Today, ice charts in Greenland waters are produced manually by the Danish Meteorological Institute (DMI) for selected regions depending on season and shipping routes. The project “Automated Downstream Sea Ice Products for Greenland Waters” or shorter “Automated Sea Ice Products” (ASIP) attempts to automate this process by means of fusion of data from instruments with different resolutions and modalities. As a part of this process data from the Advanced Microwave Scanning Radiometer (AMSR2) will be interpolated to the geometry of the SAR data acquired by Sentinel-1. In a preparatory leave-one-out cross-validation (LOOCV) study, different interpolation methods including ordinary kriging (OK) are compared. Using bias and root-mean-squared error (RMSE) as measures of precision, OK using 20-30 nearest neighbours outperforms other often used methods such as inverse distance (ID) weighting. This comes at a cost: more work needs to be done by both the operator and the computer.
The project “Automated Downstream Sea Ice Products for Greenland Waters” or shorter “Automated Sea Ice Products” (ASIP) is a cooperation between the Danish Meteorological Institute (DMI), two departments at the Technical University of Denmark (DTU), the National Space Institute (DTU Space) and the Department of Applied Mathematics and Computer Science (DTU Compute), and Harnvig Arctic & Maritime. The project is funded by Innovation Fund Denmark.
The objective of ASIP is to develop an automatic sea ice product service for Greenland waters which can meet the increasing demands for sea ice information coming from the growing group of users operating in Greenland waters. In the span from traditional, manually produced ice charts and daily downstream sea ice products at coarse resolution, there is a lack of high resolution products delivered in near-real time. ASIP intends to meet this demand by taking advantage of the vast amount of new data from the Copernicus Sentinel satellites and by using a new and innovative data fusion approach and state-of-the-art mathematical/statistical data processing methods: utilization of data from satellite sensors with different modalities/capabilities will facilitate the making of ice products that are reproducible, independent of operator, daylight, weather and season and will result in a significant increase in product temporal frequency and geographical coverage compared to existing ice products.
The statistical algorithms work directly in the Sentinel-1 scene coordinate system. In order to make use of the information in the AMSR2 data along with the radar data an alignment of the AMSR2 data to the radar coordinate system is therefore necessary. In this process of interpolating AMSR2 data to the Sentinel SAR data, in a preparatory study six methods are compared by means of leave-one-out cross-validation (LOOCV)
1. nearest neighbour (NN, one neighbour only),
2. triangulated irregular network (TIN, three neighbours only),
3. local mean (LM),
4. inverse distance (ID),
5. inverse squared distance (ID2), and 6. ordinary kriging (OK).
Bias and and root-mean-squared error (RMSE) are used as measures of precision. OK with 20-30 nearest neighbours obtains a LOOCV bias of around 0.001 K and RMSE of around 1.1 K. The second best of the six methods is ID2 which with 5-10 nearest neighbours gives a LOOCV bias of around 0.01 K and RMSE of around 3 K. When we use kriging we must estimate semivariograms and model them, this takes operator as well as computer time.
The project homepage https://asip.dk will be launched soon.
In signal and image processing principal component analysis (PCA) is often used for dimensionality reduction and feature extraction in pre-processing steps to for example classification.
In remote sensing image analysis PCA is often replaced by maximum autocorrelation factor
(MAF) or minimum noise fraction (MNF) analysis. This is done because MAF and MNF analyses incorporate spatial information in the orthogonalization of the multivariate data which is conceptually more satisfactory and which typically gives better results.
In this contribution, autocorrelation between the multivariate data and a spatially shifted version of the same data in the MAF analysis is replaced by the information theoretical, entropy and Kullback-Leibler divergence based measure mutual information. This potentially gives a more detailed decomposition of the data. Also, the orthogonality between already found components and components of higher order requested in the MAF analysis is replaced by a requirement of minimum mutual information between components.
The sketched methods are used on the well-known AVIRIS (https://aviris.jpl.nasa.gov/) Indian Pines data.
Test statistics for comparison of real (as opposed to complex) variance-covariance matrices exist in the statistics literature .
In earlier publications we have described a test statistic for the equality of two variance-covariance matrices following the complex Wishart distribution with an associated p-value . We showed their application to bitemporal change detection and to edge detection  in multilook, polarimetric synthetic aperture radar (SAR) data in the covariance matrix representation . The test statistic and the associated p-value is described in  also. In  we focussed on the block-diagonal case, we elaborated on some computer implementation issues, and we gave examples on the application to change detection in both full and dual polarization bitemporal, bifrequency, multilook SAR data.
In  we described an omnibus test statistic Q for the equality of k variance-covariance matrices following the complex Wishart distribution. We also described a factorization of Q = R2 R3 … Rk where Q and Rj determine if and when a difference occurs. Additionally, we gave p-values for Q and Rj. Finally, we demonstrated the use of Q and Rj and the p-values to change detection in truly multitemporal, full polarization SAR data.
Here we illustrate the methods by means of airborne L-band SAR data (EMISAR) [8,9]. The methods may be applied to other polarimetric SAR data also such as data from Sentinel-1, COSMO-SkyMed, TerraSAR-X, ALOS, and RadarSat-2 and also to single-pol data.
The account given here closely follows that given our recent IEEE TGRS paper .
 Anderson, T. W., An Introduction to Multivariate Statistical Analysis, John Wiley, New York, third ed. (2003).
 Conradsen, K., Nielsen, A. A., Schou, J., and Skriver, H., “A test statistic in the complex Wishart distribution and its application to change detection in polarimetric SAR data," IEEE Transactions on Geoscience and Remote Sensing 41(1): 4-19, 2003.
 Schou, J., Skriver, H., Nielsen, A. A., and Conradsen, K., “CFAR edge detector for polarimetric SAR images," IEEE Transactions on Geoscience and Remote Sensing 41(1): 20-32, 2003.
 van Zyl, J. J. and Ulaby, F. T., “Scattering matrix representation for simple targets," in Radar Polarimetry for Geoscience Applications, Ulaby, F. T. and Elachi, C., eds., Artech, Norwood, MA (1990).
 Canty, M. J., Image Analysis, Classification and Change Detection in Remote Sensing,with Algorithms for ENVI/IDL and Python, Taylor & Francis, CRC Press, third revised ed. (2014).
 Nielsen, A. A., Conradsen, K., and Skriver, H., “Change detection in full and dual polarization, single- and multi-frequency SAR data," IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 8(8): 4041-4048, 2015.
 Conradsen, K., Nielsen, A. A., and Skriver, H., "Determining the points of change in time series of polarimetric SAR data," IEEE Transactions on Geoscience and Remote Sensing 54(5), 3007-3024, 2016.
 Christensen, E. L., Skou, N., Dall, J., Woelders, K., rgensen, J. H. J., Granholm, J., and Madsen, S. N., “EMISAR: An absolutely calibrated polarimetric L- and C-band SAR," IEEE Transactions on Geoscience and Remote Sensing 36: 1852-1865 (1998).
When the covariance matrix representation is used for multi-look polarimetric synthetic aperture radar (SAR) data, the complex Wishart distribution applies. Based on this distribution a likelihood ratio test statistic for equality of two complex variance-covariance matrices and an associated p-value are given. In a case study airborne EMISAR C- and L-band SAR images covering agricultural fields and wooded areas near Foulum, Denmark, are used in single- and bi-frequency, bi-temporal change detection with full and dual polarimetry data.
This contribution deals with classification of multilook fully polarimetric synthetic aperture radar (SAR) data by learning a dictionary of crop types present in the Foulum test site. The Foulum test site contains a large number of agricultural fields, as well as lakes, wooded areas, natural vegetation, grasslands and urban areas, which makes it ideally suited for evaluation of classification algorithms. Dictionary learning centers around building a collection of image patches typical for the classification problem at hand. This requires initial manual labeling of the classes present in the data and is thus a method for supervised classification. The methods aim to maintain a proficient number of typical patches and associated labels. Data is consecutively classified by a nearest neighbor search of the dictionary elements and labeled with probabilities of each class. Each dictionary element consists of one or more features, such as spectral measurements, in a neighborhood around each pixel. For polarimetric SAR data these features are the elements of the complex covariance matrix for each pixel. We quantitatively compare the effect of using different representations of the covariance matrix as the dictionary element features. Furthermore, we compare the method of dictionary learning, in the context of classifying polarimetric SAR data, with standard classification methods based on single-pixel measurements.
This contribution deals with change detection by means of sparse principal component analysis (PCA) of simple
differences of calibrated, bi-temporal HyMap data. Results show that if we retain only 15 nonzero loadings (out
of 126) in the sparse PCA the resulting change scores appear visually very similar although the loadings are
very different from their usual non-sparse counterparts. The choice of three wavelength regions as being most
important for change detection demonstrates the feature selection capability of sparse PCA.
The iteratively re-weighted multivariate alteration detection (IR-MAD) algorithm may be used both for unsuper-
vised change detection in multi- and hyperspectral remote sensing imagery as well as for automatic radiometric
normalization of multi- or hypervariate multitemporal image sequences. Principal component analysis (PCA) as
well as maximum autocorrelation factor (MAF) and minimum noise fraction (MNF) analyses of IR-MAD images,
both linear and kernel-based (which are nonlinear), may further enhance change signals relative to no-change
background. The kernel versions are based on a dual formulation, also termed Q-mode analysis, in which the
data enter into the analysis via inner products in the Gram matrix only. In the kernel version the inner products
of the original data are replaced by inner products between nonlinear mappings into higher dimensional feature
space. Via kernel substitution, also known as the kernel trick, these inner products between the mappings are in
turn replaced by a kernel function and all quantities needed in the analysis are expressed in terms of the kernel
function. This means that we need not know the nonlinear mappings explicitly. Kernel principal component
analysis (PCA), kernel MAF and kernel MNF analyses handle nonlinearities by implicitly transforming data into
high (even in¯nite) dimensional feature space via the kernel function and then performing a linear analysis in
In image analysis the Gram matrix is often prohibitively large (its size is the number of pixels in the image
squared). In this case we may sub-sample the image and carry out the kernel eigenvalue analysis on a set of
training data samples only. To obtain a transformed version of the entire image we then project all pixels, which
we call the test data, mapped nonlinearly onto the primal eigenvectors.
IDL (Interactive Data Language) implementations of IR-MAD, automatic radiometric normalization and
kernel PCA/MAF/MNF transformations have been written which function as transparent and fully integrated
extensions of the ENVI remote sensing image analysis environment. Also, Matlab code exists which allows for
fast data exploration and experimentation with smaller datasets. Computationally demanding kernelization of
test data with training data and kernel image projections have been programmed to run on massively parallel
CUDA-enabled graphics processors, when available, giving a tenfold speed enhancement. The software will be
available from the authors' websites in the near future.
A data example shows the application to bi-temporal RapidEye data covering the Garzweiler open pit mine
in the Ruhr area in Germany.
Kernel versions of the principal components (PCA) and maximum autocorrelation factor (MAF) transformations
are used to postprocess change images obtained with the iteratively re-weighted multivariate
alteration detection (MAD) algorithm. It is found that substantial improvements in the ratio of
signal (change) to background noise (no change) can be obtained especially with kernel MAF.
Principal component analysis (PCA) is often used to detect change over time in remotely sensed images. A
commonly used technique consists of finding the projections along the two eigenvectors for data consisting of two
variables which represent the same spectral band covering the same geographical region acquired at two different
time points. If change over time does not dominate the scene, the projection of the original two bands onto the
second eigenvector will show change over time. In this paper a kernel version of PCA is used to carry out the
analysis. Unlike ordinary PCA, kernel PCA with a Gaussian kernel successfully finds the change observations in
a case where nonlinearities are introduced artificially.
The iteratively re-weighted multivariate alteration detection (IR-MAD) transformation is proving to be very
successful for multispectral change detection and automatic radiometric normalization applications in remote
sensing. Various alternatives exist in the way in which the weights (no-change probabilities) are calculated
during the iteration procedure. These alternatives are compared quantitatively on the basis of multispectral
imagery from different sensors under a range of ground cover conditions exhibiting wide variations in the amount
of change present, as well as with a partially artificial data set simulating truly time-invariant observations. A
best re-weighting procedure is recommended.
The statistical techniques of multivariate alteration detection, maximum autocorrelation factor transformation, expectation
maximization, fuzzy maximum likelihood estimation and probabilistic label relaxation are combined in a unified scheme to classify changes in multispectral satellite data. An example involving bitemporal LANDSAT TM imagery is given.