Faculty Publications
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Publications by NITK Faculty
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Item A time-dependent switching anisotropic diffusion model for denoising and deblurring images(2012) Padikkal, P.; George, S.A conditionally anisotropic diffusion based deblurring and denoising filter is introduced in this paper. This is a time-dependent curvature based model and the steady state can be attained at a faster rate, using the explicit time-marching scheme. The filter switches between isotropic and anisotropic diffusion depending on the local image features. The switching of the filter is controlled by a binary function, which returns either zero or one, based on the underlying local image gradient features. The parameters in the proposed filter can be fine-tuned to get the desired output image. The filter is applied to various kinds of input test images and the response is analyzed. The filter is found to be effective in the reconstruction of partially textured, textured, constant-intensity and color images, as is evident from the results provided. © 2011 Copyright Taylor and Francis Group, LLC.Item Gauss curvature-driven image inpainting for image reconstruction(Taylor and Francis Ltd. michael.wagreich@univie.ac.at, 2014) Padikkal, P.; George, S.In this paper, we propose a third-order Gauss curvature-driven geometric diffusion Partial Differential Equation for inpainting and reconstructing images. In Gauss curvature-driven diffusion processes, the rate of diffusion is directly proportional to the Gauss curvature value of the level curve. Since the Gauss curvature is the product of principal curvatures, its value become zero when even one of the principal curvatures is zero. Therefore, when Gauss curvature is used as a driving function for diffusion, the evolution preserves some of the meaningful structures with nonzero mean curvature values (viz. curvy edges, corners, etc.). However, the noise features always have nonzero Gauss curvature value and hence the diffusion process effectively removes them. The inpainting property of geometric PDE based on the Gauss curvature is being used in this work for reconstructing lost or degraded information. A filter is proposed to reconstruct the original images from the observed blurred and noisy images along with inpainting the desired image domain. © 2014 Copyright The Chinese Institute of Engineers.Item A convex regularization model for image restoration(Elsevier Ltd, 2014) Padikkal, P.Many variational formulations are introduced over the last few years to handle multiplicative data-dependent noise. Some of these models seek to minimize the Total Variation (TV) norm of the absolute gradient function subject to given constraints. Since the TV-norm (well-defined in the space of bounded variations (BVs)) minimization eventually results in the formation of piece-wise constant patches during the evolution process, the filtered output appears blocky. In this work the block effect (commonly known as staircase effect) is being handled by using a convex combination of TV and Tikhonov filters, which are defined in BV and L2 (square-integrable functions) spaces, respectively. The constraint for the minimizing functional is derived based on a maximum a posteriori (MAP) regularization approach, duly considering the noise distributions. Therefore, this model is capable of denoising speckled images, whose intensity is Gamma distributed. The results are demonstrated both in terms of visual and quantitative measures. © 2014 Elsevier Ltd. All rights reserved.Item Image Restoration Using Adaptive Region-Wise p-Norm Filter with Local Constraints(World Scientific, 2016) Bini, A.A.; Padikkal, P.In this work, we introduce a feature adaptive second-order p-norm filter with local constraints for image restoration and texture preservation. The p-norm value of the filter is chosen adaptively between 1 and 2 in a local region based on the regional image characteristics. The filter behaves like a mean curvature motion (MCM) [A. Marquina and S. Osher, SIAM Journal of Scientific Computing 22, 387-405 (2000)] in the regions where the p-norm value is 1 and switches to a Laplacian filter in the rest of the regions (where the p-norm value is 2). The proposed study considerably reduces stair-case effect and effectively removes noise from images while deblurring them. The noise is assumed as Gaussian distributed (with zero mean and variance ?2) and blur is linearly shift invariant (out-of-focus). The filter converges at a faster rate with semi-implicit Crank-Nicholson scheme. The regularization parameter is initialized and updated based on the local image features and therefore this filter preserves edges, structures, textures and fine details present in images very well. The method is applied on different kinds of images with different image characteristics. We show the response of the filter to various kinds of images and numerically quantify the performance in terms of standard statistical measures. © 2016 World Scientific Publishing Company.Item Image despeckling and deblurring via regularized complex diffusion(Springer London, 2017) Padikkal, P.; Bini, A.A.In this paper an image restoration and enhancement model is being proposed, which is suitable for multiplicative data-dependent speckle noise (whose intensity is Gamma distributed) under linear shift-invariant blurring artifacts. The proposed strategy devises a nonlinear second-order diffusive-reactive model for enhancing and restoring images degraded by the aforementioned scenario. The reactive term is derived based on the Maximum a posteriori (MAP) estimator, to make it adaptive to the noise distribution in the input data. This noise-adaptive reactive term helps to restore and enhance the images under data-correlated noise setup. Unlike the other second-order nonlinear diffusion methods, the proposed solution preserves edges and details and reduces piecewise constant approximation in the homogeneous intensity regions in the course of its evolution. The experimental results demonstrated in this paper duly support the above claims. © 2017, Springer-Verlag London.Item Non-local total variation regularization models for image restoration(Elsevier Ltd, 2018) Padikkal, P.; Holla Kayyar, S.H.Restoration of images corrupted by data-correlated Rayleigh noise distribution has not been studied much extensively in the literature, unlike the other noise distributions. In this paper, we analyze the degradations due to a data-correlated Rayleigh noise and a linear blurring artifact. This work employs a variance stabilization approach and two variational approaches for restoring images from their noisy and blurred observations. The split-Bregman iterative scheme is used for numerically solving the models to improve their convergence rates. Furthermore, non-local total variation and non-local total bounded variation priors are being used as regularizers in these models to improve their restoration efficiency. Various synthetic and real images (such as ultrasound and synthetic aperture radar images) are tested to show the performance of these models. © 2018 Elsevier LtdItem Image despeckling with non-local total bounded variation regularization(Elsevier Ltd, 2018) Padikkal, P.; Banothu, B.A non-local total bounded variational (TBV) regularization model is proposed for restoring images corrupted with data-correlated speckles and linear blurring artifacts. The energy functional of the model is derived using maximum a posteriori (MAP) estimate of the noise probability density function (PDF). The non-local total bounded variation prior regularizes the model while the data fidelity is derived using the MAP estimator of the noise PDF. The computational efficiency of the model is improved using a fast numerical scheme based on the Augmented Lagrange formulation. The proposed model is employed to restore ultrasound (US) and synthetic aperture radar (SAR) images, which are usually speckled and blurred. The numerical results are presented and compared. Furthermore, a detailed theoretical study of the model is performed in addition to the experimental analysis. © 2017 Elsevier LtdItem Non-local total bounded variation scheme for multiple-coil magnetic resonance image restoration(Springer New York LLC barbara.b.bertram@gsk.com, 2018) Padikkal, P.; Holla Kayyar, S.In this paper, we design a variational model for restoring multiple-coil magnetic resonance images (MRI) corrupted by non-central Chi distributed noise. The energy functional corresponding to the restoration problem is derived using the maximum a posteriori (MAP) estimator. Optimizing this functional yields the solution, which corresponds to the restored version of the image. The non-local total bounded variation prior is being used as the regularization term in the functional derived using the MAP estimation process. Further, the split-Bregman iteration scheme is being followed for fast numerical computation of the model. The results are compared with the state of the art MRI restoration models using visual representations and statistical measures. © 2017, Springer Science+Business Media, LLC.Item Non-local total variation regularization approach for image restoration under a Poisson degradation(Taylor and Francis Ltd. michael.wagreich@univie.ac.at, 2018) Holla Kayyar, S.; Padikkal, P.Poisson noise (also known as shot or photon noise) arises due to the lack of information during the image acquisition phase, it is quite common in the field of microscopic or astronomical imaging applications. In this paper, we propose a non-local total variation regularization framework with a p-norm driven data-fidelity for denoising the Poissonian images. In precise, the energy functional is derived using a Maximum A Posteriori estimator of the Poisson probability density function. The diffusion amounts to a non-local total variation minimization process, which eventually preserves fine structures while denoising the data. The numerical solution is sought under a fast converging split-Bregman iterative scheme. The proposed model is compared visually and statistically with the state-of-the-art Poisson denoising models. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.Item Noise classification and automatic restoration system using non-local regularization frameworks(Taylor and Francis Ltd. michael.wagreich@univie.ac.at, 2018) Febin, I.P.; Padikkal, P.; Bini, A.A.Medical, satellite or microscopic images differ in the imaging techniques used, hence their underlying noise distribution also are different. Most of the restoration methods including regularization models make prior assumptions about the noise to perform an efficient restoration. Here we propose a system that estimates and classifies the noise into different distributions by extracting the relevant features. The system provides information about the noise distribution and then it gets directed into the restoration module where an appropriate regularization method (based on the non-local framework) has been employed to provide an efficient restoration of the data. We have effectively addressed the distortion due to data-dependent noise distributions such as Poisson and Gamma along with data uncorrelated Gaussian noise. The studies have shown a 97.7% accuracy in classifying noise in the test data. Moreover, the system also shows the capability to cater to other popular noise distributions such as Rayleigh, Chi, etc. © 2018, © 2018 The Royal Photographic Society.