Deblurring subject to nonnegativity constraints

Snyder, Donald L.; Schulz, Timothy J.; O'Sullivan, Joseph A.

doi:10.1109/78.134477

Cited by 208 publications

(172 citation statements)

References 18 publications

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“…It has been argued that in cases where data do not belong to the set of positive real numbers, the SE does not reach a minimum [30,31], this being a fact in optical images, because the intensities captured are always nonnegative. An alternative is to use Csiszár I-divergence, which is a generalization of the Kullback-Leibler information measure between two probability mass functions (or density, in the continuous case) p and r. It is defined as [30]:…”

Section: Csiszár I-divergence Minimizationmentioning

confidence: 99%

See 1 more Smart Citation

Estimation Methods of the Point Spread Function Axial Position: A Comparative Computational Study

Zamboni

Casco

2017

J. Imaging

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The precise knowledge of the point spread function is central for any imaging system characterization. In fluorescence microscopy, point spread function (PSF) determination has become a common and obligatory task for each new experimental device, mainly due to its strong dependence on acquisition conditions. During the last decade, algorithms have been developed for the precise calculation of the PSF, which fit model parameters that describe image formation on the microscope to experimental data. In order to contribute to this subject, a comparative study of three parameter estimation methods is reported, namely: I-divergence minimization (MIDIV), maximum likelihood (ML) and non-linear least square (LSQR). They were applied to the estimation of the point source position on the optical axis, using a physical model. Methods' performance was evaluated under different conditions and noise levels using synthetic images and considering success percentage, iteration number, computation time, accuracy and precision. The main results showed that the axial position estimation requires a high SNR to achieve an acceptable success level and higher still to be close to the estimation error lower bound. ML achieved a higher success percentage at lower SNR compared to MIDIV and LSQR with an intrinsic noise source. Only the ML and MIDIV methods achieved the error lower bound, but only with data belonging to the optical axis and high SNR. Extrinsic noise sources worsened the success percentage, but no difference was found between noise sources for the same method for all methods studied.

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Section: Csiszár I-divergence Minimizationmentioning

confidence: 99%

“…Compared with the Kullback-Leibler information measure, Csiszár adjusts the p and r functions for those cases in which their integrals are not equal [31], adding the last summation term on the right side of the Equation (13). Because of this, I(p||r) has the following properties:…”

Section: Csiszár I-divergence Minimizationmentioning

confidence: 99%

Estimation Methods of the Point Spread Function Axial Position: A Comparative Computational Study

Zamboni

Casco

2017

J. Imaging

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“…The methods are all based on the hypothesis plane deconvolution used by [5] as explained in the Introduction. The main difference among the competing methods is that the deconvolution step is performed either using the Lucy-Richardson method [44], or regularized filtering (i.e., with image gradient smoothness), or Wiener filtering [45], or Levin's procedure [5]. We use the 8 masks shown in Fig.…”

Section: Performance Comparisonmentioning

confidence: 99%

Single Image Blind Deconvolution with Higher-Order Texture Statistics

Martinello

Favaro

2011

Video Processing and Computational Video

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Abstract. We present a novel method for solving blind deconvolution, i.e., the task of recovering a sharp image given a blurry one. We focus on blurry images obtained from a coded aperture camera, where both the camera and the scene are static, and allow blur to vary across the image domain. As most methods for blind deconvolution, we solve the problem in two steps: First, we estimate the coded blur scale at each pixel; second, we deconvolve the blurry image given the estimated blur. Our approach is to use linear high-order priors for texture and second-order priors for the blur scale map, i.e., constraints involving two pixels at a time. We show that by incorporating the texture priors in a least-squares energy minimization we can transform the initial blind deconvolution task in a simpler optimization problem. One of the striking features of the simplified optimization problem is that the parameters that define the functional can be learned offline directly from natural images via singular value decomposition. We also show a geometrical interpretation of image blurring and explain our method from this viewpoint. In doing so we devise a novel technique to design optimally coded apertures. Finally, our coded blur identification results in computing convolutions, rather than deconvolutions, which are stable operations. We will demonstrate in several experiments that this additional stability allows the method to deal with large blur. We also compare our method to existing algorithms in the literature and show that we achieve state-of-the-art performance with both synthetic and real data.

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“…In the astronomical community EM is known as RichardsonLucy deconvolution (Richardson 1972;Lucy 1974;Shepp and Vardi 1982). Snyder et al (1992) describe a method which maximizes the mean value of the log-likelihood for quantum noise limited data. It has been shown that this is equivalent to minimizing Csiszàr's I-divergence (Csiszàr 1991), a quantity equal to the negative of the entropy expression, −S, given in equation (7).…”

Section: Medical Image Restorationmentioning

confidence: 99%

Mammographic image restoration using maximum entropy deconvolution

Jannetta¹,

Jackson²,

Kotre³

et al. 2004

Phys. Med. Biol.

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Abstract. An image restoration approach based on a Bayesian maximum entropy method (MEM) has been applied to a radiological image deconvolution problem, that of reduction of geometric blurring in magnification mammography. The aim of the work is to demonstrate an improvement in image spatial resolution in realistic noisy radiological images with no associated penalty in terms of reduction in the signalto-noise ratio perceived by the observer. Images of the TORMAM mammographic image quality phantom were recorded using the standard magnification settings of 1.8 magnification/fine focus and also at 1.8 magnification/broad focus and 3.0 magnification/fine focus; the latter two arrangements would normally give rise to unacceptable geometric blurring. Measured point-spread functions were used in conjunction with the MEM image processing to de-blur these images. The results are presented as comparative images of phantom test features and as observer scores for the raw and processed images. Visualization of high resolution features and the total image scores for the test phantom were improved by the application of the MEM processing. It is argued that this successful demonstration of image de-blurring in noisy radiological images offers the possibility of weakening the link between focal spot size and geometric blurring in radiology, thus opening up new approaches to system optimization.

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Deblurring subject to nonnegativity constraints

Cited by 208 publications

References 18 publications

Estimation Methods of the Point Spread Function Axial Position: A Comparative Computational Study

Estimation Methods of the Point Spread Function Axial Position: A Comparative Computational Study

Single Image Blind Deconvolution with Higher-Order Texture Statistics

Mammographic image restoration using maximum entropy deconvolution

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