2023/01/18 by He Lyu, Rongrong Wang
Computer Science · Engineering · Mathematics · #Advanced Image Processing Techniques #Algorithm #Bandlimiting #Classification of discontinuities #Computer science #Fourier transform #Image and Signal Denoising Methods #Mathematical analysis #Mathematics #Physics #Quantization (signal processing) #Sigma #Sparse and Compressive Sensing Techniques #Vector quantization
paper · pdf · doi:10.1002/cpa.22089
openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
Abstract In signal quantization, it is well‐known that introducing adaptivity to quantization schemes can improve their stability and accuracy in quantizing bandlimited signals. However, adaptive quantization has only been designed for one‐dimensional signals. The contribution of this paper is two‐fold: (i) we propose the first family of two‐dimensional adaptive quantization schemes that maintain the same mathematical and practical merits as their one‐dimensional counterparts, and (ii) we show that both the traditional 1‐dimensional and the new 2‐dimensional quantization schemes can effectively quantize signals with jump discontinuities, which immediately enable the usage of adaptive quantization on images. Under mild conditions, we show that by using adaptivity, the proposed method is able to reduce the quantization error of images from the presently best to the much smaller , where s is the number of jump discontinuities in the image and P () is the total number of samples. This ‐fold error reduction is achieved via applying a total variation norm regularized decoder, whose formulation is inspired by the mathematical super‐resolution theory in the field of compressed sensing. Compared to the super‐resolution setting, our error reduction is achieved without requiring adjacent spikes/discontinuities to be well‐separated, which ensures its broad scope of application. We numerically demonstrate the efficacy of the new scheme on medical and natural images. We observe that for images with small pixel intensity values, the new method can significantly increase image quality over the state‐of‐the‐art method. © 2022 Wiley Periodicals, Inc.