ABSTRACT
In the spatial domain, we might have an image f(x, y), and a spatial filter h(x, y) for which convolution with the image results in some form of degradation. For example, if h(x, y) consists of a single line of ones, the result of the convolution will be a motion blur in the direction of the line. Thus, we may write
g(x, y) = f(x, y) ∗ h(x, y) for the degraded image, where the symbol ∗ represents spatial filtering. However, this is not all. We must consider noise, which can be modeled as an additive function to the convolution. Thus, if n(x, y) represents random errors which may occur, we have as our degraded image:
g(x, y) = f(x, y) ∗ h(x, y) + n(x, y). We can perform the same operations in the frequency domain, where convolution is replaced by multiplication, and addition remains as addition because of the linearity of the Fourier transform. Thus,
G(i, j) = F (i, j)H(i, j) +N(i, j)
represents a general image degradation, where of course F , H, and N are the Fourier transforms of f , h, and n, respectively.
