Regularization schemes involving self-similarity in imaging inverse problems

Ebrahimi, Mehran; Vrscay, Edward R.

doi:10.1088/1742-6596/124/1/012021

Cited by 5 publications

(5 citation statements)

References 17 publications

(17 reference statements)

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“…To overcome this issue, a classical approach consists of penalizing the data fitting terms derived from the linear models (4) and the noise statistics (3) with additional regularizing terms exploiting any prior information on the latent image. Various penalizations have been considered in the literature, including Tikhonov regularizations expressed in the image domain [21], [35] or in a transformed (e.g., gradient) domain [36], [37], dictionary-or patch-based regularizations [25], [30], total variation (TV) [23], [38] or regularizations based on sparse wavelet representations [39], [40].…”

Section: Robust Multiband Image Fusionmentioning

confidence: 99%

Robust Fusion of Multiband Images With Different Spatial and Spectral Resolutions for Change Detection

Ferraris

Dobigeon

Wei

et al. 2017

IEEE Trans. Comput. Imaging

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Archetypal scenarios for change detection generally consider two images acquired through sensors of the same modality. However, in some specific cases such as emergency situations, the only images available may be those acquired through different kinds of sensors. More precisely, this paper addresses the problem of detecting changes between two multiband optical images characterized by different spatial and spectral resolutions. This sensor dissimilarity introduces additional issues in the context of operational change detection. To alleviate these issues, classical change detection methods are applied after independent preprocessing steps (e.g., resampling) used to get the same spatial and spectral resolutions for the pair of observed images. Nevertheless, these preprocessing steps tend to throw away relevant information. Conversely, in this paper, we propose a method that more effectively uses the available information by modeling the two observed images as spatial and spectral versions of two (unobserved) latent images characterized by the same high spatial and high spectral resolutions. As they cover the same scene, these latent images are expected to be globally similar except for possible changes in sparse spatial locations. Thus, the change detection task is envisioned through a robust multiband image fusion method, which enforces the differences between the estimated latent images to be spatially sparse. This robust fusion problem is formulated as an inverse problem, which is iteratively solved using an efficient blockcoordinate descent algorithm. The proposed method is applied to real panchromatic, multispectral, and hyperspectral images with simulated realistic and real changes. A comparison with state-ofthe-art change detection methods evidences the accuracy of the proposed strategy.

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Section: Robust Multiband Image Fusionmentioning

confidence: 99%

Robust Fusion of Multiband Images With Different Spatial and Spectral Resolutions for Change Detection

Ferraris

Dobigeon

Wei

et al. 2017

IEEE Trans. Comput. Imaging

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“…The regularization term can be chosen from a specific task of interest, the information resulting from previous experiments or from a perceptual view on the constraints affecting the unknown model parameters [31], [32]. Various priors or regularizations have already been advocated to regularize the image SR problem include: (i) traditional generic image priors such as Tikhonov [24], [33], [34], the total variation (TV) [18], [20], [35] and the sparsity in transformed domains [36]- [39], (ii) more recently proposed image regularizations such as the gradient profile prior [8], [9], [17] or Fattal's edge statistics [40] and (iii) learning-based priors [41], [42]. The fast approach proposed in the next section is shown to be adapted to many of the existing regularization terms.…”

Section: B Problem Formulationmentioning

confidence: 99%

“…This implies that the target image x is a priori close to the imagex. The imagex can be an estimation of the HR image, Algorithm 1 FSR With Image-Domain ℓ 2 -Regularization: Implementation of the Analytical Solution (15) e.g., an interpolated version of the observed image, a restored image obtained with learning-based algorithms [7] or a cleaner image obtained from other sensors [24], [34], [48]. In such case, using Theorem 1, the solution of the problem 14iŝ…”

Section: B Solution Of the ℓ 2 -ℓ 2 Problem In The Image Domainmentioning

confidence: 99%

“…More precisely, this paper derives a closed-form expression of the solution associated with the ℓ 2 -penalized least-squares SR problem, when the observed LR image is assumed to be a noisy, subsampled and blurred version of the HR image with a spatially invariant blur. This model, referred to as ℓ 2 -ℓ 2 in what follows, underlies the restoration of an image contaminated by additive Gaussian noise and has been used intensively for the single image SR problem, see, e.g., [7], [8], [24]. The proposed solution is shown to be easily embeddable into an AL framework to handle non-Gaussian priors (i.e., non-ℓ 2 regularizations), which significantly lightens the computational burdens of several existing SR algorithms.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fast Single Image Super-Resolution Using a New Analytical Solution for <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math> </inline-formula>–<inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math> </inline-formula> Problems

Zhao

Wei

Basarab

et al. 2016

IEEE Trans. on Image Process.

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This paper addresses the problem of single image super-resolution (SR), which consists of recovering a high-resolution image from its blurred, decimated, and noisy version. The existing algorithms for single image SR use different strategies to handle the decimation and blurring operators. In addition to the traditional first-order gradient methods, recent techniques investigate splitting-based methods dividing the SR problem into up-sampling and deconvolution steps that can be easily solved. Instead of following this splitting strategy, we propose to deal with the decimation and blurring operators simultaneously by taking advantage of their particular properties in the frequency domain, leading to a new fast SR approach. Specifically, an analytical solution is derived and implemented efficiently for the Gaussian prior or any other regularization that can be formulated into an l2 -regularized quadratic model, i.e., an l2 - l2 optimization problem. The flexibility of the proposed SR scheme is shown through the use of various priors/regularizations, ranging from generic image priors to learning-based approaches. In the case of non-Gaussian priors, we show how the analytical solution derived from the Gaussian case can be embedded into traditional splitting frameworks, allowing the computation cost of existing algorithms to be decreased significantly. Simulation results conducted on several images with different priors illustrate the effectiveness of our fast SR approach compared with existing techniques.

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“…To overcome this issue, a classical approach consists of penalizing the data fitting terms derived from the linear models (4) and the noise statistics (3) with additional regularizing terms exploiting any prior information on the latent image. Various penalizations have been considered in the literature, including Tikhonov regularizations expressed in the image domain [21], [36] or a in a transformed (e.g., gradient) domain [37], [38], dictionary-or patch-based regularizations [26], [31], total variation (TV) [23], [39] or regularizations based on sparse wavelet representations [40], [41].…”

Section: Robust Multi-band Image Fusionmentioning

confidence: 99%

Robust Fusion of Multi-Band Images with Different Spatial and Spectral Resolutions for Change Detection

Ferraris¹,

Dobigeon²,

Qi³

et al. 2016

Preprint

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Archetypal scenarios for change detection generally consider two images acquired through sensors of the same modality. However, in some specific cases such as emergency situations, the only images available may be those acquired through different kinds of sensors. More precisely, this paper addresses the problem of detecting changes between two multi-band optical images characterized by different spatial and spectral resolutions. This sensor dissimilarity introduces additional issues in the context of operational change detection. To alleviate these issues, classical change detection methods are applied after independent preprocessing steps (e.g., resampling) used to get the same spatial and spectral resolutions for the pair of observed images. Nevertheless, these preprocessing steps tend to throw away relevant information. Conversely, in this paper, we propose a method that more effectively uses the available information by modeling the two observed images as spatial and spectral versions of two (unobserved) latent images characterized by the same high spatial and high spectral resolutions. As they cover the same scene, these latent images are expected to be globally similar except for possible changes in sparse spatial locations. Thus, the change detection task is envisioned through a robust multi-band image fusion method which enforces the differences between the estimated latent images to be spatially sparse. This robust fusion problem is formulated as an inverse problem which is iteratively solved using an efficient block-coordinate descent algorithm.The proposed method is applied to real panchormatic/multispectral and hyperspectral images with Part of this work has been submitted to the IEEE Int. Conf. Acoust., Speech and Signal Process. (ICASSP), 2017 [1].

show abstract

Regularization schemes involving self-similarity in imaging inverse problems

Cited by 5 publications

References 17 publications

Robust Fusion of Multiband Images With Different Spatial and Spectral Resolutions for Change Detection

Robust Fusion of Multiband Images With Different Spatial and Spectral Resolutions for Change Detection

Fast Single Image Super-Resolution Using a New Analytical Solution for <inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math> </inline-formula>–<inline-formula> <tex-math notation="LaTeX">$\ell _{2}$ </tex-math> </inline-formula> Problems

Robust Fusion of Multi-Band Images with Different Spatial and Spectral Resolutions for Change Detection

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