Shearlet-Based Adaptive Noise Reduction in CT Images

The noise in reconstructed slices of X-ray Computed Tomography (CT) is of unknown distribution, non-stationary, oriented and difficult to distinguish from main structural information. This requires the development of special post-processing methods based on the local statistical evaluation of the noise component. This paper presents an adaptive method of reducing noise in CT images employing the shearlet domain in order to obtain such an estimate. The algorithm for statistical noise assessment takes into account the distribution of signal energy in different scales and directions. The method efficiently uses the strong targeted sensitivity of shearlet systems in order to reflect more accurately the anisotropic information in the image. Because of the complex characteristics of the noise in these images, the threshold constant is determined by means of the relative entropy change criterion. The comparative analysis, which has been conducted, shows that the proposed method achieves higher values for the Peak Signal-to-Noise Ratio (PSNR), as well as lower values for the Mean Squared Error (MSE), in comparison with the other methods considered. For the MATLAB’S Shepp Logan Phantom test image, the numerical value of this superiority is on average more than 23% for the first quantitative measure, and 37% for the second. Its efficiency, which is greater than that of the wavelet-based method, is confirmed by the results obtained – the edges have been preserved during noise reduction in real CT images.