New Approaches in Image Compression and Noise Removal

Principal Component Analysis is a well-known statistical method for feature extraction and it has been broadly used in a large series of image processing applications. The multiresolution support provides a suitable framework for noise filtering and image restoration by noise suppression. The procedure used is to determine statistically significant wavelet coefficients and from this to specify the multiresolution support. In the third section, we introduce the algorithms Generalized Multiresolution Noise Removal, and Noise Feature Principal Component Analysis. The algorithm Generalized Multiresolution Noise Removal extends the Multiresolution Noise Removal algorithm to the case of general uncorrelated Gaussian noise, and Noise Feature Principal Component Analysis algorithm allows the restoration of an image using a noise decorrelation process. A comparative analysis of the performance of the algorithms Generalized Multiresolution Noise Removal and Noise Feature Principal Component Analysis is experimentally performed against the standard Adaptive Mean Variance Restoration and Minimum Mean Squared Error algorithms. In the fourth section, we propose the Compression Shrinkage Principal Component Analysis algorithm and its model-free version as Shrinkage-Principal Component Analysis based methods for noise removal and image restoration. A series of conclusive remarks are supplied in the final section of the paper.