DIGITAL IMAGE PROCESSING Instructors: Dr J. Shanbehzadeh M.Gholizadeh M.Gholizadeh

DIGITAL IMAGE PROCESSING Instructors: Dr J. Shanbehzadeh M.Gholizadeh M.Gholizadeh ( J.Shanbehzadeh M.Gholizadeh )

Road map of chapter A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only- Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering A Model of the Image Degradation/Restoration Process 5.2 Noise Models Restoration in the Presence of Noise Only-Spatial Filtering Periodic Noise Reduction by Frequency Domain Filtering 5.5 Linear, Position-Invariant Degradations 5.6 Estimating the degradation Function Inverse Filtering Minimum Mean Square Error (Wiener) Filtering ( J.Shanbehzadeh M.Gholizadeh )

Road map of chapter Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections Geometric Mean Filter 5.10 Constrained Least Square Filtering Image Reconstruction from Projections 5.11 ( J.Shanbehzadeh M.Gholizadeh )

Preview Goal of R RR Restoration: Improve Image Quality Example Degraded Image Knowledge Of Image Creation Process Develop Degradation Model Develop Inverse Degradation Process Apply Inverse Degradation Process Input Image d (r,c ) Output Image I(r,c ) ( J.Shanbehzadeh M.Gholizadeh )

Restoration Restoration is an objective process compared to image enhancement: Image restoration is to restore a degraded image back to the original image. Image Enhancement is to manipulate the image so that it is suitable for a specific application. Contrast stretching is an enhancement technique while debluring function is considered a restoration. Only consider in this chapter a degraded digital image. Restoration Restoration can be categorized as two groups: Deterministic methods are applicable to images with little noise and a known degradation Stochastic methods try to find the best restoration according to a particular stochastic criterion, e.g., a least square method Preview ( J.Shanbehzadeh M.Gholizadeh )

5.1 A Model of the Image Degradation/Restoration Process ( J.Shanbehzadeh M.Gholizadeh )

A Model of the Image Degradation/Restoration Process 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Spatial domain: additive noise The degraded image in Spatial domain is where h(x,y) is a system that causes image distortion and h(x,y) is noise. Frequency domain : blurring The degraded image in Frequency domain is Where the terms in capital letters are Fourier transforms. Objective: obtain an estimate of A Model of the Image Degradation/Restoration Process 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Three types of degradation that can be easily expressed mathematically Relative motion of the camera and object Wrong lens focus Atmospheric turbulence A Model of the Image Degradation/Restoration Process 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Noise Models Spatial and Frequency Properties of NoiseSome Important Noise Probability Density FunctionsPeriodic NoiseEstimation of Noise Parameters 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

The Principal Source of Noise Noise arise … During Image Acquisition Environment conditions Quality of sensing elements For x. Two factors for CCD: light level and sensor temperature Image Transmission 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Noise Models Spatial and Frequency Properties of NoiseSome Important Noise Probability Density FunctionsPeriodic NoiseEstimation of Noise Parameters Spatial and Frequency Properties of Noise 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Spatial and Frequency Properties of Noise White noise: The Fourier spectrum of noise is constant. This terminology is a carryover from the physical properties of white light, which contains nearly all frequencies in the visible spectrum in equal properties. We assume in this chapter: Noise is independent of spatial coordinates A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Noise Models Spatial and Frequency Properties of NoiseSome Important Noise Probability Density FunctionsPeriodic NoiseEstimation of Noise Parameters Some Important Noise Probability Density Functions 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Noise Probability Density Functions Noise cannot be predicted but can be approximately described in statistical way using the probability density function (PDF). The statistical properties of the gray level of spatial noise can be considered random variables characterized by a PDF A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Most Common PDFs of Noises Gaussian noise Are used frequently in practice The PDF of a Gaussian random variable, Z, is given by: Rayleigh noise The PDF of Rayleigh noise: Erlang (Gamma) noise The PDF of Erlang noise : 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Most Common PDFs of Noises Exponential noise The PDF of exponential noise : Uniform noise The PDF of uniform noise is given by: Impulse noise (Salt and pepper) The PDF of impulse noise is given by: If b>a gray level b will appear as a light dot; If either P a or P b is zero, the impulse is called unipolar If neither probability is zero (bipolar), and especially if they are approximately equal: salt and pepper noise 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Most Common PDFs of Noises z PDF tells how much each z value occurs A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Noise Factors Gaussian noise: electronic circuit noise and sensors noise due to poor illumination and /or temperature Rayleigh noise: helpful in characterizing noise phenomena in rang imaging Exponential and gamma noise: application in laser imaging Impulse noise: found in quick transient such as faulty- switching ; is the only one that is visually indicative Uniform noise: basis for random number generator Difficult to differentiate visually between the five image (Fig 5.4(a) ~Fig5.4(b)) 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Image Degradation with Additive Noise Degraded imagesOriginal image Histogram 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )

Original image Histogram Degraded images Image Degradation with Additive Noise 5.1- A Model of the Image Degradation/Restoration Process 5.2- Noise Models 5.3- Restoration in the Presence of Noise Only-Spatial Filtering 5.4- Periodic Noise Reduction by Frequency Domain Filtering Linear, Position-Invariant Degradations 5.6- Estimating the degradation Function 5.7- Inverse Filtering 5.8- Minimum Mean Square Error (Wiener) Filtering 5.9- Constrained Least Square Filtering Geometric Mean Filter Image Reconstruction from Projections ( J.Shanbehzadeh M.Gholizadeh )