Degradation Estimation :Some more examples

Since image restoration algorithms are designed to exploit characteristic of a signal and its degradation, accurate knowledge of the degradation is essential to developing a successful image restoration algorithm. There are two approaches to obtaining information about degradation. One approach is to gather information from the degraded image itself. If we can identify regions in the image where the image intensity is approximately uniform, for instance the sky, it may be possible to estimate the power spectrum or the probability density function of the random background noise from the intensity fluctuations in the uniform background regions. An another example, if an image is blurred and we can identify a region in the degraded image where the original undergraded signal is known, we may be able to estimate the blurring functions . Let us denote the known original undergraded signal in a particular region of the images as and the degraded image in the same region as . Then is approximately related to by

	(6.2.1)

Since and are assumed known , can be estimated from (6.2.1). If is the impulse , is given by . This may be the case for a star in the night sky.

Another approach to obtaining knowledge about degradation is by studying the mechanism that caused the degradation. For example, consider an analog* image blurred by a planar motion of the imaging system during exposure. Assuming that there is no degradation in the imaging system except the motion blur, we can express the degraded image as

	(6.2.2)

where and represent the horizontal and vertical translations of at time t relative to the imaging system, and T is the duration of exposure. In the Fourier transform domain, (6.2.2) can be expressed as

	(6.2.3)

where is the Fourier transform of .Simplify (6.2.3), we obtain

	(6.2.4a)

where		(6.2.4b)

From (6.2.4), it is clear that the planar motion blur can be viewed as convolution of with whose Fourier transform is given by (6.2.4b). The function is sometimes referred to as the blurring function, since typically is of lowpass character and blurs the image. It is also referred to as the point spread function, since it spreads an impulse. When there is no motion and thus and is 1 and is . If there is linear motion along the x direction so that and then in (6.2.4) reduces to

	(6.2.5)

A discrete image may be approximately modeled by

	(6.2.6)

where the discrete-space Fourier transform of , is the aliased version of in (6.2.4b). Other instances in which the degradation may be estimated from its mechanism include film grain noise, blurring due to diffraction-limited optics, and speckle noise.