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Radio interferometers are an array of antennas capable of sampling the sky collecting radio signals from specific sources. Each antenna's signal is correlated with every other signal to collect a large number of samples of the sky but on the uv-plane in order to cover the Fourier plane as much as possible. As it can be seen these noisy, irregular and sparse samples are a set of complex numbers in the uv plane called visibilities. Additionally, the process of solving the problem of reconstruct an image from these data is called Image Synthesis.
Supposing that the uv-plane is completely sampled a simple relationship between image and data (van Cittert-Zernike theorem) can be expressed mathematically:
is called primary beam and is the solid angle reception pattern of the individual antennas, 
are the visibilities in a certain 
position and I(x,y) is the image in the pixel 
. In this case, a Fourier inversion can be applied to to recover 
.
Since in a real scenario, radio-interferometers collect noisy and irregular samples of data, the problem is then not well defined. A naive approach to solve this problem would be to sample the Fourier domain at discrete points on a regular grid (see next image on the right) using the sampling function
and a convolution kernel 
.
If a an inverse Fourier transform of the gridded data is done then we would obtain a poor quality image due to the incomplete spatial sampling of the interferometric array. This image is called dirty image and an example of the protoplanetary disk HL-Tauri is shown below.
It is clear that this image is not useful to study the rings of the disk and to make conclusions about the planet formation in it.
Many algorithms have been proposed for solving the image synthesis problem. A colloquially known procedure in radio astronomy is the CLEAN heuristic. Image reconstruction in CLEAN is performed in image plane using a convolution relationship, and it is quite efficiently implemented using Fast Fourier Transforms. However, this traditional approach incorporates a number of approximations and compromises. For example, the algorithm is supervised. This means that the user most of the times indicates iteratively in which region of the image the algorithm should focus. Also, statistical interpretation of resulting images and remaining artifacts are far to be described by a well founded theory.
In this context, GPUVMEM is a framework that allows scientists and radio astronomers to do image synthesis using a Bayesian approach to solve the inverse problem. This process takes Fourier space data taken by a radio-interferometer like ALMA, ATCA, VLA, or a set of radio-interferometers as EHT, and returns an image from a certain a radio source.
