Constrained and Unconstrained Inverse Potts Modelling for Joint Image Super-Resolution and Segmentation

Mylonopoulos, Dario; Cascarano, Pasquale; Calatroni, Luca; Piccolomini, Elena Loli

doi:10.5201/ipol.2022.393

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…where A ∈ R n×n is a known measurement operator and η ∈ R n is random noise with standard deviation σ η . Linear inverse problems are at the core of many applications [1][2][3][4][5]. However, since most inverse problems are ill-posed, it is common to formulate the solution x * ∈ R n of (1) as a minimizer of a regularized objective function…”

Section: Introductionmentioning

confidence: 99%

Constrained Regularization by Denoising With Automatic Parameter Selection

Cascarano,

Benfenati,

Kamilov

et al. 2024

IEEE Signal Process. Lett.

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Regularization by Denoising (RED) is a well-known method for solving image restoration problems by using learned image denoisers as priors. Since the regularization parameter in the traditional RED does not have any physical interpretation, it does not provide an approach for automatic parameter selection. This letter addresses this issue by introducing the Constrained Regularization by Denoising (CRED) method that reformulates RED as a constrained optimization problem where the regularization parameter corresponds directly to the amount of noise in the measurements. The solution to the constrained problem is solved by designing an efficient method based on alternating direction method of multipliers (ADMM). Our experiments show that CRED outperforms the competing methods in terms of stability and robustness, while also achieving competitive performances in terms of image quality.

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Section: Introductionmentioning

confidence: 99%

Constrained Regularization by Denoising With Automatic Parameter Selection

Cascarano,

Benfenati,

Kamilov

et al. 2024

IEEE Signal Process. Lett.

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“…For example, well established methods such as the discrepancy principle, L-curve, or cross-validation [16] have been considered for Gaussian noise, while the discrepancy principle has been adapted also in the presence of Poisson noise [17,18]. Alternatively, another interesting approach consists of recasting the optimization problem (2) as a constrained one [19][20][21]: namely, x * ∈ argmin…”

Section: Introductionmentioning

confidence: 99%

“…Another grand challenge for the model-based approach is the design of an effective regularization functional ρ(x) capable of capturing intricate image features. Some examples include the well-known Tikhonov regularization [22], known as ridge regression in statistical contexts, and its variant that promotes diffuse components on the final reconstruction; the total variation functional, which aims to preserve sharp edges [2,23,24]; the ℓ p -norms regularizers, with 0 ≤ p ≤ 1, which induce sparsity on the image and/or gradient domains [19,25,26]; and the elastic-net functional [4], which is a convex combination of ℓ 1 and ℓ 2 norms.…”

Section: Introductionmentioning

confidence: 99%

Constrained Plug-and-Play Priors for Image Restoration

Benfenati,

Cascarano

2024

J. Imaging

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The Plug-and-Play framework has demonstrated that a denoiser can implicitly serve as the image prior for model-based methods for solving various inverse problems such as image restoration tasks. This characteristic enables the integration of the flexibility of model-based methods with the effectiveness of learning-based denoisers. However, the regularization strength induced by denoisers in the traditional Plug-and-Play framework lacks a physical interpretation, necessitating demanding parameter tuning. This paper addresses this issue by introducing the Constrained Plug-and-Play (CPnP) method, which reformulates the traditional PnP as a constrained optimization problem. In this formulation, the regularization parameter directly corresponds to the amount of noise in the measurements. The solution to the constrained problem is obtained through the design of an efficient method based on the Alternating Direction Method of Multipliers (ADMM). Our experiments demonstrate that CPnP outperforms competing methods in terms of stability and robustness while also achieving competitive performance for image quality.

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“…Following recent works [4,12], we will consider in this work a piggy-back primal-dual algorithm computing solutions of the lowerlevel problem and of the adjoint states at the same time. We consider both the problem of image deblurring (A = H ∈ R 𝑛×𝑛 , a structured circulant convolution matrix) and superresolution (A = SH ∈ R 𝑚×𝑛 ) and, in the latter case, we resort to Fourier-based approaches previously proposed in [40] and used, e.g., in [34,31] for computing proximal updates in a closed-form. 2 We consider square images of size √ 𝑛 × √ 𝑛 for simplicity, with…”

Section: Introductionmentioning

confidence: 99%

Bilevel learning of regularization models and their discretization for image deblurring and super-resolution

Bubba¹,

Calatroni²,

Catozzi³

et al. 2023

Preprint

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Bilevel learning is a powerful optimization technique that has extensively been employed in recent years to bridge the world of model-driven variational approaches with data-driven methods. Upon suitable parametrization of the desired quantities of interest (e.g., regularization terms or discretization filters), such approach computes optimal parameter values by solving a nested optimization problem where the variational model acts as a constraint. In this work, we consider two different use cases of bilevel learning for the problem of image restoration. First, we focus on learning scalar weights and convolutional filters defining a Field of Experts regularizer to restore natural images degraded by blur and noise. For improving the practical performance, the lower-level problem is solved by means of a gradient descent scheme combined with a line-search strategy based on the Barzilai-Borwein rule. As a second application, the bilevel setup is employed for learning a discretization of the popular total variation regularizer for solving image restoration problems (in particular, deblurring and super-resolution). Numerical results show the effectiveness of the approach and their generalization to multiple tasks.

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Constrained and Unconstrained Inverse Potts Modelling for Joint Image Super-Resolution and Segmentation

Cited by 5 publications

References 15 publications

Constrained Regularization by Denoising With Automatic Parameter Selection

Constrained Regularization by Denoising With Automatic Parameter Selection

Constrained Plug-and-Play Priors for Image Restoration

Bilevel learning of regularization models and their discretization for image deblurring and super-resolution

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