Efficient Blind Image Separation Using Finite Ridgelet Transform

This paper deals with the problem of blind separation of digital images from noisy mixtures. It proposes the application of a blind separation algorithm on Ridgelet Transform (RT) of the mixed images, instead of performing the separation on the mixtures in the time domain. Ridgelet transform is a new directional multi-resolution transform and is more suitable for describing the signals with high dimensional singularities. Finite Ridgelet Transform (FRIT) is a discrete version of the ridgelet transform with high numerical precision as the continuous ridgelet transform and it has low computational complexity. Compared with time domain, ridgelets find more applications in image separation, because it represents smooth and edge parts of an image with sparsity. In addition, the representation of ridgelets contains more directional information. The mixture images are extracted using ICA, which is based on a blind source separation technique. The simulation results reveal that the performance of ridgelet transform is better when compared to time domain in digital image separation. The Peak Signal-to-Noise Ratio (PSNR), Signal-to-Noise Ratio (SNR), Root Mean Square Error (RMSE) and Segmental Signal-to-Noise Ratio (SNRseg) are used to evaluate the quality of the separated images.