Search-Order Coding Method with Indicator-elimination Property

[[abstract]]Vector quantization (VQ) is a widely used technique for many applications especially for lossy image compression. Since VQ significantly reduces the size of a digital image, it can save the costs of storage space and image delivery. Search-order coding (SOC) was proposed for improving the performance of VQ in terms of compression rate. However, SOC requires extra data (i.e. indicators) to indicate source of codewords so the compression rate may be affected. To overcome such a drawback, in this paper, a search-order coding with the indicator-elimination property was proposed by using a technique of reversible data hiding. The proposed method is the first one using such a concept of data hiding to achieve a better compression rate of SOC. From experimental results, the performance of the SOC method can be successfully improved by the proposed indicator eliminated search-order coding method in terms of compression rate. In addition, compared with other relevant schemes, the proposed method is also more flexible than some existing schemes

Search-Order Coding Method with Indicator-elimination Property

[[abstract]]Vector quantization (VQ) is a widely used technique for many applications especially for lossy image compression. Since VQ significantly reduces the size of a digital image, it can save the costs of storage space and image delivery. Search-order coding (SOC) was proposed for improving the performance of VQ in terms of compression rate. However, SOC requires extra data (i.e. indicators) to indicate source of codewords so the compression rate may be affected. To overcome such a drawback, in this paper, a search-order coding with the indicator-elimination property was proposed by using a technique of reversible data hiding. The proposed method is the first one using such a concept of data hiding to achieve a better compression rate of SOC. From experimental results, the performance of the SOC method can be successfully improved by the proposed indicator eliminated search-order coding method in terms of compression rate. In addition, compared with other relevant schemes, the proposed method is also more flexible than some existing schemes

Efficient and Robust Compressed Sensing Using Optimized Expander Graphs

Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any n-dimensional vector that is k-sparse can be fully recovered using O(klog n) measurements and only O(klog n) simple recovery iterations. In this paper, we improve upon this result by considering expander graphs with expansion coefficient beyond 3/4 and show that, with the same number of measurements, only O(k) recovery iterations are required, which is a significant improvement when n is large. In fact, full recovery can be accomplished by at most 2k very simple iterations. The number of iterations can be reduced arbitrarily close to k, and the recovery algorithm can be implemented very efficiently using a simple priority queue with total recovery time O(nlog(n/k))). We also show that by tolerating a small penal- ty on the number of measurements, and not on the number of recovery iterations, one can use the efficient construction of a family of expander graphs to come up with explicit measurement matrices for this method. We compare our result with other recently developed expander-graph-based methods and argue that it compares favorably both in terms of the number of required measurements and in terms of the time complexity and the simplicity of recovery. Finally, we will show how our analysis extends to give a robust algorithm that finds the position and sign of the k significant elements of an almost k-sparse signal and then, using very simple optimization techniques, finds a k-sparse signal which is close to the best k-term approximation of the original signal