IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 6, NO. 3, JULY 2009 587 Lossy-to-Lossless Hyperspectral Image Compression Based on Multiplierless Reversible Integer TDLT/KLT Lei Wang, Jiaji Wu, Member, IEEE, Licheng Jiao, Senior Member, IEEE, and Guangming Shi, Member, IEEE Abstract—We proposed a new transform scheme of multipli- erless reversible time-domain lapped transform and Karhunen– Loève transform (RTDLT/KLT) for lossy-to-lossless hyperspectral image compression. Instead of applying discrete wavelet transform (DWT) in the spatial domain, RTDLT is applied for decorrelation. RTDLT can be achieved by existing discrete cosine transform and pre- and postfilters, while the reversible transform is guaranteed by a matrix factorization method. In the spectral direction, re- versible integer low-complexity KLT is used for decorrelation. Owing to completely reversible transform, the proposed method can realize progressive lossy-to-lossless compression from a single embedded code-stream file. Numerical experiments on benchmark images show that the proposed transform scheme performs better than 5/3DWT-based methods in both lossy and lossless compres- sions, comparable with the optimal 9/7DWT-FloatKLT-based lossy compression method. Index Terms—Discrete cosine transform (DCT), hyperspectral image compression, integer transform, Karhunen–Loève trans- form (KLT), lossy-to-lossless compression, time-domain lapped transform (TDLT). I. I NTRODUCTION H YPERSPECTRAL images have wide applications nowa- days such as in atmospheric detecting, remote sensing, military affairs, and so on. However, the volume of hyperspec- tral image is so large that a 16-bit AVIRIS image with size of 512 × 512 × 224 will occupy 112 MB. Therefore, efficient compression algorithms are required to reduce the cost of equipment storage or bandwidth. Lossy-to-lossless compression will be of great importance in telemedicine and satellite communications for legal reasons or research requirements. To realize scalable coding, most of the state-of-the-art compression methods adopt 3-D discrete wavelet transform (DWT) [1]–[3] or DWT/Karhunen–Loève transform (KLT) [4]–[6], where 9/7 floating-point filter is al- Manuscript received October 21, 2008; revised January 17, 2009 and March 13, 2009. First published June 16, 2009; current version published July 4, 2009. This work was supported in part by the National Science Foundation of China under Grants 60607010 and 60672125, by the Program for Cheung Kong Scholars and Innovative Research Team in University (IRT0645), and by the Key Scientific and Technological Innovation Special Projects of Shaanxi “13115” under Grant 2007ZDKG-55. The authors are with the Key Laboratory of Intelligent Perception and Image Understanding of Ministry of Education of China, Institute of Intelli- gent Information Processing, Xidian University, Xi’an 710071, China (e-mail: wanglei0912@mail.xidian.edu.cn; wujj@mail.xidian.edu.cn; lchjiao@mail. xidian.edu.cn; gmshi@xidian.edu.cn). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/LGRS.2009.2021674 ways used for decorrelation in lossy compression. Lossless compression schemes include methods based on vector quan- tization, prediction, integer transform, and so on. Although prediction-based methods perform well, they do not have the ability of realizing progressive lossy-to-lossless compression which is owned by transform-based method [7]. Sweldens [8], [9] proposed the lifting scheme for the realization of wavelet transforms (WTs). Bilgin et al. [10] introduced reversible integer WT in the application of 3-D image compression. Xiong et al. [11] applied 3-D integer WT in medical image compression and pointed out that the transform has to be unitary to achieve good lossy coding performance. Some researchers have studied integer KLT for spectral decorrelation. Hao and Shi [12] proposed reversible integer KLT, and Galli and Salzo [13] improved it. However, in spatial domain, integer WTs are still applied as common methods. A drawback of a wavelet- based compression method is that 5/3DWT is usually applied instead of 9/7DWT in lossy-to-lossless compression schemes, and this will lead to performance degradation. Another disad- vantage of DWT is that it cannot compete with DCT due to the constraint of CPU and computer memory, particularly in real- time and low-complexity applications, because the computing complexity of WT increases exponentially when the image size increases [14]. DCT has its own special advantages such as low memory cost, flexibility at block-by-block level, parallel processing, etc. Tran et al. [15] have designed pre- and postfilters to improve the performance of DCT and called the combination as time- domain lapped transform (TDLT). The rationale behind this method is that, within the filtered block, the pixels are as homogenous as possible, and this will be helpful for improving transform efficiency. Although TDLT performs even better than DWT does in the energy compatibility and lossy compression, it does not perform well in the lossless compression where the reversible transform is required. In fact, for hyperspectral image compression, completely reversible transform method is always required to realize lossy-to-lossless coding. In this letter, we take a practical and innovative approach to replace integer WT with integer reversible TDLT (RTDLT) in the spatial domain, and the RTDLT is realized by the improved matrix factorization method. RTDLT can realize integer re- versible transform, and hence, we adopted a progressive lossy- to-lossless hyperspectral image compression method based on RTDLT and reversible KLT (RKLT). Block transforming coeffi- cients in the spatial domain would be reorganized into subband 1545-598X/$25.00 © 2009 IEEE