{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:41:21Z","timestamp":1787319681040,"version":"build-2736575974"},"reference-count":43,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>Image denoising is a fundamental operation in image processing and holds considerable practical importance for various real-world applications. Arguably several thousands of papers are dedicated to image denoising. In the past decade, state-of-the-art denoising algorithms have been clearly dominated by nonlocal patch-based methods, which explicitly exploit patch self-similarity within the targeted image. However, in the past two years, discriminatively trained local approaches have started to outperform previous nonlocal models and have been attracting increasing attention due to the additional advantage of computational efficiency. Successful approaches include cascade of shrinkage fields (CSF) and trainable nonlinear reaction diffusion (TNRD). These two methods are built on the filter response of linear filters of small size using feed forward architectures. Due to the locality inherent in local approaches, the CSF and TNRD models become less effective when the noise level is high and consequently introduce some noise artifacts. In order to overcome this problem, in this paper we introduce a multiscale strategy. To be specific, we build on our newly developed TNRD model, adopting the multiscale pyramid image representation to devise a multiscale nonlinear diffusion process. As expected, all the parameters in the proposed multiscale diffusion model, including the filters and the influence functions across scales, are learned from training data through a loss-based approach. Numerical results on Gaussian and Poisson denoising substantiate that the exploited multiscale strategy can successfully boost the performance of the original TNRD model with a single scale. As a consequence, the resulting multiscale diffusion models can significantly suppress the typical incorrect features for those noisy images with heavy noise. It turns out that multiscale TNRD variants achieve better performance than state-of-the-art denoising methods.<\/jats:p>","DOI":"10.1137\/16m1093707","type":"journal-article","created":{"date-parts":[[2017,8,3]],"date-time":"2017-08-03T14:18:13Z","timestamp":1501769893000},"page":"1234-1257","source":"Crossref","is-referenced-by-count":7,"title":["Image Denoising via Multiscale Nonlinear Diffusion Models"],"prefix":"10.1137","volume":"10","author":[{"given":"Wensen","family":"Feng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Qiao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuanyang","family":"Xi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yunjin","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,8,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/TIP.2013.2262284"},{"key":"atypb2","unstructured":"J. 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