3.2. NOISE SMOOTHING
In addition to enhancement of images 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.
3.2.1.Lowpass 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 highfrequency 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.
Lowpass filtering can also be used together with highpass filtering in processing an image prior to its degradation by noise. In applications such as image coding, an original undegraded image is available for processing prior to its degradation by noise, for instance, quantization noise. In such applications, the undegraded 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.
Examples of impulse responses of lowpass filters tvpically used for image enhancement are shown in Figure 3.14. To illustrate the performance of lowpass filtering for image enhancement, two examples are considered. Figure 3.15(a) shows an original noise-free image of 256 x 168 pixels, and Figure 3.15(b) shows an image degraded by wideband Gaussian random noise at an SNR of 15 dB. The SNR is defined as 10 log10 (image variance/noise variance). Figure 3.15(c) shows the result of lowpass filtering the degraded image. The lowpass filter used is shown in Figure 3.14(c). In Figure 3.15, lowpass filtering clearly reduces the additive noise, but at the same time it blurs the image. Blurring is a primary limitation of lowpass filtering. Figure 3.16(a) shows an original image of 512 x 512 pixels with 8 bits/pixel. Figure 3.16(b) shows the image coded by a PCM system with Roberts’s pseudonoise technique at 2 bits/pixel. Figure 3.16(c) shows the result of highpass filtering before coding and lowpass filtering after coding. The highpass and lowpass filters used in this example are those in Figure 3.8(c) and Figure 3.34(c). respectively.
