Multiscale Tikhonov-Total Variation Image Restoration Using Spatially Varying Edge Coherence Exponent

Abstract

Edge preserving regularization using partial differential equation (PDE)-based methods although extensively studied and widely used for image restoration, still have limitations in adapting to local structures. We propose a spatially adaptive multiscale variable exponent-based anisotropic variational PDE method that overcomes current shortcomings, such as over smoothing and staircasing artifacts, while still retaining and enhancing edge structures across scale. Our innovative model automatically balances between Tikhonov and total variation (TV) regularization effects using scene content information by incorporating a spatially varying edge coherence exponent map constructed using the eigenvalues of the filtered structure tensor. The multiscale exponent model we develop leads to a novel restoration method that preserves edges better and provides selective denoising without generating artifacts for both additive and multiplicative noise models. Mathematical analysis of our proposed method in variable exponent space establishes the existence of a minimizer and its properties. The discretization method we use satisfies the maximum-minimum principle which guarantees that artificial edge regions are not created. Extensive experimental results using synthetic, and natural images indicate that the proposed multiscale Tikhonov-TV (MTTV) and dynamical MTTV methods perform better than many contemporary denoising algorithms in terms of several metrics, including signal-to-noise ratio improvement and structure preservation. Promising extensions to handle multiplicative noise models and multichannel imagery are also discussed.

Nonrigid registration of medical image based on adaptive local structure tensor and normalized mutual information

“…The local structure tensor does not produce the problem abovementioned, and can also still be extracted under the condition of the local gradient loss. At the same time, it directly uses the image intensity matrix to perform operations, which can effectively preserve the structural and gradient information of the image pixel, provide a more meaningful description than the gradient information. Therefore, this paper proposes a new similarity measure which combines NMI and local structure tensor.…”

Structure tensor adaptive total variation for image restoration

“…(1) be ( λ + (x, y, σ) , λ − (x, y, σ) ) which are the maximum and minimum, respectively, and λ + ≥ λ − (from here on we drop the spatial (x, y) and scale ( σ ) dependency in our notations for simplicity). The eigenvalues encode local information on σ neighborhood and can provide robust feature detections that can be utilized for low-level image processing steps [9,10]. This can be seen in an example image, see Figure 2.…”

Image smoothing via unsupervised learning

“…This regularization idea can also be interpreted as an image prior formulated in a deep network [Ulyanov et al 2018] or image denoising engine [Romano et al 2017]. Discussions about the L p -norm regularization can also be found in [Bach et al 2012;Chung and Vese 2009;Prasath et al 2015]. Interestingly, [Mrázek et al 2006 [Farbman et al 2008] and BLF [Tomasi 1998].…”