Method for estimating a convolution product

A Method for generating an image by processing a measurement function (ƒ), the measurement function being representative of measurements acquired by a detector, the measurement function being defined in a starting space, according to first coordinates (ri), the method including the estimation, at second coordinates (uj) of said starting space, of a value of a product of convolution (f*g) of the measurement function (ƒ) with a convolution kernel (g), defined on a support, called the convolution support (Ω), the method comprising:

• acquiring measurements by a detector;
• establishing the measurement function (ƒ), according to first coordinates (ri) of the starting space on the basis of the measurements (15) arising from the detector;
• and
• defining second coordinates in the starting space (uj),
• wherein the method further comprises, for each second coordinate (uj):
• a) on the basis of the convolution support (Ω), defining a centered convolution support (Ωj), associated with said second coordinate (uj), in such a way that said second coordinate (uj) constitutes the center of said centered convolution support (Ωj);
• b) defining a mesh of said centered convolution support (Ωj), to associate a surface element (Si,j) with each first coordinate (ri) included in said centered convolution support (Ωj);
• c) determining a weighting factor (∂i,j) associated with each first coordinate (ri) included in said centered convolution support (Ωj);
• d) computing a product of convolution of said measurement function (ƒ) with said kernel (g) according to said centered convolution support (Ωj), by weighting a value ƒ(ri) of the measurement function, at each first coordinate (ri) included in said centered convolution support (Ωj), with the weighting factor (∂i,j) associated with said first coordinate (ri), determined during step c);
• e) estimating a value of said convolution product (f*g(uj)) at said second coordinate (uj) as a function of the computation carried out during step d);
• wherein steps a) to e) are implemented, for each second coordinate (uj), by at least one microprocessor,
• wherein during step b), the mesh is defined in such a way that each surface element (Si,j) is contained in said centered convolution support (Ωj) and in such a way that the weighting factor (∂i,j) associated with one and the same first coordinate (ri) varies as a function of the second coordinate (uj), and
• wherein the method further comprises performing an inverse Fourier Transform or a Fourier Transform on the estimated values of said convolution product at the second coordinates and generating an image representing measurements based on an output of the inverse Fourier Transform or based on an output of the Fourier Transform.