Dual Polynomial Thresholding for Transform Denoising in Application to Local Pixel Grouping Method

Thresholding operators have been used successfully for denoising signals, mostly in the wavelet domain. These operators transform a noisy coefficient into a denoised coefficient with a mapping that depends on signal statistics and the value of the noisy coefficient itself. This paper demonstrates that a polynomial threshold mapping can be used for enhanced denoising of Principal Component Analysis (PCA) transform coefficients. In particular, two polynomial threshold operators are used here to map the coefficients obtained with the popular local pixel grouping method (LPG-PCA), which eventually improves the denoising power of LPG-PCA. The method reduces the computational burden of LPG-PCA, by eliminating the need for a second iteration in most cases. Quality metrics and visual assessment show the improvement.