Optimal estimation in signal-dependent noise

Froehlich, Gary K.; Walkup, John F.; Asher, Robert B.

doi:10.1364/josa.68.001665

Cited by 30 publications

(10 citation statements)

References 5 publications

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“…To provide practical experimental results of our method, we shall refer to the affine noise variance model [5], which is one of the most suitable for modeling the noise in digital image sensors. According to this model, the noise variance is approximated as…”

Section: Methods a Problem Statementmentioning

confidence: 99%

Indirect Estimation of Signal-Dependent Noise With Nonadaptive Heterogeneous Samples

Azzari

Foi

2014

IEEE Trans. on Image Process.

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Abstract-We consider the estimation of signal-dependent noise from a single image. Unlike conventional algorithms that build a scatterplot of local mean-variance pairs from either small or adaptively selected homogeneous data samples, our proposed approach relies on arbitrarily large patches of heterogeneous data extracted at random from the image. We demonstrate the feasibility of our approach through an extensive theoretical analysis based on mixture of Gaussian distributions. A prototype algorithm is also developed in order to validate the approach on simulated data as well as on real camera raw images.

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Section: Methods a Problem Statementmentioning

confidence: 99%

Indirect Estimation of Signal-Dependent Noise With Nonadaptive Heterogeneous Samples

Azzari

Foi

2014

IEEE Trans. on Image Process.

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“…(31) the lower bound on the variance in the signal-dependent case is smaller than that achievable in the case of signal-independent noise [6]. This indicates the potential performance improvement for the inclusion of signal-dependent noise model.…”

Section: The Image Observation Modelmentioning

confidence: 97%

“…Fll"' Fllll (6) with F flo being the transpose of F ~>ll· Using the formula for the inversion of a partitioned matrice [7. p.l83-184]. the CRLB for the desired parameter vector a is given by Cov (a) ;;l:: :F,,-1 where a is any unbiased estimator of a and the reduced information matrix F,, is…”

Section: F = £[ ()Lnp(6) ()Lnp(6)]mentioning

confidence: 99%

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Theoretical Development of Performance Bounds for Image Restoration

Hung

Basart

1990

Review of Progress in Quantitative Nondestructive Evaluation

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. it is inappropriate to choose a particular measure as a benchmark of performance evaluation for a wide range of applications. :\lore 1mportantly. none of these quality measures can be used as a performance bound which usually indicates how much potential performance can be improved for a specific restoration scheme. Therefore. it is extremely important to develop theoretical performance bounds under a variety of image and noise models for general image restoration schemes.The multiparameter Cramer-Rao lower bound (CRLB) was originally developed for statistical inference [2]. It has been extensively adopted to provide the best attainable variance bound for any unbiased estimator in the area of statistical signal processing [3). In this paper. we first briefly summarize the fundamental theoretical results of the CRLB and define a general image formation and recording model used often for image restoration. A closed-form expression of the Fisher information matrix for a vector Gaussian random observation is then derived. This result is further used to develop the associated CRLBs for various classes of image and noise models. Finally. an application of the developed results to signal-dependent noise models (e.g. film-grain noise in X-ray I\'DE images) is presented. indicating the models' potential performance improvements for the case of extremely low signal-to-noise ratios. THE CRLB FOR MCLTIPLE PARAMETER ESTI:\1ATIO:\ ERRORSThe CRLB is often used to evaluate statistical efficiency of estimators. For example. the maximum likelihood estimate is well known to be asymptotically unbiased and efficient. This means that the estimator's variance achieves the CRLB as the sample size approaches infinity. In thispaper. we will use fundamental theoretical results of the CRLB. which are stated as follows:Consider a probability density function p (r '6) that governs a probabilistic mapping from a parameter space 0 into an observation space r. For a general parameter estimation problem. we are often interested in estimating the parameter vector 9 from the observation vector r. l"nder certain regularity conditions. the gene~alized Cramer-Rao inequality asserts that the covariance matrix of any unbiased estimate 6 of nonrandom parameter vector 6 satisfies [2. p.l94)

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“…To simulate this optical noise and the white noise created by different sources localized in the image processing system, we used the model proposed by Froehlich et al 15 A noisy irradiance I'(m, n) was computed from I(m, n) by degrading each pixel with additive noise, so I'(m,n) = I(m,n) + kI(m,n)ni + n2 ,…”

Section: Computer Simulationmentioning

confidence: 99%