Spatial Frequency

Spatial domain also called as image domain where each pixel or data point has a position and intensity value. This is the domain where we usually see the images and can understand the meaning of various parts of it.

Spatial frequency domain where image is represented in terms of frequency components. In this domain, each point represent a frequency with its amplitude and phase.

Amplitude of the frequency tells the intensity level and phase tells about the structure of the image where intensity should be placed.

Fourier Transformation

Fourier transformation is the part which actually coverts spatial domain to spatial frequency domain.

spatial domain ----- fft -----> spatial frequency domain
spatial frequency domain <----- ifft ---- spatial domain

Frequency region in image

In spatial frequency domain, signals are composed of complex sinusoidal waves. Low-frequency are usually located at the center of the image where the intensity changes slowly. This is where the large structures are present. And we move farther, the intensity level goes down and intensity changes rapidly which results high-frequency regions.

Sampling

We can create the original image by selecting bunch of visibilities samples in spatial frequency domain.

Refer notebook.