A Kalman-filtering approach for non-uniformity correction in infrared focal-plane array sensors

In this thesis, a Kalman filter is developed to estimate the temporal drift in the gain and the offset of each detector in focal-plane array sensors from scene data. The basic rationale of this technique is that the gain and the offset are thought of as unknown time-varying state variables to be optimally and recursively estimated from current and past scene observations. The gain and offset are assumed constant over fixed-length observation vectors; however, these parameters may slowly drift from vector to vector according to a temporal discrete-time Gauss-Markov process. The Kalman filter input is a sequence of observation vectors, corresponding to blocks of observed frames, and the output at any time is the state vector containing current estimates of the gain and offset for each detector in each block of frames. The observation model assumes that the input irradiance at each detector is a uniformly-distributed random variable in a range that is common to all detectors in the focal-plane array. This assumption, which is termed the constant-range assumption, has also been proven useful and effective in prior non-uniformity correction techniques. In addition, the constant-range assumption gives rise to an observation model that involves a random observation matrix leading to a non-traditional Kalman filter. The strength of the proposed technique is in its recursive nature and computational efficiency. The Kalman filter is able to employ the information contained in past blocks of frames (i.e., old estimates of the detector gain and bias) and to optimally update it using the current block of frames. The efficacy of the reported technique is demonstrated by applying it to sequences of simulated data as well as to sequences of real infrared data. The performance of the Kalman filter is evaluated by means of four performance parameters. The correctability parameter evidences that the Kalman filter is able to reduce the fixed-pattern noise to a level below the temporal noise. It is also shown using the roughness, the root mean square error, and the mean square error parameters that the Kalman filter is able to compensate for the fixed-pattern-noise.