Kernel - Based Image Denoising
employing semi-parametric regularization.

We have developed a novel approach, based on the theory of Reproducing Kernel Hilbert Spaces (RKHS), for the problem of Noise Removal in the spatial domain. The proposed methodology has the advantage that it is able to remove any kind of additive noise (impulse, gaussian, uniform e.t.c.) from any digital image, in contrast to the most common denoising technics that are noise-dependent. The problem is cast as an optimization task in a RKHS, by taking advantage of the celebrated Representer Theorem in its semi-parametric formulation. The semi-parametric formulation, although known in theory, has so far found limited, to our knowledge, application. However, in the image denoising problem its use is dictated by the nature of the problem itself. The need for edge preservation naturally leads to such a modelling. Examples verify that in the presence of gaussian noise the proposed methodology performs well compared to wavelet based techniques and outperforms them significantly in the presence of impulse or mixed noise.

For more information you have to read the paper. See below a list of downloads

1) paper (preprint)              

2) code (implemented in C)              

3) Windows Executable

4) Test examples (excel file with input parameters-results and images rar file)

5) Instructions (readme)

Examples:

               
                            (a)                                                                 (b)                                                           (c)

Fig. 1
(a) The lena image obtained from the Waterloo Image Repository.
(b) The lena image corrupted by 30% of additive impulse noise (the impulses are uniformly distributed in [-128, 128])  (PSNR=16.60 dB).
(c) The denoised image according to the proposed methodology (PSNR=33.20 dB).

               
                            (a)                                                                (b)                                                            (c)

Fig. 2
(a) The lena image obtained from the Waterloo Image Repository.
(b) The lena image corrupted by 50% of additive impulse noise (the impulses are uniformly distributed in [-128, 128])   (PSNR=14.41 dB).
(c) The denoised image according to the proposed methodology (PSNR=30.71 dB).

               
                            (a)                                                              (b)                                                             (c)

Fig. 3
(a) The lena image obtained from the Waterloo Image Repository.
(b) The lena image corrupted by additive gaussian noise (σ=20)  (PSNR=22.14 dB).
(c) The denoised image according to the proposed methodology (PSNR=31.12 dB).

               
                            (a)                                                            (b)                                                             (c)

Fig. 4
(a) The lena image obtained from the Waterloo Image Repository.
(b) The lena image corrupted by 20% of additive impulse noise (the impulses are uniformly distributed in [-128, 128]) and additive gaussian noise (σ=10)  (PSNR=17.98 dB).
(c) The denoised image according to the proposed methodology (PSNR=32.27 dB).