Sparse Signal Subspace Decomposition Based on Adaptive Over-complete Dictionary

Signal subspace methods (SSM) are efficient techniques to reduce dimensionality of data and to filter out noise [1]. The fundamental idea under SSM is to project the data on a basis made of two subspaces, one mostly containing the signal and the other the noise. The two subspaces are separated by a thresholding criterion associated with some measures of information. The two most popular methods of signal subspace decomposition are wavelet shrinkage [2] and Principal Component Analysis (PCA) [3]. Both techniques have proved to be quite efficient. However, wavelet decomposition depending on signal statistics is not equally adapted to different data, and requires some knowledge on prior distributions or parameters of signals to efficiently choose the thresholds for shrinkage. A significant advantage of the PCA is its adaptability to data. The separation criterion is based on energy which may be seen as a limitation in some cases as illustrated in the next section. In recent years, sparse coding has attracted significant interest in the field of signal denoising [4].