Solomon A. Tesfamicae¹ and Faraz Barzideh², ¹Norwegian University of Science and Technology (NTNU), Norway and ²University of Stavanger (UiS), Norway

This paper provides a compressive sensing (CS) method of denoising images using Bayesian framework. Some images, for example like magnetic resonance images (MRI) are usually very weak due to the presence of noise and due to the weak nature of the signal itself. So denoising boosts the true signal strength. Under Bayesian framework, we have used two different priors: sparsity and clusterdness in an image data as prior information to remove noise. Therefore, it is named as clustered compressive sensing based denoising (CCSD). After developing the Bayesian framework, we applied our method on synthetic data, Shepp-logan phantom and sequences of fMRI images. The results show that applying the CCSD give better results than using only the conventional compressive sensing (CS) methods in terms of Peak Signal to Noise Ratio (PSNR) and Mean Square Error (MSE). In addition, we showed that this algorithm could have some advantages over the state-of-the-art methods like Block-Matching and 3D Filtering(BM3D).

Denoising, Bayesian framework, Sparse prior, Clustered prior, posterior, Compressive sensing, LASSO, Clustered Compressive Sensing