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. Soft Wavelet thresholding denoising of the noisy mixtures is recommended in this paper as a preprocessing step for noise reduction. 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 ridgelet transform, which is a numerical precision as the continuous ridgelet transform and has low computational complexity. Comparing with time domain, ridgelets find more application on image separation, hence it represents smooth and edge parts of image with sparsity. In addition, the representation of ridgelets contains more directional information. The mixtures images are extracted using ICA which is based on blind source separation technique. The simulation results reveal that the performance of ridgelet transform is better when compared to time domain in digital images 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.