This paper presents a follow-up to last year's SPIE meeting where we presented a residual encoding method to control maximum absolute error (MAE) based on JPEG2000 Part 2 standard and which was applied to hyperspectral data. In this paper, we evaluate an improved version of the approach on the ultraspectral sounder satellite data made available by NOAA. The data set used consists of a subset of 1,501 bands out of the 2,378 total and where each band is an image of size 90 by 135 pixels. Each pixel or data value is a digital count integer that requires 12 - 14 bits to represent. We present compression performance using a transform in the band (z- or cross-component) direction. We use either the Karhunen-Loeve transform or the discrete wavelet transform with a non-uniform bit-rate allocation to take advantage of the energy compaction. One of the main features of this compression scheme is that residuals (original minus the decompressed values) are also coded in order to control the MAE; therefore, lossless compression can also be accomplished by using a desired MAE of 0.5. In all cases, the quantized residuals are losslessly encoded using the embedded block coding with optimized truncation (EBCOT) bit-plane encoding method that is part of JPEG2000 Part 1. Finally, our recent algorithm for automatically choosing the best (smallest total) combination of the two contributing bit rates is also extended to the 3-dimensional case. The two rates are: (1) the Open Loop rate for the lossy compression using JPEG2000 Part 2 by itself and (2) the EBCOT rate that results from the coding of the quantized residuals. The basis for the approach is the modeling of the residuals using generalized Gaussian random variables. Results for lossless and near-lossless compression will be presented using both an exhaustive search and the automatic search method for finding the minimum overall bit rate.
This paper presents a study on the compression of hyperspectral satellite data using JPEG 2000 and residual encoding (RE). The first step in the process is to apply a decorrelating transform in the spectral-direction or z-direction. In most cases in this study, the Karhunen-Loeve Transform (KLT) is used. For comparison, some examples are also included where the discrete wavelet transform (DWT) is used for this purpose as well as examples with a purely 2-D approach that uses no z-direction transform. Bit-rate allocation techniques are used in order to take advantage of the energy compaction obtained when applying a transform in the z-direction. The transformed slices and their corresponding bit rates are input into JPEG 2000 in order to obtain the compressed bit stream. In this study, the compressed bit stream is decompressed at the encoder side in order to compute the recovered data. These data are then subtracted from the original data in order to calculate the residuals, which are then quantized and losslessly encoded separately using JPEG2000 itself in order to control the maximum absolute error (MAE). An analysis between using and omitting residual encoding with respect to MAE is included. It is observed that a decrease in the MAE by a factor of 3 is achieved for this data with very small overhead when the residual encoding is utilized. The two data sets used in this study are the well known Cuprite radiance imagery from AVIRIS and a set from the Hyperion satellite system, both of which are available in 16 bits per value form.
A Zerotree (ZT) coding scheme is applied as a post-processing stage to avoid transmitting zero data in the High-Speed Pyramid (HSP) image compression algorithm. This algorithm has features that increase the capability of the ZT coding to give very high compression rates. In this paper the impact of the ZT coding scheme is analyzed and quantified. The HSP algorithm creates a discrete-time multiresolution analysis based on a hierarchical decomposition technique that is a subsampling pyramid. The filters used to create the image residues and expansions can be related to wavelet representations. According to the pixel coordinates and the level in the pyramid, N2 different wavelet basis functions of various sizes and rotations are linearly combined. The HSP algorithm is computationally efficient because of the simplicity of the required operations, and as a consequence, it can be very easily implemented with VLSI hardware. This is the HSP's principal advantage over other compression schemes. The ZT coding technique transforms the different quantized image residual levels created by the HSP algorithm into a bit stream. The use of ZT's compresses even further the already compressed image taking advantage of parent-child relationships (trees) between the pixels of the residue images at different levels of the pyramid. Zerotree coding uses the links between zeros along the hierarchical structure of the pyramid, to avoid transmission of those that form branches of all zeros. Compression performance and algorithm complexity of the combined HSP-ZT method are compared with those of the JPEG standard technique.