Practical Poissonian-Gaussian Noise Modeling and Fitting for Single-image Raw-data Alessandro Foi, Mejdi Trimeche, Vladimir Katkovnik, and Karen Egiazarian.

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Presentation transcript:

Practical Poissonian-Gaussian Noise Modeling and Fitting for Single-image Raw-data Alessandro Foi, Mejdi Trimeche, Vladimir Katkovnik, and Karen Egiazarian Department of Signal Processing, Tampere University of Technology

Noise Modeling for General Cases Noisy Images Variant Acquisition Devices Image Processing Output Images Noise Model It is hard to construct a general noise model!

Noise Modeling for Specific Case Noisy Images Image Processing Output Images Noise Model Foi, A., M. Trimeche, V. Katkovnik, and K. Egiazarian, “Practical Poissonian-Gaussian noise modeling and fitting for single-image raw- data”, IEEE Trans. Image Process., vol. 17, no. 10, pp , October 2008.

An Example of Application: Sharpness Enhancement Noisy Image Sharpness Enhancement Output Image Noise Model Original Image Enhanced Image with Noise Suppression

Application with Noise Model Spatial Index Intensity

Application with Noise Model Scene Radiance Image Sensor Camera Processing Output Image Camera System Denoising, Demosaicing, Deblurring, Compression Raw-Data Noise Modeling

Noise Model Scene Light Photon Sensor Electrical Devices Image Raw-data Poisson Noise Gaussian Noise Signal-dependentSignal-independent Camera Sensor

Noise Model

Poissonian-Gaussian Noise Poisson: Gaussian: Overall Variance of z: Overall Standard-deviation of z:

Noise Level Function Intensity Standard-deviation Intensity Standard-deviation a = , , , b = a = 0.4 2, b = , ,

Poissonian-Gaussian Noise

Raw-data Modeling Overall Standard-deviation of z: 1.Quantum Efficiency 2.Pedestal Parameter 3.Analog Gain Efficiency ↑  a↓ The percentage of photons hitting the photoreactive surface that will produce an electron

Noise Model Sensor Model Noise Model

Sensor Parameter and Noise Parameter Sensor Parameter: ISO-number  Gain Temperature Shutter Time

Sensor Parameter and Noise Parameter

Two Stages of Noise Estimation Local estimation of multiple expectation/standard-deviation pairs. Global parametric model fitting. Intensity Standard-deviation

Two Stages of Noise Estimation Local Estimation Intensity Standard-deviation Global Parametric Model Fitting

Local Estimation Local Expectation/ Standard-deviation Pair Locally Smoothed Value Locally Detail Value

Wavelet Analysis Local Expectation/ Standard-deviation Pair Locally Smoothed Value Locally Detail Value Noise Component

Wavelet Analysis Noise Component For Smooth Region

Wavelet Analysis Noise Component For Smooth Region

Smooth Region Segmentation Smooth Region Segmentation Edge Detection Smoothing

Level Sets Segmentation Smooth Region Segmentation Smooth Region … Level Segmentation Intensity 01 …

Local Estimation of y i … Estimation

Local Estimation of σ i … This factor, which comes from the mean of the chi-distribution with n − 1 degrees of freedom, makes the estimate unbiased for normally and identically independently distributed (i.i.d.)

Global Fitting Intensity Standard-deviation

Clipping Effect Intensity Spatial Index 1 0 Intensity Spatial Index 1 0 Clipping from above Clipping from below

Clipping Effect Intensity Standard-deviation

Clipping Model Original Signal Clipped Signal

Clipping Model Original Signal Clipped Signal

Clipping Effect Original Signal Clipped Signal

Clipping Model For Image Noise Original Signal Clipped Signal

Clipping Correction Ideal EstimationEstimation under Clipping Direct Transformation Inverse Transformation

Direct Transformation Clipped from Ideal

Direct Transformation Clipped from Ideal

Clipping Correction Ideal EstimationEstimation under Clipping Direct Transformation Inverse Transformation

Ideal EstimationEstimation under Clipping Direct Transformation Inverse Transformation

Clipping from above and below Intensity Spatial Index 1 0 Clipping from above Clipping from below

Correction Results Intensity Standard-deviation

Algorithm Overview Wavelet Analysis Input Image Smooth Region Segmentation Smooth Region Segmentation Level Sets Segmentation Level Sets Segmentation Local Estimation Clipping Correction Clipping Correction Global Fitting Global Fitting

Experiments Original y Observation z degraded by Poissonian and Gaussian noise with parameters χ = 100 (a = 0.01) and b = 0.042

Results Intensity Standard-deviation Reduce the influence of fine textures and edges Standard-deviation Intensity

Test Image Intensity

Test Image Intensity

Test Image Intensity

Test Image Intensity Test Image

Denoising Clipped Signals Foi, A.,.Practical denoising of clipped or overexposed noisy images., Proc. 16th European Signal Process. Conf., EUSIPCO 2008, Lausanne, Switzerland, August Original Signal Clipped Estimated Signal Spatial Index

Denoising Clipped Signals Noisy Image

Denoising Clipped Signals (FujiÞlm FinePix S9600 Camera), Denoised Result

Denoising Clipped Signals Denoised and Debiased Result