Multi-valued nonlinear image filtering

Multi-Valued nonlinear filtering is a new and powerful type of nonlinear filtering. Multi-valued filters are based on two complex non-linearities. One non-linearity is based on the replacement of the integer brightness values of the discrete image, by complex values that are roots of unity. Another complex nonlinear effect is carried out by the activation function of multi-valued neurons. It is well known that nonlinear filters are much more powerful than linear ones (e.g. for noise removal) because of the higher effect of any nonlinear averaging of the signal in comparison with the linear one. Evidently, two complex nonlinearities, which are a fundamental background of the Multi-Valued filtering, define specific and very effective nonlinear averaging of the signal. Correspondingly, the complex non-linearity of the MVN activation function may be successfully used both to reduce high frequencies (for noise removal) and to amplify high and medium frequencies (for extraction of details).

Multi-valued nonlinear filtering provides more powerful results for noise removal when compared to L-filters, order-statistics, and median filters.

On the other hand Multi-valued filters may be connected with other nonlinear filters. For example the application of the multi-valued technique inside the rank-order filter establishes rank-order multi-valued filtering, which is a unique instrument for speckle noise reduction. Multi-valued filters effectively keep the signal from blurring and simultaneously ensure extremely effective noise reduction. They are especially effective for the reduction and removal of speckle, Gaussian, and uniform noise.

Another application of multi-valued filtering is Global and High frequency correction, which leads to extraction of image details.

Examples

(click on the images to enlarge,
make sure you don't have pop-ups disabled)

White Noise Reduction

Noisy image, PSNR=5.3	Multi-valued filtering, 3x3 window, 2 iterations, weighting template (Image boundaries are preserved with the highest accuracy, PSNR=12.1)

Speckle Noise Reduction

Radar satellite noisy image	Multi-valued filtering, 3x3 window, 5 iterations, weighting template (Image boundaries are preserved with the highest accuracy)	Enhanced difference of the filtered image from the original image