Efficient gradient projection methods for edge-preserving removal of Poisson noise

Zanella, Riccardo; Boccacci, Patrizia; Zanni, Luca; Bertero, M.

doi:10.1088/0266-5611/25/4/045010

Cited by 140 publications

(173 citation statements)

References 30 publications

Supporting

Mentioning

169

Contrasting

Order By: Relevance

“…Then, [43] showed that, for large λ: In the case of deconvolution, we have y = P(Hx + b) and thus y is a Poisson random variable with mean Hx + b. So, from this statement and (43), [43] defined:…”

Section: A State Of Artmentioning

confidence: 95%

“…Finally, we would like to mention also the recent work of Bertero et al [43] in which is introduced a discrepancy principle for Poisson noise. First, let us consider the following function:…”

Section: A State Of Artmentioning

confidence: 95%

“…We detail this technique in this section as the Gaussian approximation is often made in the domain of Poisson deconvolution. To the best of our knowledge, only [43] have proposed both a method to select the regularizing parameter especially designed to take into account the Poisson statistics of the noise and an algorithm which also deals with Poisson noise. We also recall their method.…”

Section: A State Of Artmentioning

confidence: 99%

See 2 more Smart Citations

Sparse Poisson Noisy Image Deblurring

Carlavan

Blanc‐Féraud

2012

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

Abstract-Deblurring noisy Poisson images has recently been subject of an increasingly amount of works in many areas such as astronomy or biological imaging. In this paper, we focus on confocal microscopy which is a very popular technique for 3D imaging of biological living specimens which gives images with a very good resolution (several hundreds of nanometers), even though degraded by both blur and Poisson noise. Deconvolution methods have been proposed to reduce these degradations and we focus in this paper on techniques which promote the introduction of explicit prior on the solution. One difficulty of these techniques is to set the value of the parameter which weights the trade-off between the data term and the regularizing term. Actually, only few works have been devoted to the research of an automatic selection of this regularizing parameter when considering Poisson noise so it is often set manually such that it gives the best visual results. We present here two recent methods to estimate this regularizing parameter and we first propose an improvement of these estimators which takes advantage of confocal images. Following these estimators, we secondly propose to express the problem of Poisson noisy images deconvolution as the minimization of a new constrained problem. The proposed constrained formulation is well suited to this application domain since it is directly expressed using the anti log-likelihood of the Poisson distribution and therefore does not require any approximation. We show how to solve the unconstrained and constrained problem using the recent Alternating Direction technique and we present results on synthetic and real data using well-known priors such as Total Variation and wavelet transforms. Among these wavelet transforms, we specially focus on the Dual-Tree Complex Wavelet transform and on the dictionary composed of Curvelets and undecimated wavelet transform.

show abstract

Section: A State Of Artmentioning

confidence: 95%

Section: A State Of Artmentioning

confidence: 95%

Section: A State Of Artmentioning

confidence: 99%

See 1 more Smart Citation

Sparse Poisson Noisy Image Deblurring

Carlavan

Blanc‐Féraud

2012

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

show abstract

“…In order to fully define the SPDHG method, we focus on the strategy to compute a suitable scaling matrix D k , adapting to our case the split gradient strategy proposed in [1] for nonnegatively constrained differentiable problems, which demonstrated to be very effective in several applications (see [16,6] and references therein). The key point of this approach consists in finding a subgradient decomposition of the form…”

Section: Endmentioning

confidence: 99%

A fast subgradient algorithm in image super-resolution

Lazzaro

Piccolomini

Ruggiero

et al. 2017

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

View the article online for updates and enhancements. Abstract. In this paper we propose an −subgradient method for solving a constrained minimization problem arising in super-resolution imaging applications. The method, compared to the state-of-the-art methods for single image super-resolution on some test problems, proves to be very efficient, both for the reconstruction quality and the computational time. IntroductionImage super-resolution reconstruction is the process of obtaining High Resolution (HR) images from observed Low Resolution (LR) images. The problem of super-resolution is of great importance in many applications, such as medicine or object recognition (face, bar codes, ...), where the electronic imaging devices are equipped with low resolution cameras, while HR images are finally desired. The super-resolution process can be performed from a single image (SISR) or from multiple images of the same scene (MISR), such as in the case of videos or medical imaging devices for example. In this paper, we will consider only the case of SISR. The SIRS problem is ill-posed, since identical LR images can be generated from different HR images. Furthermore, in addition to being connected by a down-sampling operator, the HR and LR images are related by a Point Spread Function (as a simple convolution, for example), that is an ill-posed operator. The different approaches, present in literature for image super-resolution, can generally be grouped into four categories: interpolation-based algorithms, example-based algorithms, sparse-representation-based algorithms and reconstruction-based algorithms (see [5] and the references therein). The reconstruction-based algorithms are aimed at solving a minimization problem, where the objective function is the sum of a fidelity term related to the data noise and a regularization term, representing the prior on the solution and, at the same time, enabling to face the ill-posedness of the problem. This formulation has the advantage of simultaneously exploiting the degradation model and the information contained in the prior, thus reducing noise and artifacts in the HR reconstructed image [5,12].We consider a reconstruction-based algorithm to address a minimization problem where the fidelity term is the 2 -norm, the regularization term is the discrete Total Variation (TV) function and the solution is constrained to be nonnegative. This model has been widely treated for the deblurring applications and many algorithms have been proposed for its solution, such as, for example, [11,13,14]. The Bregman method proposed in [14] has been later used in [12] for image super-resolution. In this paper we propose a scaling -subgradient method presented in [2] for deblurring of images corrupted by Poisson noise. The method has a fast computational

show abstract

“…In [24] (see also [3]) statistical arguments were used to show that τ I = 1 2 n is a good estimate in case of moderate Poisson noise. In [5] this estimate was improved in case f has many zero components.…”

Section: Primal-dual Algorithmsmentioning

confidence: 99%

Epigraphical Projection for Solving Least Squares Anscombe Transformed Constrained Optimization Problems

Harizanov

Pesquet

Steidl

2013

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. This papers deals with the restoration of images corrupted by a non-invertible or ill-conditioned linear transform and Poisson noise. Poisson data typically occur in imaging processes where the images are obtained by counting particles, e.g., photons, that hit the image support. By using the Anscombe transform, the Poisson noise can be approximated by an additive Gaussian noise with zero mean and unit variance. Then, the least squares difference between the Anscombe transformed corrupted image and the original image can be estimated by the number of observations. We use this information by considering an Anscombe transformed constrained model to restore the image. The advantage with respect to corresponding penalized approaches lies in the existence of a simple model for parameter estimation. We solve the constrained minimization problem by applying a primal-dual algorithm together with a projection onto the epigraph of a convex function related to the Anscombe transform. We show that this epigraphical projection can be efficiently computed by Newton's methods with an appropriate initialization. Numerical examples demonstrate the good performance of our approach, in particular, its close behaviour with respect to the I-divergence constrained model.

show abstract

Efficient gradient projection methods for edge-preserving removal of Poisson noise

Cited by 140 publications

References 30 publications

Sparse Poisson Noisy Image Deblurring

Sparse Poisson Noisy Image Deblurring

A fast subgradient algorithm in image super-resolution

Epigraphical Projection for Solving Least Squares Anscombe Transformed Constrained Optimization Problems

Contact Info

Product

Resources

About