運動劣化画像のパラメータ推定

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A modified method for the parameter estimation in the case of motion blur is presented here. It is based on the principle that the power spectrum of the motion point spread function contains zero crossings. The obseverd noisy image g is modeled by, g= h⨂f+w (1) where ⨂ stands for convolution computation, f the ideal image, h point spread function(PSF), w observation noise, and the size of g, h, f, w is N^2. Neglecting the effect of noise and taking Fourier transform on both sides of Eq. (1) yields, G(u,v)=H(u,v)F(u,v)(2) By simple calculation, the Fourier transform of motion blur PSF can be easily given by, [numerical formula] (3) where L is the length of motion. Obviously, zeros will appear in H periodically. In other words, peaks and valleys will appear in |G|^2. Fig.1 is an example showing these peaks and valleys without additional noise. Note we have taken log magnitude of the power spectrum, or these peaks and valleys can not be seen because the range between them is very narrow. Typically valley values are above 0.1 and peak values below 1. Their range is less than 0.9, completely negligible comparing with the whole range of power spectrum that is usually around a million. But when logarithm is taken, the range between a peak and a valley is about 1 which is comparable with the whole range of power spectrum, 6〜8 Now what if white noise is added to the blurred image? The power spectrum of white noise is a constant, namely its variance. It contributes to power spectrum as a DC term, and tends to flatten the power spectrum as the SNR decreases. As an example, for an image in our study, its variance is about 2000, if we let SNR be 30dB, then the variance of noise should be 2. This DC term in power spectrum makes the typical peak and valley values be about log(3) and log(2.1), their difference is 0.15. Clearly the range between the peak and valley is much reduced, so it becomes far more difficult to detect peak and valley in power spectrum. When SNR decreases further, it would become worse. Our method is simple, namely subtracting from power spectrum the DC term which is an estimate of noise power spectrum. By doing so, we can significantly extend the range between the peak and valley, especially when SNR is very low. Fig.2 demonstrates the effectiveness of our method. The solid and dot lines represent respectively the modified and the classical power spectrum.
社団法人電子情報通信学会の論文
1996-09-18

運動劣化画像のパラメータ推定

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