Density compensation function in filtered backprojection

An imaging system comprising:

• a sensor configured to receive imaging data, wherein the imaging data comprises projection data for a computed tomography (CT) scan, a single-photon emission computerized tomography (SPECT) scan, or a positron emission tomography (PET) scan of a patient;
• a processor operatively coupled to the sensor and configured to:
• identify a degree of interaction between measured points of the projection data located at a radius from a center of a projection space;
• determine, based at least in part on the degree of interaction between the measured points, density weights for a density compensation filter;
• apply the density compensation filter to the projection data to generate filtered projection data;
• and
• convert the filtered projection data from a polar coordinate system to a Cartesian coordinate system by way of gridding, wherein the conversion results in filtered and gridded projection data;
• and
• perform a transform to generate a CT image, a SPECT image, or a PET of the patient based at least in part on the filtered and gridded projection data.

A method for reconstructing an image, the method comprising:

• receiving, by a transceiver of a computing system, imaging data, wherein the imaging data comprises k-space data or projection data resulting from a scan of a patient;
• identifying, by a processor of the computing system, a degree of interaction between measured points of the k-space data or measured points of the projection data;
• determining, by the processor and based at least in part on the degree of interaction between the measured points, density weights for a density compensation filter;
• applying, by the processor, the density compensation filter to the projection data to generate filtered projection data or to the k-space data to generate filtered k-space data;
• and
• converting, by the processor, the filtered projection data or the filtered k-space data from a polar coordinate system to a Cartesian coordinate system by way of gridding, wherein the conversion results in filtered and gridded projection data or filtered and gridded k-space data with uniform density weights across k-space;
• and
• performing, by the processor, a Fourier transform based at least in part on the filtered and gridded k-space data or a Radon transform based at least in part on the filtered and gridded projection data to generate an image of the patient.