Reversible System Based on Block-PCA

Traditional principal components analysis (PCA) is a useful method to reduce dimension of data nowadays. However, PCA method only be employed on dimensions decrease. In this paper, we propose a block-based principal components analysis method to make a reversible transform system. Firstly, the input 1-D or 2-D signal is divided to the same size parts. And then the parts are converted to PCA operation inputs. Next, the projection coefficients are calculated via the signals which decrease its mean and the eigenvector that is obtained from decomposition of covariance matrix. We define the operation is block-PCA transform, and the projection coefficients that is a new domain is different with normal domain. In inverse transform operation, we use inverted based function to recover original signals. In experimental result, we employ signal-noise-rate (SNR) and peak-signal-noise-rate to prove our proposed system is a reversible system that inverse transform process can recover original signals losslessly. In addition, we also check this system which has the data hiding capacity. Finally, without considered quantization, we compare the compressing rate of capacity with exist reversible system. The result shows our system has lower capacity.