A 4-quadrant Curvelet Transform for Denoising Digital Images

The conventional discrete wavelet transform (DWT) introduces artifacts during denoising of images containing smooth curves. Finite ridgelet transform (FRIT) solved this problem by mapping the curves in terms of small curved ridges. However, blind application of FRIT all over an image is computationally heavy. Finite curvelet transform (FCT) selectively applies FRIT only to the tiles containing small portions of a curve. In this work, a novel curvelet transform named as 4-quadrant finite curvelet transform (4QFCT) based on a new concept of 4-quadrant finite ridgelet transform (4QFRIT) has been proposed. An image is band pass filtered and the high frequency bands are divided into small non-overlapping square tiles. The 4QFRIT is applied to the tiles containing at least one curve element. Unlike FRIT, the 4QFRIT takes 4 sets of radon projections in all the 4 quadrants and then averages them in time and frequency domains after denoising. The proposed algorithm is extensively tested and benchmarked for denoising of images with Gaussian noise using mean squared error (MSE) and peak signal to noise ratio (PSNR). The results confirm that 4QFCT yields consistently better denoising performance quantitatively and visually.