Gaussian Blurring-Deblurring for Improved Image Compression

The deblurring of Gaussian blur by inverting the action of the diffusion equation has long been known. This technique is interesting but without much practical application since the images have to be blurred by convolution with a Gaussian to be "de-blur-able" with this technique. In this paper we investigate the possibility to use this blurring-deblurring process as a pre-post-processing step in classical image compression. It is known indeed that the compressibility of an image increases with the blurring, with a relation between compression ratio (CR) and the blurring scale, sigma (σ ), which we show to be roughly linear. So, by preprocessing and image with Gaussian blurring before compression, the CR will increase. The technique of deblurring Gaussian blur is then used as a post-processing step after decompression. Of course, quantisation of the blurred image prior to deblurring decreases the quality of the deblurring, introducing new errors. Hence, the quantisation step introduced by the compression algorithm also affects the deblurring performed in the postprocessing step, resulting in a smaller Peak Signal to Noise Ratio (PSNR). In this article, the complementary effects of increased CR and decreased PSNR on the PSNR/CR-curve of various compression algorithms are studied in function of sigma, of the order of the deblurring, and of the compression technique.