Abstract
Blind Deconvolution problem is a challenging task in several scientific imaging domains, such as Microscopy, Medicine and Astronomy. The Point Spread Function inducing the blur effect on the ...acquired image can be solely approximately known, or just a mathematical model may be available. Blind deconvolution aims to reconstruct the image when only the recorded data is available. In the last years, among the standard variational approaches, Deep Learning techniques have gained interest thanks to their impressive performances. The Deep Image Prior framework has been employed for solving this task, giving rise to the so-called neural blind deconvolution (NBD), where the unknown blur and image are estimated via two different neural networks. In this paper, we consider microscopy images, where the predominant noise is of Poisson type, hence signal-dependent: this leads to consider the generalized Kullback–Leibler as loss function and to couple it with regularization terms on both the blur operator and on the image. Furthermore, we propose to modify the standard NBD formulation problem, by including for the blur kernel an upper bound which depends on the optical instrument. A numerical solution is obtained by an alternating Proximal Gradient Descent-Ascent procedure, which results in the Double Deep Image Prior for Poisson noise algorithm. We evaluate the proposed strategy on both synthetic and real-world images, achieving promising results and proving that the correct choice of the loss and regularization functions strongly depends on the application at hand.
We prove a result on the existence and uniqueness of the solution of a new feature-preserving nonlinear nonlocal diffusion equation for signal denoising for the one-dimensional case. The partial ...differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal.
•The deconvolution of high contrast images consisting of very bright stars and smooth structures around the stars is studied.•To restore the region around the stars, the object can be regarded as ...superposition of point source and extended source.•When the position of the point source is known, we introduce a regularization term only for the diffuse component.•We give conditions for the solution of the related variational problem for Poisson data with Tikhonov-like regularization.•In presence of an overestimation of the regularization parameter, we solve by the inexact Bregman iteration with SGP method.
In this paper we consider the deconvolution of high contrast images consisting of very bright stars (point component) and smooth structures underlying the stars (diffuse component). A typical case is a weak diffuse jet line emission superimposed to a strong stellar continuum. In order to reconstruct the diffuse component, the original object can be regarded as the sum of these two components. When the position of the point sources is known, a regularization term can be introduced for the second component. An approximation of the original object can be obtained by solving a reduced variational problem whose unknowns are the intensities of the stars and the diffuse component. We analyze this problem when the detected image is corrupted by Poisson noise and Tikhonov-like regularization is used, giving conditions for the existence and the uniqueness of the solution. Furthermore, since only an overestimation of the regularization parameter is available, we propose to solve the variational problem by inexact Bregman iteration combined with a Scaled Gradient Projection method (SGP). Numerical simulations show that the images obtained with this approach enable us to reconstruct the original intensity distribution around the point source with satisfactory accuracy.
Aims. High-dynamic range images of astrophysical objects present some difficulties in their restoration because of the presence of very bright point-wise sources surrounded by faint and smooth ...structures. We propose a method that enables the restoration of this kind of images by taking these kinds of sources into account and, at the same time, improving the contrast enhancement in the final image. Moreover, the proposed approach can help to detect the position of the bright sources. Methods. The classical variational scheme in the presence of Poisson noise aims to find the minimum of a functional compound of the generalized Kullback-Leibler function and a regularization functional: the latter function is employed to preserve some characteristic in the restored image. The inexact Bregman procedure substitutes the regularization function with its inexact Bregman distance. This proposed scheme allows us to take under control the level of inexactness arising in the computed solution and permits us to employ an overestimation of the regularization parameter (which balances the trade-off between the Kullback-Leibler and the Bregman distance). This aspect is fundamental, since the estimation of this kind of parameter is very difficult in the presence of Poisson noise. Results. The inexact Bregman procedure is tested on a bright unresolved binary star with a faint circumstellar environment. When the sources’ position is exactly known, this scheme provides us with very satisfactory results. In case of inexact knowledge of the sources’ position, it can in addition give some useful information on the true positions. Finally, the inexact Bregman scheme can be also used when information about the binary star’s position concerns a connected region instead of isolated pixels.
Image regularization for Poisson data Benfenati, A; Ruggiero, V
Journal of physics. Conference series,
11/2015, Letnik:
657, Številka:
1
Journal Article
Recenzirano
Odprti dostop
Recently, Poisson noise has become of great interest in many imaging applications. When regularization strategies are used in the so-called Bayesian approach, a relevant issue is to find rules for ...selecting a proper value of the regularization parameter. In this work we compare three different approaches which deal with this topic. The first model aims to find the root of a discrepancy equation, while the second one estimates such parameter by adopting a constrained, approach. These two models do not always provide reliable results in presence of low counts images. The third approach presented is the inexact Bregman procedure, which allows to use an overestimation of the regularization parameter and moreover enables to obtain very promising results in case of low counts images and High Dynamic Range astronomical images.
This work deals with the solution of image restoration problems by an iterative regularization method based on the Bregman iteration. Any iteration of this scheme requires the exact computation of ...the minimizer of a function. However, in some image reconstruction applications, it is either impossible or extremely expensive to obtain exact solutions of these subproblems. In this paper, we propose an inexact version of the iterative procedure, where the inexactness in the inner subproblem solution is controlled by a criterion that preserves the convergence of the Bregman iteration and its features in image restoration problems. In particular, the method allows us to obtain accurate reconstructions also when only an overestimation of the regularization parameter is known. The introduction of the inexactness in the iterative scheme allows us to address image reconstruction problems from data corrupted by Poisson noise, exploiting the recent advances about specialized algorithms for the numerical minimization of the generalized Kullback-Leibler divergence combined with a regularization term. The results of several numerical experiments enable us to evaluate the proposed scheme for image deblurring or denoising in the presence of Poisson noise.
Diffuse optical tomography (DOT) is an emerging diagnostic technique which uses near-infra-red light to investigate the optical coefficients distribution in biological tissues. The surface of the ...tissue is illuminated by light sources, then the outgoing light is measured by detectors placed at various locations on the surface itself. In order to reconstruct the optical coefficients, a mathematical model of light propagation is employed: such model leads to the minimization of the discrepancy between the detected data and the corresponding theoretical field. Due to severe ill-conditioning, regularization techniques are required: common procedures consider mainly ℓ1-norm (LASSO) and ℓ2-norm (Tikhonov) regularization. In the present work we investigate two original approaches in this context: the elastic-net regularization, previously used in machine learning problems, and the Bregman procedure. Numerical experiments are performed on synthetic 2D geometries and data, to evaluate the performance of these approaches. The results show that these techniques are indeed suitable choices for practical applications, where DOT is used as a cheap, first-level and almost real-time screening technique for breast cancer detection.
The aim of this note is to examine the sources of nonlinearity arising in the kinetic theory of active particles. We show how nonlinearities enter the different terms of the theory, giving rise to ...possible developments toward the modeling of different types of complex systems, mainly living and social ones, where proliferative–destructive processes must be included. Finally, some research perspectives are discussed.
To analyze bowel and urinary function in patients with posterior deep infiltrating endometriosis (DIE) >30 mm in largest diameter at transvaginal ultrasound before and after surgical nerve-sparing ...excision.
Prospective observational study (Canadian Task Force classification III).
Tertiary care university hospital in Bologna, Italy.
Twenty-five patients with posterior DIE were included in the study between June 2011 and December 2012. Patients did not receive hormone therapy for at least 3 months before and 6 months after surgery.
Patients underwent urodynamic studies and anorectal manometry before and after nerve-sparing laparoscopic excision of the posterior DIE nodule.
Intestinal and urinary function was evaluated in patients with bulky posterior DIE using urodynamic and anorectal manometry. Results of urodynamic studies and anorectal manometry were similar before and after nerve-sparing surgical excision of the posterior DIE nodule. Urodynamic studies demonstrated a high prevalence of voiding dysfunction, whereas anorectal manometry showed no reduction in rectoanal inhibitory reflex and hypertone of the internal anal sphincter.
Patients with posterior DIE >30 mm in greatest diameter demonstrate preoperative dysfunction at urodynamic study and anorectal manometry, probably due to DIE per se. The nerve-sparing surgical approach seems not to influence the motility or sensory capacity of the bladder and the rectosigmoid colon.
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