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OPTIMAL GRAPH LAPLACIAN REGULARIZATION FOR NATURAL IMAGE DENOISING
"... Image denoising is an underdetermined problem, and hence it is important to define appropriate image priors for regularization. One recent popular prior is the graph Laplacian regularizer, where a given pixel patch is assumed to be smooth in the graphsignal domain. The strength and direction of th ..."
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Image denoising is an underdetermined problem, and hence it is important to define appropriate image priors for regularization. One recent popular prior is the graph Laplacian regularizer, where a given pixel patch is assumed to be smooth in the graphsignal domain. The strength and direction of the resulting graphbased filter are computed from the graph’s edge weights. In this paper, we derive the optimal edge weights for local graphbased filtering using gradient estimates from nonlocal pixel patches that are selfsimilar. To analyze the effects of the gradient estimates on the graph Laplacian regularizer, we first show theoretically that, given graphsignal hD is a set of discrete samples on continuous function h(x, y) in a closed region Ω, graph Laplacian regularizer (hD)TLhD converges to a continuous functional SΩ integrating gradient norm of h in metric space G — i.e., (∇h)TG−1(∇h) — over Ω. We then derive the optimal metric space G?: one that leads to a graph Laplacian regularizer that is discriminant when the gradient estimates are accurate, and robust when the gradient estimates are noisy. Finally, having derived G? we compute the corresponding edge weights to define the Laplacian L used for filtering. Experimental results show that our image denoising algorithm using the perpatch optimal metric space G? outperforms nonlocal means (NLM) by up to 1.5 dB in PSNR. Index Terms — graph Laplacian regularization, metric space, image denoising, inverse imaging problem 1.
INTERBLOCK CONSISTENT SOFT DECODING OF JPEG IMAGES WITH SPARSITY AND GRAPHSIGNAL SMOOTHNESS PRIORS
"... Given the prevalence of JPEG compressed images on the Internet, image reconstruction from the compressed format remains an important and practical problem. Instead of simply reconstructing a pixel block from the centers of assigned DCT coefficient quantization bins (hard decoding), we propose to jo ..."
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Given the prevalence of JPEG compressed images on the Internet, image reconstruction from the compressed format remains an important and practical problem. Instead of simply reconstructing a pixel block from the centers of assigned DCT coefficient quantization bins (hard decoding), we propose to jointly reconstruct a neighborhood group of pixel patches using two image priors while satisfying the quantization bin constraints. First, we assume that a pixel patch can be approximated as a sparse linear combination of atoms from an offlinelearned overcomplete dictionary. Second, we assume that a patch, when interpreted as a graphsignal, is smooth with respect to an appropriately defined graph that captures the estimated structure of the target image. Finally, neighboring patches in the optimization have sufficient overlaps and are forced to be consistent, so that blocking artifacts typical in JPEG decoded images are avoided. To find the optimal group of patches, we formulate a constrained optimization problem and propose a fast alternating algorithm to find locally optimal solutions. Experimental results show that our proposed algorithm outperforms stateoftheart soft decoding algorithms by up to 1.47dB in PSNR. Index Terms — image decoding, sparse signal representation, graph signal processing 1.
JOINT DENOISING AND CONTRAST ENHANCEMENT OF IMAGES USING GRAPH LAPLACIAN OPERATOR
"... Images and videos are often captured in poor light conditions, resulting in lowcontrast images that are corrupted by acquisition noise. To recreate a highquality image for visual observation, the captured image must be denoised and contrastenhanced. Conventional methods perform these two tasks ..."
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Images and videos are often captured in poor light conditions, resulting in lowcontrast images that are corrupted by acquisition noise. To recreate a highquality image for visual observation, the captured image must be denoised and contrastenhanced. Conventional methods perform these two tasks in two separate stages: an image is first denoised, followed by an enhancement procedure. In this paper, we propose to jointly denoise and enhance an image in one unified optimization framework. The crux of the optimization rests on the definition of the enhancement operator, described by a graph Laplacian matrix H. The operator must enhance the high frequency details of the original image without amplifying additive noise. We propose a graphbased lowpass filtering approach to denoise edge weights in the graph, resulting in a more robust estimate of H. Experimental results show that our proposed joint approach can outperform the separate approach in demonstrable image quality. Index Terms — image restoration, graph signal processing 1.