NOISE SMOOTHING

In addition to enhancement of image by contrast and dynamic range modification, images can also be enhanced by reducing degradations that may be present. This area of image enhancement overlaps with image restoration. In this section, we discuss very simple algorithms that attempt to reduce random noise and salt-and-pepper type of noise.

5.6.1 Low pass Filtering

The energy of a typical image is primarily concentrated in its low-frequency components. This is due to the high spatial correlation among neighboring pixels. The energy of such forms of image degradation as wideband random noise is typically more spread out over the frequency domain. By reducing the high-frequency components while preserving the low-frequency components, lowpass filtering reduces a large amount of noise at the expense of reducing a small amount of signal.

Examples of impulse responses of lowpass filters typically used for image enhancement are shown in Figure (5.18 ). To illustrate the performance of lowpass filtering for image enhancement, two examples are considered. Figure (5.19) shows an original noise-free image of 256x256 pixels, and an image degraded by wideband Gaussian random noise at an SNR of 15dB. The SNR is defined as 10 log 10 (image variance/noise variance). Figure (5.19) shows the result of lowpass filtering the degraded image. The lowpass filter used is shown in Figure (5.18). In Figure, lowpass filtering clearly reduces additive noise, but at the same time it blurs the image. Blurring is a primary limitation of lowpass filtering. Figure (5.20) shows an original image of 512 x 512 pixels with 8 bits/pixel. Figure shows the image coded by a PCM system with Roberts's pseudonoise technique at 2 bits/pixel and the results of highpass filtering before coding and lowpass filtering after coding.

Low pass filtering can also be used together with high pass filtering in processing an image prior to its degradation by noise. In applications such as image coding, an original undergraded image is available for processing prior to its degraded image can be highpass filtered prior to its degradation and then lowpass filtered after degradation. This may result in some improvement in the quality or intelligibility of the resulting image. For example, when the degradation is due to wideband random noise, the effective SNR (signal-to-noise ratio) of the degraded image is much lower in the high-frequency components than in the low-frequency components, due to the lowpass character of a typical image. Highpass filtering prior to the degradation significantly improves the SNR in the high-frequency components at the expense of small SNR decrease in the low-frequency components.