Digital Coding of Waveforms

Spectral transforms are widely used for the codification of remote-sensing imagery, with the Karhunen-Loeve transform (KLT) and wavelets being the two most common transforms. The KLT presents a higher coding performance than the wavelets. However, it also carries several disadvantages: high computational cost and memory requirements, difficult implementation, and lack of scalability. In this paper, we introduce a novel transform based on the KLT, which, while obtaining a better coding performance than the wavelets, does not have the mentioned disadvantages of the KLT. Due to its very small amount of side information, the transform can be applied in a line-based scheme, which particularly reduces the transform memory requirements. Extensive experimental results are conducted for the Airborne Visible/Infrared Imaging Spectrometer and Hyperion images, both for lossy and lossless and in combination with various hyperspectral coders. The results of the effects on Reed Xiaoli anomaly detection and k-means clustering are also included. The theoretical and experimental evidences suggest that the proposed transform might be a good replacement for the wavelets as a spectral decorrelator in many of the situations where the KLT is not a suitable option.

http://deic.uab.cat/~iblanes/papers/2010_10-IEEE-TGRS-POT.pdf

Pairwise Orthogonal Transform for Spectral Image Coding

The Karhunen-Loeve transform (KLT) is widely used in hyperspectral image compression because of its high spectral decorrelation properties. However, its use entails a very high computational cost. To overcome this computational cost and to increase its scalability, in this paper, we introduce a multilevel clustering approach for the KLT. As the set of different multilevel clustering structures is very large, a two-stage process is used to carefully pick the best members for each specific situation. First, several candidate structures are generated through local search and eigenthresholding methods, and then, candidates are further screened to select the best clustering configuration. Two multilevel clustering combinations are proposed for hyperspectral image compression: one with the coding performance of the KLT but with much lower computational requirements and increased scalability and another one that outperforms a lossy wavelet transform, as spectral decorrelator, in quality, cost, and scalability. Extensive experimental validation is performed, with images from both the AVIRIS and Hyperion sets, and with JPEG2000, 3D-TCE, and CCSDS-Image Data Compression recommendation as image coders. Experiments also include classification-based results produced by k-means clustering and Reed-Xiaoli anomaly detection.

Cost and Scalability Improvements to the Karhunen–Loêve Transform for Remote-Sensing Image Coding

2010 ieee international geoscience and remote sensing symposium

Quality scalability is a fundamental feature of JPEG2000, achieved through the use of quality layers that are optimally formed in the encoder by rate-distortion optimization techniques. Two points, related with the practical use of quality layers, may need to be addressed when dealing with JPEG2000 code-streams: 1) the lack of quality scalability of code-streams containing a single or few quality layers and 2) the rate-distortion optimality of windows of interest transmission. Addressing these two points, this paper proposes a mechanism that, without using quality layers, provides competitive quality scalability to code-streams. Its main key-feature is a novel characterization of the code-blocks rate-distortion contribution that does not use distortion measures based on the original image, or related with the encoding process. Evaluations against the common use of quality layers, and against a theoretical optimal coding performance when decoding windows of interest or when decoding the complete image area, suggest that the proposed method achieves close to optimal results.

http://www.deic.uab.cat/~francesc/research/rd_optimization/2008_07-IEEE_TCSVT.pdf

JPEG2000 Quality Scalability Without Quality Layers

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

http://www.cs.utep.edu/vladik/2004/olg04-5b.pdf

Rate distortion optimal bit allocation methods for volumetric data using JPEG 2000

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.

Assessment of KLT and bit-allocation strategies in the application of JPEG 2000 to the battlescale forecast meteorological data

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.

Compressing three-dimensional GRIB meteorological data using KLT and JPEG 2000

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.

/pdf/comparison-of-bit-allocation-methods-for-compressing-three-mqnhsign4q.pdf

Comparison of bit allocation methods for compressing three-dimensional meteorological data after applying KLT

We evaluate a compression scheme that exploits inter-slice redundancy in medical imaging that is compatible with the JPEG 2000 core coding system extensions (part 2). The scheme consists of applying a decorrelating transform in the cross-slice vertical direction subsequently compressing each slice with a core part 1 JPEG 2000 coder. The rates for each slice are chosen according to a heuristic log-based allocation algorithm. Two transforms were considered, the KLT and the DWT 9/spl times/7. A gain of up to 4-4 dB in RMSE was achieved using the DWT 9/spl times/7 over a baseline JPEG 2000 system that uses no decorrelating transform.

E. Vidal

Papers

Rate distortion optimal bit allocation methods for volumetric data using JPEG 2000

Assessment of KLT and bit-allocation strategies in the application of JPEG 2000 to the battlescale forecast meteorological data

Compressing three-dimensional GRIB meteorological data using KLT and JPEG 2000

Comparison of bit allocation methods for compressing three-dimensional meteorological data after applying KLT

Compression of three-dimensional medical image data based on JPEG 2000