A General Selective Averaging Method for Piecewise Constant Signal and Image Processing

Piecewise constant signals and images, which are sampled from piecewise constant functions, are an important kind of data. Typical examples include bar code signals, images of texts, hand-written signatures, Quick Response codes (QR codes), logos and cartoons. Selective averaging method is a powerful technique for this kind of signal and image denoising. In this paper, we propose a general selective averaging method (GSAM) to use more flexible weights compared to the previous one. Some convergence results and a probabilistic interpretation are provided for its iterated version. For the choice of the weight parameter, we discuss its influence on the asymptotic rate of convergence. We also study its influence on the denoising results with a moderate number of iterations. Then, our method is compared to the iterated neighborhood filter in signal denoising. In 2D case, we propose a novel extension called the alternating GSAM (AGSAM). We similarly introduce an alternating neighborhood filter. Experimental results demonstrate that our method is especially effective for Gaussian noise removal from noisy piecewise constant signals and images.