An epigraphical convex optimization approach for multicomponent image restoration using non-local structure tensor

Chierchia, Giovanni; Pustelnik, Nelly; Pesquet, Jean-Christophe; Pesquet‐Popescu, Béatrice

doi:10.1109/icassp.2013.6637873

Cited by 12 publications

(11 citation statements)

References 29 publications

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“…In this paper a lifted POCS method [44,45] which does not require any regularization parameter or upper bound on the l 1 -norm of the signal is used to estimate the TF distribution. The algorithm is iterative.…”

Section: Tf Reconstruction Using Sparsitymentioning

confidence: 99%

Cross-term-free time–frequency distribution reconstruction via lifted projections

Deprem

Çetin

2015

IEEE Trans. Aerosp. Electron. Syst.

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A crucial aspect of time-frequency (TF) analysis is the identification of separate components in a multicomponent signal. The Wigner-Ville distribution is the classical tool for representing such signals, but it suffers from cross-terms. Other methods, which are members of Cohen's class of distributions, also aim to remove the cross-terms by masking the ambiguity function (AF), but they result in reduced resolution. Most practical time-varying signals are in the form of weighted trajectories on the TF plane, and many others are sparse in nature. Therefore, in recent studies the problem is cast as TF distribution reconstruction using a subset of AF domain coefficients and sparsity assumption. Sparsity can be achieved by constraining or minimizing the l 1 norm. In this article, an l 1 minimization approach based on projections onto convex sets is proposed to obtain a high-resolution, cross-term-free TF distribution for a given signal. The new method does not require any parameter adjustment to obtain a solution. Experimental results are presented.

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Section: Tf Reconstruction Using Sparsitymentioning

confidence: 99%

Cross-term-free time–frequency distribution reconstruction via lifted projections

Deprem

Çetin

2015

IEEE Trans. Aerosp. Electron. Syst.

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“…where X ( ) r denotes the r-th column vector of matrix X ( ) defined in (9). Note that, for both CC-NLTV and ST-NLTV, we set τ ≡ 1, Q = 11, Q = 5, δ = 35 and M = 14, as this setting was observed to yield the best numerical results.…”

Section: Color Photographymentioning

confidence: 99%

A Nonlocal Structure Tensor-Based Approach for Multicomponent Image Recovery Problems

Chierchia

Pustelnik

Pesquet‐Popescu

et al. 2014

IEEE Trans. on Image Process.

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Nonlocal total variation (NLTV) has emerged as a useful tool in variational methods for image recovery problems. In this paper, we extend the NLTV-based regularization to multicomponent images by taking advantage of the structure tensor (ST) resulting from the gradient of a multicomponent image. The proposed approach allows us to penalize the nonlocal variations, jointly for the different components, through various l(1, p)-matrix-norms with p ≥ 1. To facilitate the choice of the hyperparameters, we adopt a constrained convex optimization approach in which we minimize the data fidelity term subject to a constraint involving the ST-NLTV regularization. The resulting convex optimization problem is solved with a novel epigraphical projection method. This formulation can be efficiently implemented because of the flexibility offered by recent primal-dual proximal algorithms. Experiments are carried out for color, multispectral, and hyperspectral images. The results demonstrate the interest of introducing a nonlocal ST regularization and show that the proposed approach leads to significant improvements in terms of convergence speed over current state-of-the-art methods, such as the alternating direction method of multipliers.

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“…The new method does not require a regularization parameter. Concept of epigraph is first used in signal reconstruction problems in [35,36]. We also independently developed epigraph based algorithms in [37].…”

Section: Epigraph Of a Convex Cost Functionmentioning

confidence: 99%

“…Actually, Combettes and Pesquet and other researchers including us used a similar convex set in denoising and other signal restoration applications [4,20,34,36]. The following convex set in R N describes all signals whose TV is bounded by an upper bound :…”

Section: Denoising Using Pescmentioning

confidence: 99%

Denoising using projections onto the epigraph set of convex cost functions

Tofighi

Kose

Çetin

2014

2014 IEEE International Conference on Image Processing (ICIP)

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A new denoising algorithm based on orthogonal projections onto the epigraph set of a convex cost function is presented. In this algorithm, the dimension of the minimization problem is lifted by one and feasibility sets corresponding to the cost function using the epigraph concept are defined. As the utilized cost function is a convex function in RN, the corresponding epigraph set is also a convex set in RN+1. The denoising algorithm starts with an arbitrary initial estimate in RN+1. At each step of the iterative denoising, an orthogonal projection is performed onto one of the constraint sets associated with the cost function in a sequential manner. The method provides globally optimal solutions for total-variation, ℓ1, ℓ2, and entropic cost functions.1 © 2014 IEEE

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An epigraphical convex optimization approach for multicomponent image restoration using non-local structure tensor

Cited by 12 publications

References 29 publications

Cross-term-free time–frequency distribution reconstruction via lifted projections

Cross-term-free time–frequency distribution reconstruction via lifted projections

A Nonlocal Structure Tensor-Based Approach for Multicomponent Image Recovery Problems

Denoising using projections onto the epigraph set of convex cost functions

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