1. Example Results (Case 1) This shows our estimation technique applied to real data. The information loss (in other words which values to drop) was simulated according to the CCSDS specification. However all the data is real. Because the true values are available, this scenario allows us to evaluate the performance of our estimation. Shown at the top is the real data with a simulated loss of part of a packet. The restored image is shown in the middle. For comparison the original image is shown at the bottom. Our algorithm restores the missing data accurately. Example Results (Case 2) Here we show a second example with different statistics. In spite of the complex structure of the data, the restoration is able to restore the missing values accurately without visible artifacts. It is important to note that only the band with simulated packet loss is shown here. The recovery method uses measurements from other bands at the same spatial pixel to produce the restoration. Error Mitigation for CCSD Compressed Imager data By: George Bonev, Fazlul Shahriar Advisors: Irina Gladkova, Michael Grossberg, Srikanth Gottipati Key Issues Errors Unavoidable o Forward Error Correction (FEC) Encoding Helps o FEC only reduces number of errors Compression - Decompression can magnify errors o One bit error in compressed file may cause many errors on decompression Rice Standard Error Strategy: Bit Plane Encoding o Extra Protection for higher order bits Packetization o Error only allowed to propagate to end of packet o Packet size up to implementer Packet Size Trade-off: Big Packets Good for compression Sensitive to errors Small Packets Less sensitive to errors Bad for compression In case of error: Standard (CCSDS) Specifies Error Treatment Dummy values filled from error to end of packet Bad packets/pixels can be noted in header Error Mitigation: Is it possible to estimate the missing data? Use the statistics of the rest of the data Possible if missing data is a local function of the remainder Non-Parametric Regression This graph, obtained directly from three channels of SEVIRI data, illustrates why it is possible to accurately estimate missing data. The XYZ coordinates of the cloud of blue points are the gray level values in each of three bands. As is seen the blue points in 3D lie very close to a 2D surface. If a value is missing, for example Z, due to packet loss, then only the X and Y are known. A simulated sample of such points is shown in yellow. The red points are the corresponding XYZ points with the true Z that must be estimated. We have developed a method using non-parametric estimation to estimate the missing value, using a non- parametric regression technique. Error MitigationTechnique Statistical Estimate Uses all available data Both spatial and spectral Probabilistic approximation to Maximum Likelihood estimator Header maintains list of values estimated End user has locations of estimated values in header Always has option to disregard estimates This image was taken from a SEVIRI dataset. Packet loss was simulated along a scan line according to the CCSDS specification. Dummy values, represented in blue start, at a pixel and run along one or more scan lines. References: [1] Ef ros, A. and Leung, T., Texture synthesis by non-parametric sampling," Proceedings of 7th International Conference on Computer Vision, 10331038 (1999). [2] Efros, A. and Freeman, W., Image quilting for texture synthesis and transfer," in [Proceedings of SIG- GRAPH], (August 2001). [3] Piazza, E. and Pellegrini, P., Digital error correction for remote sensed multispectral images," in [Digital Signal Processing Proceedings, DSP 97], 2, 825{828 (July 1997). This research has been funded by NOAA-CREST grant # NA06OAR4810162