A proximal iteration for deconvolving Poisson noisy images using sparse representations

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key contributions are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a {\it non-linear} degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. $\ell_1$-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Finally, a GCV-based model selection procedure is proposed to objectively select the regularization parameter. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of the noise. These results also suggest that using sparse-domain regularization may be tractable in many deconvolution applications with Poisson noise such as astronomy and microscopy

A new steplength selection for scaled gradient methods with application to image deblurring

Gradient methods are frequently used in large scale image deblurring problems since they avoid the onerous computation of the Hessian matrix of the objective function. Second order information is typically sought by a clever choice of the steplength parameter defining the descent direction, as in the case of the well-known Barzilai and Borwein rules. In a recent paper, a strategy for the steplength selection approximating the inverse of some eigenvalues of the Hessian matrix has been proposed for gradient methods applied to unconstrained minimization problems. In the quadratic case, this approach is based on a Lanczos process applied every m iterations to the matrix of the most recent m back gradients but the idea can be extended to a general objective function. In this paper we extend this rule to the case of scaled gradient projection methods applied to non-negatively constrained minimization problems, and we test the effectiveness of the proposed strategy in image deblurring problems in both the presence and the absence of an explicit edge-preserving regularization term

Segmentation-assisted detection of dirt impairments in archived film sequences

A novel segmentation-assisted method for film dirt detection is proposed. We exploit the fact that film dirt manifests in the spatial domain as a cluster of connected pixels whose intensity differs substantially from that of its neighborhood and we employ a segmentation-based approach to identify this type of structure. A key feature of our approach is the computation of a measure of confidence attached to detected dirt regions which can be utilized for performance fine tuning. Another important feature of our algorithm is the avoidance of the computational complexity associated with motion estimation. Our experimental framework benefits from the availability of manually derived as well as objective ground truth data obtained using infrared scanning. Our results demonstrate that the proposed method compares favorably with standard spatial, temporal and multistage median filtering approaches and provides efficient and robust detection for a wide variety of test material

Properties of sunspots in cycle 23: I. Dependence of brightness on sunspot size and cycle phase

In this paper we investigate the dependence of umbral core brightness, as well as the mean umbral and penumbral brightness on the phase of the solar cycle and on the size of the sunspot. Albregtsen & Maltby (1978) reported an increase in umbral core brightness from the early to the late phase of solar cycle from the analysis of 13 sunspots which cover solar cycles 20 and 21. Here we revisit this topic by analysing continuum images of more than 160 sunspots observed by the MDI instrument on board the SOHO spacecraft for the period between 1998 March to 2004 March, i.e. a sizable part of solar cycle 23. The advantage of this data set is its homogeneity, with no seeing fluctuations. A careful stray light correction, which is validated using the Mercury transit of 7th May, 2003, is carried out before the umbral and penumbral intensities are determined. The influence of the Zeeman splitting of the nearby NiI spectral line on the measured 'continuum' intensity is also taken into account. We did not observe any significant variation in umbral core, mean umbral and mean penumbral intensities with solar cycle, which is in contrast to earlier findings for the umbral core intensity. We do find a strong and clear dependence of the umbral brightness on sunspot size, however. The penumbral brightness also displays a weak dependence. The brightness-radius relationship has numerous implications, some of which, such as those for the energy transport in umbrae, are pointed out.Comment: 16 pages, 21 postscript figures, accepted for publication in A&