A novel statistical approach is undertaken for the adaptive estimation of the gain and bias nonuniformity in infrared focal-plane array sensors from scene data. The gain and the bias of each detector are regarded as random state variables modeled by a discrete-time Gauss–Markov process. The proposed Gauss–Markov framework provides a mechanism for capturing the slow and random drift in the fixed-pattern noise as the operational conditions of the sensor vary in time. With a temporal stochastic model for each detector’s gain and bias at hand, a Kalman filter is derived that uses scene data, comprising the detector’s readout values sampled over a short period of time, to optimally update the detector’s gain and bias estimates as these parameters drift. The proposed technique relies on a certain spatiotemporal diversity condition in the data, which is satisfied when all detectors see approximately the same range of temperatures within the periods between successive estimation epochs. The performance of the proposed technique is thoroughly studied, and its utility in mitigating fixed-pattern noise is demonstrated with both real infrared and simulated imagery.

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Kalman filtering for adaptive nonuniformity correction in infrared focal-plane arrays.

We describe a new, to our knowledge, scene-based nonuniformity correction algorithm for array detectors. The algorithm relies on the ability to register a sequence of observed frames in the presence of the fixed-pattern noise caused by pixel-to-pixel nonuniformity. In low-to-moderate levels of nonuniformity, sufficiently accurate registration may be possible with standard scene-based registration techniques. If the registration is accurate, and motion exists between the frames, then groups of independent detectors can be identified that observe the same irradiance (or true scene value). These detector outputs are averaged to generate estimates of the true scene values. With these scene estimates, and the corresponding observed values through a given detector, a curve-fitting procedure is used to estimate the individual detector response parameters. These can then be used to correct for detector nonuniformity. The strength of the algorithm lies in its simplicity and low computational complexity. Experimental results, to illustrate the performance of the algorithm, include the use of visible-range imagery with simulated nonuniformity and infrared imagery with real nonuniformity.

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Scene-based Nonuniformity Correction with Video Sequences and Registration

A scene-based algorithm is developed to compensate for bias nonuniformity in focal-plane arrays. Nonuniformity can be extremely problematic, especially for mid- to far-infrared imaging systems. The technique is based on use of estimates of interframe subpixel shifts in an image sequence, in conjunction with a linear-interpolation model for the motion, to extract information on the bias nonuniformity algebraically. The performance of the proposed algorithm is analyzed by using real infrared and simulated data. One advantage of this technique is its simplicity; it requires relatively few frames to generate an effective correction matrix, thereby permitting the execution of frequent on-the-fly nonuniformity correction as drift occurs. Additionally, the performance is shown to exhibit considerable robustness with respect to lack of the common types of temporal and spatial irradiance diversity that are typically required by statistical scene-based nonuniformity correction techniques.

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An Algebraic Algorithm for Nonuniformity Correction in Focal-Plane Arrays

A computationally efficient method for image registration is investigated that can achieve an improved performance over the traditional two-dimensional (2-D) cross-correlation-based techniques in the presence of both fixed-pattern and temporal noise. The method relies on transforming each image in the sequence of frames into two vector projections formed by accumulating pixel values along the rows and columns of the image. The vector projections corresponding to successive frames are in turn used to estimate the individual horizontal and vertical components of the shift by means of a one-dimensional (1-D) cross-correlation-based estimator. While gradient-based shift estimation techniques are computationally efficient, they often exhibit degraded performance under noisy conditions in comparison to cross-correlators due to the fact that the gradient operation amplifies noise. The projection-based estimator, on the other hand, significantly reduces the computational complexity associated with the 2-D operations involved in traditional correlation-based shift estimators while improving the performance in the presence of temporal and spatial noise. To show the noise rejection capability of the projection-based shift estimator relative to the 2-D cross correlator, a figure-of-merit is developed and computed reflecting the signal-to-noise ratio (SNR) associated with each estimator. The two methods are also compared by means of computer simulation and tests using real image sequences.

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Projection-based image registration in the presence of fixed-pattern noise

In this paper, we present a simple and effective scene-based nonuniformity correction (NUC) method for infrared focal plane arrays based on interframe registration. This method estimates the global translation between two adjacent frames and minimizes the mean square error between the two properly registered images to make any two detectors with the same scene produce the same output value. In this way, the accumulation of the registration error can be avoided and the NUC can be achieved. The advantages of the proposed algorithm lie in its low computational complexity and storage requirements and ability to capture temporal drifts in the nonuniformity parameters. The performance of the proposed technique is thoroughly studied with infrared image sequences with simulated nonuniformity and infrared imagery with real nonuniformity. It shows a significantly fast and reliable fixed-pattern noise reduction and obtains an effective frame-by-frame adaptive estimation of each detector's gain and offset.

/pdf/scene-based-nonuniformity-correction-algorithm-based-on-1jlgpyb6h4.pdf

Scene-based nonuniformity correction algorithm based on interframe registration.

A statistical algorithm has been developed to compensate for the fixed-pattern noise associated with spatial nonuniformity and temporal drift in the response of focal-plane array infrared imaging systems. The algorithm uses initial scene data to generate initial estimates of the gain, the offset, and the variance of the additive electronic noise of each detector element. The algorithm then updates these parameters by use of subsequent frames and uses the updated parameters to restore the true image by use of a least-mean-square error finite-impulse-response filter. The algorithm is applied to infrared data, and the restored images compare favorably with those restored by use of a multiple-point calibration technique.

/pdf/statistical-algorithm-for-nonuniformity-correction-in-focal-58zjhk06sy.pdf

Statistical algorithm for nonuniformity correction in focal-plane arrays.

Recent developments in staring focal plane technology have spawned significant interest in the application of gated laser radar systems to battlefield remote sensing. Such environments are characterized by rapidly changing atmospheric seeing conditions and significant image distortion caused by long slant-range paths through the most dense regions of the atmosphere. Limited weight, space, and computational resources tend to prohibit the application of adaptive optic systems to mitigate atmospheric image distortion. We demonstrate and validate the use of a fast, iterative, maximum a posteriori (MAP) estimator to estimate both the original target scene and the ensemble-averaged atmospheric optical transfer function parameterized by Fried's seeing parameter. Wide-field-of-view sensor data is simulated to emulate images collected on an experimental test range. Simulated and experimental multiframe motion-compensated average images are deconvolved by the MAP estimator to produce most likely estimates of the truth image as well as the atmospheric seeing condition. For comparison, Fried's seeing parameter is estimated from experimentally collected images using a knife-edge response technique. The MAP estimator is found to yield seeing condition estimates within approximately 6% using simulated speckle images, and within approximately 8% of knife-edge derived truth for a limited set of experimentally collected image data.

Ernest E. Armstrong

Papers

Scene-based Nonuniformity Correction with Video Sequences and Registration

Statistical algorithm for nonuniformity correction in focal-plane arrays.

Maximum a posteriori image and seeing condition estimation from partially coherent two-dimensional light detection and ranging images