Digital Image Processing Lecture 4 Image Restoration and Reconstruction Second Semester Azad University Islamshar Branch

Image Restoration The main aim of restoration is to improve an image in some predefined way. Image restoration tries to reconstruct or recover an image which was degraded using a priori knowledge of degradation. Here we model the degradation and apply the inverse process to recover the original image. Enhancement techniques take advantage of the psychophysical aspects of human visual system. for example contrast stretching is an enhancement method as it is concerned with the pleasing aspects of a viewer, whereas removl of image blur is a restoration process.

In this model, we assume that there is an additive noise term, operating on an input image f(x,y) to produce a degraded image g(x,y). Given g(x,y) and some information about degradation function H, and knowledge about noise term η (x,y). The aim of restoration is to get an estimate f(x,y) of original image. The more we know about H and term η, we get better results. Model of Image Degradation / Restoration Process

Noise Sources The principal sources of noise in digital images arise during image acquisition and/or transmission. Image acquisition e.g., light levels, sensor temperature, etc. Transmission e.g., lightning or other atmospheric disturbance in wireless network

Noise Models White noise The Fourier spectrum of noise is constant Gaussian noise Electronic circuit noise, sensor noise due to poor illumination and/or high temperature Rayleigh noise Range imaging periodic noise With the exception of spatially periodic noise, we assume: Noise is independent of spatial coordinates Noise is uncorrelated with respect to the image itself

Erlang (gamma) noise: Laser imaging Exponential noise: Laser imaging Uniform noise: Least descriptive; Basis for numerous random number generators Impulse noise: quick transients, such as faulty switching Noise Models

Gaussian Noise 70% of its values will be in the range 95% of its values will be in the range

Noise Models Rayleigh Noise

Noise Models Erlang (Gamma) Noise

Exponential Noise Noise Models

Uniform Noise Noise Models

Impulse (Salt-and-Pepper) Noise Noise Models

PDF of noises

Examples of Noise: Original Image

Examples of Noise: Noisy Images(1)

Examples of Noise: Noisy Images(2)

Periodic Noise Periodic noise in an image arises typically from electrical or electromechanical interference during image acquisition. Periodic noise can be reduced significantly via frequency domain filtering

Estimation of Noise Parameters The shape of the histogram identifies the closest PDF match

Estimation of Noise Parameters

Restoration in the Presence of Noise Only ̶ Spatial Filtering

Spatial Filtering: Mean Filters Generally, a geometric mean filter achieves smoothing comparable to the arithmetic mean filter, but it tends to lose less image detail in the process

Spatial Filtering: Mean Filters It works well for salt noise, but fails for pepper noise. It does well also with other types of noise like Gaussian noise. Q is the order of the filter. It is well suited for reducing the effects of salt-and-pepper noise. Q>0 for pepper noise and Q<0 for salt noise.

Arithmetic and geometric mean filters are good for removing random noise like Gaussian or uniform noise. Contraharmonic filer is good for impulse noise. But it must be known before hand that whether the noise is dark or light to fix the Q value. Contraharmonic filer vs Arithmetic and geometric mean filters

Spatial Filtering: Example (1)

Spatial Filtering: Example (2)

Spatial Filtering: Example (3)

Spatial Filtering: Order-Statistic Filters

A filter formed by averaging these remaining pixels is called an alpha-trimmed mean filter

Spatial Filtering: Order-Statistic Filters (Example)

Spatial Filtering: Adaptive Filters Adaptive, Local Noise Reduction Filters

Spatial Filtering: Adaptive Filters Adaptive, Local Noise Reduction Filters

Adaptive, Local Noise Reduction Filters(Example)

Spatial Filtering: Adaptive Filters Adaptive Median Filters

Spatial Filtering: Adaptive Filters Adaptive Median Filters

Example: Adaptive Median Filters

Periodic Noise Reduction by Frequency Domain Filtering Periodic noise may occur if the imaging equipment (the acquisition or networking hardware) is subject to electronic disturbance of a repeating nature, such as be caused by electric motor. 1. Band reject filtering A filter consists of ones with a ring of zeros.

Homework 6 2. Read a gray scale image and add Gaussian noise with 0 mean then apply the Adaptive Mean Filter to reduction noise. 1.Produce a sub image of a colour image and add 5% salt & pepper noise and try to clean noise by following filters: 1.Arithmetic mean filter 2.Harmonic mean filter 3.Contrahormonic mean filter 4.Median filter 5.Max filter 6.Min filter 7.Mid point filter Which methods gives the best results ? 3. Load an image and make periodic noise and finally clear the Noise with Fast Foureir Transform. 4.Search which of the defined filters have best results on different noisy image