within the routine  700  implements the noise calculation process performed by the image noise calculator  100 . A code segment  720  performs the principal components transformation described above with reference to  FIG. 4A . Following completion of such principal components transformation, a code segment  730   a  ( FIG. 8A) and 730   b  ( FIG. 8B ) implements the endmember selection process described with reference to  FIGS. 4A and 4B  beginning with step  280 . It is observed that the code segment  730   a  and  730   b  calls the function rgrow  740  ( FIGS. 9A-9C ) and the function unconstr  750  ( FIG. 11 ). The function rgrow  740  calls the function bdist  760  ( FIG. 10 ), which is operative to compute the Bhattacharyya distance between a pair of Gaussian distributions. 
   Referring again to  FIG. 8B , a code segment  770  performs the adaptive linear unmixing process described with reference to  FIGS. 5 ,  6 A and  6 B. The code segment  770  calls the function rcmlpix  780  ( FIGS. 12A-12B ), which performs the bulk of such unmixing process. Finally, a code segment  790  implements, through a called function rcmcompw  800  ( FIG. 13 ), the encoding process performed by the encoding module  130 . 
   Although the above application has been described primarily in the context of particular embodiments and applications, one skilled in the art can readily appreciate that the teachings of the present invention may be applied to other embodiments and applications. Thus, the application is meant only to be limited by the scope of the appended claims.