In recent years, Low-rank matrix recovery from corrupted noise matrix has attracted interests as a very effective method
in high-dimensional data. And its fast algorithm has become a research focus. This paper we first review the basic theory
and typical accelerated algorithms. All these methods are proposed to mitigating the computational burden, such as the
iteration count before convergence, especially the frequent large-scale Singular Value Decomposition (SVD). For better
convergence, we employ the Augmented Lagrange Multipliers to solve the optimization problem. Recent the endeavors
have focused on smaller-scale SVD, especially the method based on submatrix. Finally, we present numerical
experiments on large-scale date.
Classical compression methods of remote sensing (RS) panchromatic images are much the same as the traditional compression ones, in which distributions of different surface features are not taken into account. Instead, RS panchromatic images are divided into blocks in our method and those blocks can be classified into several categories by analyzing their intensity distributions. Afterwards, each category is compressed separately. According to Shannon’s theorem 3, a source with given distribution and distortion has a unique theoretical minimum bitrate. Hence, under a given compression quality, the theoretical minimum bitrate of each category can be calculated using rate-distortion theory. Meanwhile, each category may have its own distortion due to the user’s different quality requirements. Our method performs well in reducing the redundancy of surface features which users do not care about so that more “valid data” would be obtained from the compressed images. Furthermore, it also provides flexibility between fixed compression ratio and quality-based compression.