In an electronic imaging system, samples are taken on a square lattice of the Fo
ID: 2081218 • Letter: I
Question
In an electronic imaging system, samples are taken on a square lattice of the Fourier transform of an object function. Explain how a distortion free reconstruction of the object can be obtained from the samples provided the object function is of finite extent and an infinite number of sufficiently closely spaced samples are available. In practice, samples can only be taken over a square region centered at the origin of the Fourier transform plane. If all unavailable samples are assumed to be zero, how is the reconstruction related to the original object?Explanation / Answer
An absolutely distortion free image is impossible to get in any electronics imaging system. Methods are employed to reduce the distortion in the reconstructed image or correct the distortion in the reconstructed image. The various ways for this to be done are stillbeing researched and there is no final answer as to which one is best for all applications.
One patented method for reducing the sitortions formed in fourier transform reconstructed images is to manipulate the values by a pre-determined procedure that subjects the image values to unwanted distortion, and then applying to the projection samples or image values a correction function that corresponds to the predefined procedure.
Some of the methods aim to correct distortion directly in the image space by a magnetic field mapping of the image. For eg: Susceptibility-induced magnetic field gradients (SFGs) in regions with large static field inhomogeneities in echo-planar imaging (EPI).
Other methods work in the k-space data and apply a phase correction before doing the fourier transform re-construction.
Other popular methods include Grey value substitution where the method firstly detects the noise value, then a value nearby is used to replace the noise value. After that, a median filter is used to do noise reduction further more. And wavelet transformation etc.
Information relaterd to the methods and ddetailed explanations are found online as all methods cannot be explained in detail here
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