Image reconstruction

Image reconstruction is the computational recovery of an image from measurements made by a sensing system. It estimates a spatial representation from data that may be incomplete, noisy, or indirect.

Inverse problem: An inverse problem infers hidden causes or properties from their observable effects. Image reconstruction is an inverse problem: it infers an image from measurements generated by that image.
Sampling theorem: A result specifying conditions under which a continuous signal can be recovered from discrete samples. Sampling density determines whether spatial detail can be recovered without aliasing.
Computed tomography: An imaging method that reconstructs cross-sectional images from X-ray measurements taken at multiple angles. It is a canonical case of recovering an image from indirect projections.
Image formation: The physical and computational processes by which a scene produces an image in a sensing system. Image formation maps scenes to sensor data; reconstruction runs an estimate in the opposite direction.
Forward model: A mathematical description of how a system maps an underlying object to observable measurements. It predicts the sensor data that each candidate image would produce.
Point spread function: A system's response to a point source, describing how it blurs spatial information. It characterizes blur that reconstruction may need to reverse.
Magnetic resonance imaging: A medical imaging technique that uses magnetic fields and radio waves to measure signals from atomic nuclei. Its measurements are often reconstructed from incomplete samples in spatial-frequency space.
Image deconvolution: The recovery of a sharper image by compensating for blur modeled as convolution. Deconvolution is a specific reconstruction problem with a blur-based measurement model.
Regularization: A method for stabilizing an ill-posed problem by favoring solutions with specified properties. It limits implausible image estimates when measurements alone do not determine a unique solution.
Measurement noise: Random or systematic variation in observed data that is not part of the underlying signal. Noise can make direct inversion unstable and shapes the reconstruction's uncertainty.

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