James F. Scholl

Phase grating design for a dual-band snapshot imaging spectrometer

Infrared spectral features have proved useful in the identification of threat objects. Dual-band focal-plane arrays (FPAs) have been developed in which each pixel consists of superimposed midwave and long-wave photodetectors [Dyer and Tidrow, Conference on Infrared Detectors and Focal Plane Arrays (SPIE, Bellingham, Wash., 1999), pp. 434-440]. Combining dual-band FPAs with imaging spectrometers capable of interband hyperspectral resolution greatly improves spatial target discrimination. The computed-tomography imaging spectrometer (CTIS) [Descour and Dereniak, Appl. Opt. 34, 4817-4826 (1995)] has proved effective in producing hyperspectral images in a single spectral region. Coupling the CTIS with a dual-band detector can produce two hyperspectral data cubes simultaneously. We describe the design of two-dimensional, surface-relief, computer-generated hologram dispersers that permit image information in these two bands simultaneously.

Higher-dimensional wavelet transforms for hyperspectral data compression and feature recognition

The dominant image processing tasks for hyperspectral data are compression and feature recognition. These tasks go hand-in-hand. Hyperspectral data contains a huge amount of information that need to be processed (and often very quickly) depending on the application. The discrete wavelet transform is the ideal tool for this type of data structure. There are applications that require such processing (especially feature recognition or identification) be done extremely fast and efficiently. Furthermore the higher number of dimensions implies a number of different ways to do these transforms. Much of the work in this area to the present time has been focused on JPEG2000 type compression of each component image involving fairly sophisticated coding techniques; relatively little attention has been paid to other configurations of wavelet transforms of such data, as well as rapid feature identification where compression may not be necessary at all. This paper describes other versions of the 3D wavelet transform that allow the resolution in both the spatial domain and spectral domain to be adjusted separately. Other issues associated with low complexity feature recognition with and without compression using versions of the 3D hyperspectral wavelet transforms will be discussed along with some illustrative calculations.

Evaluations of classification and spectral unmixing algorithms using ground based satellite imaging

Abundances of material components in objects are usually computed using techniques such as linear spectral unmixing on individual pixels captured on hyperspectral imaging devices. However, algorithms such as unmixing have many flaws, some due to implementation, and others due to improper choices of the spectral library used in the unmixing (as well as classification). There may exist other methods for extraction of this hyperspectral abundance information. We propose the development of spatial ground truth data from which various unmixing algorithm analyses can be evaluated. This may be done by implementing a three-dimensional hyperpspectral discrete wavelet transform (HSDWT) with a low-complexity lifting method using the Haar basis. Spectral unmixing, or similar algorithms can then be evaluated, and their effectiveness can be measured by how well or poorly the spatial and spectral characteristics of the target are reproduced at full resolution (which becomes single object classification by pixel).

Fast wavelet based feature extraction of spatial and spectral information from hyperspectral datacubes

An ongoing problem for feature extraction in hyperspectral imagery is that such data consumes large amounts of memory and transmittance bandwidth. In many applications, especially on space based platforms, fast, low power feature extraction algorithms are necessary, but not feasible. To overcome many of the problems due to the large volume of hyperspectral data we have developed a fast, low complexity feature extraction algorithm that is a combination of a fast integer-valued hyperspectral discrete wavelet transform (HSDWT) using a specialized implementation of the Haar basis and an improved implementation of linear spectral unmixing. The Haar wavelet transform implementation involves a simple weighted sum and a weighted difference between pairs of numbers. Features are found by using a small subset of the transform coefficients. More refined spatial and/or spectral identifications can then be made by localized fast inverse Haar transforms using very small numbers of additional coefficients in the spatial or spectral directions. The computational overhead is reduced further since much of the information used for linear spectral unmixing is precomputed and can be stored using a very small amount of additional memory.

Compact methods for measuring stress birefringence

The recent development of channelled spectropolarimetry presents opportunities for spectropolarimetric measurements of dynamic phenomena in a very compact instrument. We present measurements of stress-induced birefringence in an ordinary plastic by both a reference rotating-compensator fixed-analyzer polarimeter and a channelled spectropolarimeter. The agreement between the two instruments shows the promise of the channelled technique and provides a proof-of-principle that the method can be used for a very simple conversion of imaging spectrometers into imaging spectropolarimeters.

Computational modeling of the imaging system matrix for the CTIS imaging spectrometer

Imaging systems such as the Computed Tomographic Imaging Spectrometer (CTIS) are modeled by the matrix equation g = Hf, which is the discretized form of the general imaging integral equation.. The matrix H describes the contribution to each element of the image g from each element of the hyperspectral object cube f. The vector g is the image of the spatial/spectral projections of f on a focal plane array (FPA). The matrix H is enormous, sparse and rectangular. It is extremely difficult to discretize the integral operator to obtain the matrix operator H. Normally H is constructed empirically from a series of monochromatic calibration images, which is a time consuming process. However we have been able to synthetically construct H by numerically modeling how the optical and diffractive elements in the CTIS project monochromatic point source data onto the FPA. We can evaluate a CTIS system by solving the imaging equation for f using both the empirical and synthetic H from some test data g. Comparison between the two results provides a means to evaluate and improve CTIS system calibration procedures noting that the synthetic system matrix H represents a baseline ideal system.

Model based compression of the calibration matrix for hyperspectral imaging systems

In hyperspectral imaging systems with a continuous-to-discrete (CD) model, the goal is to solve the matrix equation g = Hθ + n for θ. Here g is a data vector obtained on pixels on a focal plane array (FPA), and n is the additive pixel noise vector. The hyperspectral object cube f(x, y, λ) to be recovered is represented by θ, which is the vectorized set of expansion coefficients of f with respect to a family of functions. The imaging operator is the system matrix H of which its columns represent the projection of each expansion function onto the FPA. Hence an estimate of the object cube f(x, y, λ) is reconstructed from these recovered expansion function projection coefficients. Furthermore H is equivalently a calibration matrix, and amenable to an analytic description. Since the number of expansion functions is large, and the number of pixels on an FPA is large, H becomes huge and very unwieldy to store. We describe a means by which we can reduce the effective size of H by taking advantage of the analytic model of the imaging system and converting H into a series of look-up tables. By this method we have been able to drastically reduce the storage requirements for H from terabytes to sub-megabyte sizes. We provide an example of this technique in isoplanatic and polychromatic calibration of a flash hyperspectral imaging system. These sets of lookup tables are expansion function independent and also independent of object cube sampling.

Hyperspectral feature classification with alternate wavelet transform representations

The effectiveness of many hyperspectral feature extraction algorithms involving classification (and linear spectral unmixing) are dependent on the use of spectral signature libraries. If two or more signatures are roughly similar to each other, these methods which use algorithms such as singular value decomposition (SVD) or least squares to identify the object will not work well. This especially goes for these procedures which are combined with three-dimensional discrete wavelet transforms, which replace the signature libraries with their corresponding lowpass wavelet transform coefficients. In order to address this issue, alternate ways of transforming these signature libraries using bandpass or highpass wavelet transform coefficients from either wavelet or Walsh (Haar wavelet packet) transforms in the spectral direction will be described. These alternate representations of the data emphasize differences between the signatures which lead to improved classification performance as compared to existing procedures.

Normalized difference vegetation index calculations from JPEG2000-compressed Landsat 7 images

An ongoing problem in remote sensing is that imagery generally consumes considerable amounts of memory and transmittance bandwidth, thus limiting the amount of data acquired. The use of high quality image compression algorithms, such as the wavelet-based JPEG2000, has been proposed to reduce much of the memory and bandwidth overhead; however, these compression algorithms are often lossy and the remote sensing community has been wary to implement such algorithms for fear of degradation of the data. We explore this issue for the JPEG2000 compression algorithm applied to Landsat-7 Enhanced Thematic Mapper (ETM+) imagery. The work examines the effect that lossy compression can have on the retrieval of the normalized difference vegetation index (NDVI). We have computed the NDVI from JPEG2000 compressed red and NIR Landsat-7 ETM+ images and compared with the uncompressed values at each pixel. In addition, we examine the effects of compression on the NDVI product itself. We show that both the spatial distribution of NDVI and the overall NDVI pixel statistics in the image change very little after the images have been compressed then reconstructed over a wide range of bitrates.

Hyperspectral datacube estimations of binary stars with the Computed Tomographic Imaging Spectrometer (CTIS)

Using mathematical techniques recently adapted for the analysis of hyperspectral imaging systems such as the CTIS, we have performed datacube reconstructions for a number of binary star systems. The CTIS images in the visible (420nm to 720nm) wavelength range were obtained in 2001 using the 3.67m Advanced Electro Optical System (AEOS) of the Maui Space Surveillance System (MSSS). These methods used an analytical model of the CTIS to construct an imaging system operator from optical, focal plane array and Computer Generated Holographic (CGH) disperser parameters in the CTIS. We used the adjoint of this operator to construct matched filtered estimates of the datacubes from the image data. In these reconstructions we are able to simultaneously obtain information on the geometry and relative photometry of the binary systems as well as the spectrum for each component of the system.