在現代的影像壓縮技術中，為了實現高壓縮率，編碼器利用了幀(frame)內部空間上的相關性(intra frame coding)和幀與幀在時間上的相關性(inter frame coding)，而在解碼端，解回一幀所需的複雜度遠小於編碼端。然而，在某些應用上，我們會使用一些缺乏記憶體與計算能力的裝置。分散式影像編碼(distributed video coding)在此情境下有很大的幫助，根據分散式來源編碼(distributed source coding)的概念，分散式影像編碼強調在一個低複雜度的編碼器，與一個計算能力較高的解碼器，這種概念類似壓縮感知(compressive sensing)。因此，在本篇論文中，我們討論如何將壓縮感知應用在分散式影像編碼上。我們提出一個採用小波(wavelet)與壓縮感知處理的分散式影像編碼方法， 利用再小波頻域上的差值找出影像的稀疏(sparse)表示，我們同時利用skip block、量化(Quantization)及熵編碼(Entropy coding)降低bit-rate，在解碼端利用簡單的side information幫助解碼。我們主要的貢獻在進一步地降低編碼器的編碼時間，和其他分散式影像編碼演算法相比，實驗結果展示我們所提出編碼器能更省能量，這讓我們提出的編碼器有能力應用在一些電力與計算能力有限的裝置上。

In the modern video compression techniques, for achieving high compressive rate, the encoder would exploit all spatial (intra coding) and temporal (inter coding) correlation on every frame. The complexity to decode a frame is much less than to encode one. However, in some applications we would adopt some devices which lack memory and computing ability. Distributed Video Coding (DVC) is helpful in this situation. Based on the theoretic results of Distributed Source Coding (DSC), DVC focuses on a lower complexity encoder and a powerful decoder. This feature is very similar to the concept of Compressive Sensing (CS). Therefore, in this thesis, we discuss how to employ CS into DVC. We proposed a wavelet-based distributed video coding method with compressive sensing. To find a sparse representation for video frames, we use the difference on the wavelet domain. We also adopt skip block, quantization, and entropy coding to reduce the bit-rate. We use simple side information for helping decoder. The main contributions of our works are further reduction of complexity and coding time of the encoder. Compared with other DVC algorithms, the experimental results shows proposed encoder can save more energy. This makes the proposed encoder is able to be implemented in the devices with limited power or computational ability.

[1] D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, vol. 52, no. 4, pp. 1289-1306, September 2006.
[2] E.J. Candès and M.B. Wakin, ”An Introduction to Compressive Sampling,” IEEE Signal Processing Magazine, pp. 21-30, March 2008.
[3] E. Candès, J. Romberg, and T. Tao, “Robust Uncertainty Principles: Exact Signal Reconstruction From Highly Incomplete Frequency Information,” IEEE Transactions on Information Theory, vol. 52, no. 2, pp. 489-509, Feb. 2006.
[4] Rice Single-Pixel Camera Project, http://dsp.rice.edu/cscamera
[5] M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Processing Magazine, vol. 25, pp. 83-91, 2008.
[6] M.B. Wakin, J.N. Laska, M.F. Duarte, D. Baron, S. Sarvotham, D. Takhar, K.F. Kelly, and R.G. Baraniuk, “An Architecture for Compressive Imaging,” in Proc. IEEE Conf. Image Processing (ICIP ‘06), pp. 1273-1276, 2006.
[7] J. Romberg, “Imaging via compressive sampling,” IEEE Signal Processing Magazine, vol. 25, no. 2, pp. 14-20, Mar. 2008
[8] J. D. Slepian and J. K. Wolf, “Noiseless coding of correlated information sources,” IEEE Transactions on Information Theory, vol. IT-19, pp. 471–480, Jul. 1973.
[9] A. D. Wyner and J. Ziv, “The rate-distortion function for source coding with side information at the decoder,” IEEE Transactions on Information Theory, vol. IT-22, no. 1, pp. 1–10, Jan. 1976.
[10] A. Aaron, R. Zhang and B. Girod, “Wyner-Ziv coding of motion video,” in Proc. Conf. on Asilomar Conference on Signals and Systems, Pacific Grove, CA, Nov. 2002.
[11] B. Girod, A. Aaron, S. Rane and D. Rebollo-Monedero, “Distributed video coding,” in Proc. IEEE Conf. on Special Issue on Video Coding and Delivery, vol. 93, no. 1, pp. 71-83, January 2005.
[12] J. Tropp and A. C. Gilbert, “Signal Recovery from Random Measurements via Orthogonal Matching Pursuit,” IEEE Transactions on Information Theory, vol.53-12, pp.4655-4666, Dec. 2007.
[13] M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE Journal of selected topics in signal processing, vol.1-4, pp.586–597, 2007. Matlab code on http://www.lx.it.pt/~mtf/GPSR.
[14] R. Tibshirani, “Regression shrinkage and selection via the lasso,” Journal of Royal Statistical Society: Series B, vol. 58, pp. 267-288, 1996.
[15] C. Luo, F. Wu, J. Sun, C. W. Chen, "Compressive data gathering for large-scale wireless sensor networks", in Proc. Conf. on Mobile Computing and Networking (MobiCom), pp. 145-156, 2009.
[16] Z. Charbiwala, S. Chakraborty, S. Zahedi, Y. Kim, M. B. Srivastava, T. He, and C. Bisdikian, “Compressive Oversampling for Robust Data Transmission in Sensor Networks.” in Proc. IEEE Conf. Computer Communications (INFOCOM), San Diego, CA, March 2010.
[17] T. T. Do, T. D. Tran, and L. Gan, “Fast compressive sampling with structurally random matrices,” in Proc. IEEE Conf. on Acoustics, Speech and Signal Processing (ICASSP ‘08), pp. 3369-3372, May 2008. Matlab code on http://thanglong.ece.jhu.edu/CS/
[18] J. Meng, H. Li, and Z. Han, “Sparse Event Detection in Wireless Sensor Networks using Compressive Sensing,” in Proc. Conf. Information Sciences and Systems (CISS), 2009.
[19] J. Yang, J. Wright, T. Huang, and Y. Ma, “Image Super-Resolution as Sparse Representation of Raw Image Patches,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition (CVPR ‘08), pp. 1-8, 2008.
[20] D. Venkatraman and A. Makur, “A Compressive Sensing Approach To Object-based Surveillance Video Coding,” in Proc. IEEE Conf. on Acoustics, Speech and Signal Processing (ICASSP ‘09), pp. 3513-3516, 2009.
[21] T.T. Do, Y. Chen, D.T. Nguyen, N. Nguyen, L. Gan, and T.D. Tran, “Distributed Compressed Video Sensing,” in Proc. IEEE Conf. on Image Processing (ICIP ‘09), pp. 1393-1396, 2009.
[22] L. W. Kang and C. S. Lu, “Distributed Compressive Video Sensing,” in Proc. IEEE Conf. on Acoustics, Speech and Signal Processing (ICASSP ‘09), pp. 1169-1172, 2009.
[23] J. Prades-Nebot, Y. Ma, and T. Huang, “Distributed Video Coding using Compressive Sampling,” in Proc. Picture Coding Symposium, 2009.