In this paper, minimization of the maximum absolute error (MAE) is achieved under a JPEG 2000 framework when a compression ratio is specified. The process is founded on our recent JPEG 2000-based algorithm for minimizing bit rate for a desired MAE using a residual coding approach [Lucero, A., et al., 2006; Lucero, A., et al., 2005; Yee, Y., et al., 2007] that uses the EBCOT coder separately. This type of algorithm uses the lossy and lossless capabilities of JPEG 2000 to achieve a desired MAE or a desired total bit rate. The technique to achieve the lowest MAE possible for a specified average bit rate is developed here for application to 3-D scientific data sets. Lossy compression is applied to the original data, while lossless compression is employed on the quantized residuals (the difference between the original and the lossy decompressed data). The lowest MAE is achieved by optimizing the allocation of the desired total bit rate between the two contributing rates corresponding to the lossy and the lossless compression steps. The methodology for achieving minimum MAE and results for 3-D meteorological data are presented here.

Computer modeling programs that generate three-dimensional (3-D) data on fine grids are capable of generating very large amounts of information. These data sets, as well as 3-D sensor/measured data sets, are prime candidates for the application of data compression algorithms. A very flexible and powerful compression algorithm for imagery data is the newly released JPEG 2000 standard. JPEG 2000 also has the capability to compress volumetric data, as described in Part 2 of the standard, by treating the 3-D data as separate slices. As a decoder standard, JPEG 2000 does not describe any specific method to allocate bits among the separate slices. This paper proposes two new bit allocation algorithms for accomplishing this task. The first procedure is rate distortion optimal (for mean squared error), and is conceptually similar to postcompression rate distortion optimization used for coding codeblocks within JPEG 2000. The disadvantage of this approach is its high computational complexity. The second bit allocation algorithm, here called the mixed model (MM) approach, mathematically models each slice's rate distortion curve using two distinct regions to get more accurate modeling at low bit rates. These two bit allocation algorithms are applied to a 3-D Meteorological data set. Test results show that the MM approach gives distortion results that are nearly identical to the optimal approach, while significantly reducing computational complexity.

The problem of optimal bit rate allocation for 3-D JPEG2000 compression is dicussed. In this paper we consider data where the 2-D slices are compressed using JPEG2000, and the third dimension is decorrelated using the Karhunen-Loeve Transform. Here two new methods are proposed. The first approach is called the Rate Distortion Optimal (RDO) method and is based on Post-Compression Rate-Distortion (PCRD) optimization concept. The second approach is here called the Mixed Model (MM) approach and consists of extending the traditional high-resolution model with a region that is accurate for low bit rates. The proposed bit allocation methods are tested by applying them to Meteorological (Met) data. The specific data set used was generated by the Battlescale Forecast Model (BFM). The test results shows that these approach significantly reduces the computational complexity.

This paper presents the latest results of an ongoing project to assess the impact of lossy compression applied to three-dimensional meteorological data. The main innovative outcomes presented are based on different bit allocation techniques used to compress Karhunen-Loeve transformed data. The transform is applied in the z-direction (between slices) as suggested in the JPEG2000 Part 2 standard. New results using these bit allocation techniques are presented on two data sets. The performance results are presented in terms of SNR, root-mean squared error (RMSE), and the maximum absolute error (MAE) for the entire cube of data.

This paper focuses on the parameters selection that optimizes JPEG 2000 compression for meteorological data. In particular, a procedure for bit rate allocation for different slices of data is proposed. The selection is based on the variances of individual slices and a mixed model approximation of MSE. The solution of the constrained minimization problem for MSE is obtained using Lagrange multipliers. This procedure allows the incorporation of other constraints in this problem such as noninteger bit rates, limited range of possible bit rates, etc. Experimental results are given for all six variables. The reduction of MSE also led to the reduction of maximum absolute error in most cases.

In this paper, a study on 3D GRIB (GRIdded Binary) meteorological data is presented. The study consists of statistical analysis and lossy compression experiments on the data. In order to achieve compression ratios in the range of 10 to 100, lossy JPEG2000 compression was used on horizontal slices of the data. When compressing the data, an evaluation was performed to determine benefits of pre-processing the data by applying a set of different transforms in the z-direction. The transforms used in the z-direction included the Karhunen-Loeve transform (KLT) and the 9/7 wavelet filters. Results obtained in the data analysis and compression are presented.