Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

Ono, Shunsuke

doi:10.1109/icassp.2019.8682191

Cited by 20 publications

(7 citation statements)

References 32 publications

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“…The second constraint characterizes sparse noise the zero-centered ℓ 1 ball with the radius η > 0. Using such a data-fidelity constraint instead of an additive data-fidelity term makes it easy to adjust hyperparameters since ε and η can be determined based only on noise intensity (independent of the other terms in the objective function), as addressed, for example, in [25]- [28]. The third constraint is a box constraint with µ < μ which represents the dynamic range of u.…”

Section: B Problem Formulationmentioning

confidence: 99%

Graph Spatio-Spectral Total Variation Model for Hyperspectral Image Denoising

Takemoto¹,

Naganuma²,

Ono³

2022

Preprint

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The spatio-spectral total variation (SSTV) model has been widely used as an effective regularization of hyperspectral images (HSI) for various applications such as mixed noise removal. However, since SSTV computes local spatial differences uniformly, it is difficult to remove noise while preserving complex spatial structures with fine edges and textures, especially in situations of high noise intensity. To solve this problem, we propose a new TV-type regularization called Graph-SSTV (GSSTV), which generates a graph explicitly reflecting the spatial structure of the target HSI from noisy HSIs and incorporates a weighted spatial difference operator designed based on this graph. Furthermore, we formulate the mixed noise removal problem as a convex optimization problem involving GSSTV and develop an efficient algorithm based on the primal-dual splitting method to solve this problem. Finally, we demonstrate the effectiveness of GSSTV compared with existing HSI regularization models through experiments on mixed noise removal. The source code will be available at https://www.mdi.c.titech.ac.jp/publications/gsstv.

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Section: B Problem Formulationmentioning

confidence: 99%

Graph Spatio-Spectral Total Variation Model for Hyperspectral Image Denoising

Takemoto¹,

Naganuma²,

Ono³

2022

Preprint

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“…The first and second constraints are spatial and temporal zero-gradient constraints on stripe noise, respectively, and the third one is a Frobenius norm ball constraint with the radius ε for datafidelity to X . The data-fidelity constraint has an important advantage over the standard additive data-fidelity in terms of facilitating hyperparameter settings, as addressed in [15,16,17,18,19]. If stripe noise is temporally variant, we remove the second constraint.…”

Section: Problem Formulationmentioning

confidence: 99%

Zero-Gradient Constraints for Destriping of Remote-Sensing Data

Naganuma

Takeyama

Ono

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper proposes an effective and efficient destriping method for remote-sensing data. Destriping of remotesensing data is an essential task because stripe noise not only degrades the visual quality but also seriously affects subsequent processing. We formulate the destriping problem as a convex optimization problem involving zero-gradient constraints, where the constraints are designed to exploit the fact that the spatial and temporal gradients of stripe noise equal to zero. Our method imposes such strong constraints on stripe noise, and thus can fully capture the nature of stripe noise, leading to very effective destriping. Also, operations required for handling the zero-gradient constraints in optimization are simple, which enables us to develop an efficient algorithm for solving the problem by a primal-dual splitting method. We demonstrate the advantages of our method over existing methods on destriping experiments using remote-sensing data.

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“…Epigraphical techniques have already been successfully applied to handling involved norm ball constraints, e.g., multiclass SVM [19], randomized data-fidelity constraints [20], (non-local) TV, total generalized variation (TGV), and (nonlocal) structure-tensor TV (STV) constraints [21]- [23]. In these methods, a mixed norm constraint is decoupled into 2 The proximity operator, denoted as prox γf : R N → R N , is defined for a function f ∈ Γ 0 (R N ) (Γ 0 (R N ) is the set of proper lower semicontinuous convex functions on R N [8]) and an index γ ∈ (0, ∞) by [8] prox γf (x) := argmin y∈R N γf (y) + 1 2 x − y 2 2 .…”

Section: A Related Workmentioning

confidence: 99%

Epigraphical Reformulation for Non-Proximable Mixed Norms

Kyochi

Ono

Selesnick

2020

ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper proposes an epigraphical relaxation (ERx) technique for non-proximable mixed norm minimization. Mixed norm regularization methods play a central role in signal reconstruction and processing, where their optimization relies on the fact that the proximity operators of the mixed norms can be computed efficiently. To bring out the power of regularization, sophisticated layered modeling of mixed norms that can capture inherent signal structure is a key ingredient, but the proximity operator of such a mixed norm is often unavailable (nonproximable). Our ERx decouples a layered non-proximable mixed norm into a norm and multiple epigraphical constraints. This enables us to handle a wide range of non-proximable mixed norms in optimization, as long as both the proximal operator of the outermost norm and the projection onto each epigraphical constraint are efficiently computable. Moreover, under mild conditions, we prove that ERx does not change the minimizer of the original problem despite relaxing equality constraints into inequality ones. We also develop new regularizers based on ERx: one is decorrelated structure-tensor total variation for color image restoration, and the other is amplitude-spectrum nuclear norm (ASNN) for low-rank amplitude recovery. We examine the power of these regularizers through experiments, which illustrates the utility of ERx.

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Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

Cited by 20 publications

References 32 publications

Graph Spatio-Spectral Total Variation Model for Hyperspectral Image Denoising

Graph Spatio-Spectral Total Variation Model for Hyperspectral Image Denoising

Zero-Gradient Constraints for Destriping of Remote-Sensing Data

Epigraphical Reformulation for Non-Proximable Mixed Norms

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