Robust PCA neural networks for random noise reduction of the data

The paper presents a principal component analysis (PCA) approach to the reduction of noise contaminating the data. The PCA performs the role of lossy compression and decompression. The compression/decompression provides the means of coding the data and then recovering it with some losses, dependent on the realized compression ratio. In this process some part of the information contained in the data is lost. When the loss tolerance is equal to the noise strength, the noise and the loss tolerance are augmented and the decompressed signal is deprived of noise. This way of noise filtering has been checked on examples of 1-dimensional and 2-dimensional data and the results of numerical experiments are included