Reduction of Image Blurring

An image degraded by blurring can be modeled as

	(6.4.1)

In (6.4.1), the degraded image is the result of convolving the original image with an impulse response . The sequence is called the point spared function or the blurring function. The degradation that may be modeled by convolution noise includes blurring due to lens misfocus, motion, and atmospheric turbulence.

The problem of reducing image blur can be classified into two categories. One is the deconvolution problem, in which is assumed to be known. The second is the blind deconvolution problem, where is not known and must be estimated from the available information. In Section 6.4.1, we discuss inverse filtering, a standard approach to solving the deconvolution problem. In section 6.4.2, we discuss algoratirhms developed to solve the blind deconvolution problem.

6.4.1 Inverse Filtering

When the blurring function is assumed known, one approach to deblurring is inverse filtering. From (6.4.1)

	(6.4.2)

From (6.4.2)

	(6.4.3)

From (6.4.3), a system that recovers from is an inverse filter, shown in Figure 6.11.

The inverse filter in Figure 6.11 tends to be very sensitive to noise. When is very small, is very large, and small noise in the frequency regions where is very large may be greatly emphasized. One method of lessening the noise sensitivity problem is to limit frequency response

	(6.4.4)

The inverse filter and its variation in (6.3.4) can be implemented in a variety of ways. We may design a filter whose frequency response approximates the desired one, using the standard 2D filter design techniques, and then convolve the blurred image with the designed filter. Alternatively, we can implement the system, using DFTs and inverse DFTs in a manner analogous to the Wiener filter implementation discussed in Section 6.2.1.