Removing Noise

Fourier Transforms

Fourier Transforms are useful in removing harmonic noise like:

Fourier Transforms are also useful in removing noise from video signals and CCDs.

Fourier transforms convert an image from one where intensity varies over space into one where the intensity varies with frequency. After an image has been described (transformed) as a series of frequencies and phase, that information can then be analyzed using a power spectrum. The power spectrum is a two-dimensional map that plots the frequency of pixel intensity values. Low frequencies lie close to the origin and high frequencies close to the edges. From the analysis suitable filters can be applied to remove those parts of the image that correspond to the noise in the image. The image can then be re-transformed back into the original image, only without the noise.

A Discrete Fourier Transform is a Fourier transform that uses a series which has values that have both a real and an imaginary component. Discrete Fourier transforms reveal periodicities in the data as well as the relative strengths of those periodicities.

Discrete Fourier Transforms can take a long time to compute. To reduce computing time, Fast Fourier Transforms can be used, which reduce the number of computations from 2N2 to 2N Lg N. However, using a Fast Fourier Transform requires that the number of points in the series be a power of 2.

The following functions provide Fourier transform capabilities:

Function Description
L_AllocFTArray Allocates a FTARRAY structure large enough to hold Fourier Transform coefficients
L_DFTBitmap Computes the Discrete Fourier Transform of an image or the Inverse Discrete Fourier Transform, whichever is specified.
L_FFTBitmap Computes the Fast Fourier Transform of an image or the Inverse Fast Fourier Transform, whichever is specified.
L_FreeFTArray Frees the 2D storage array that was allocated by L_AllocFTArray.
L_FTDisplayBitmap Converts the frequency harmonics amplitude or phase to a bitmap. It allows displaying the results of FFT and DFT as a bitmap.
L_FrqFilterBitmap Filters the frequency harmonics according to the range rectangle.
L_FrqFilterMaskBitmap Creates a mask filter for use in removing specific frequency components from a bitmap.
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