Digital restoration of images degraded by general motion blurs

Abstract

A state space model for two-dimensional motion blurs is descdbed and is employed in developing recursive restoration procedures for images degraded by motion blurs. Inverse system methods and Kalman/Bncy estimation techniques are invoked in deriving the restoration algorithms for the noise-free and noisy cases, respeCtmely. Computer implementations demonstrate the effectiveness of the new restoration schemes.

Two-dimensional block Kalman filtering for image restoration

“…The strip filtering scheme in [SI requires an order of computations of 0 ( M 2 L 3 ) per each output pixel, where M in this reference is the strip width and L is the order of the AR process. If L is chosen to be equal to M (as in our block state-space model), the order of computations becomes (3 ( M 5 ) per each output pixel which is larger than that of the block Kalman filter.…”

“…However, the periodic nature of the scanning procedure gives rise to nonstationarity of the output image. Later, this approach was extended to the general motion blur [3]. The main problems in extending the standard 1-D recursive filtering techniques to the 2-D case are not only due to the difficulty in establishing a suitable 2-D recursive model, but also the high dimensionality of the resulting state vectors.…”

A Minimum-Error, Minimum-Correlation Filter For Images

“…The estimator k =ay is co-linear with y and the constant a is varied to minimize the 2 length of the error vector e =x -R. The minimum occurs for a =ao =e (a 2 2 ) +a when the error e is orthogonal to the observation vector y. Note, however, in this solution that the error vector e has a non -zero component ex along x, which means that the error is correlated with x.…”

“…This estimator produces fuzzy image reconstructions, because, in attempting to smooth the noise, there is too much smoothing of the features and detail of the object. There have been notable attempts to improve on the Wiener estimator through non-linear estimators, such as maximum likelihood (ML), maximum apriori probability (MAP), and maximum entropy (ME) estimators and through constrained linear estimators [1][2][3][4][5][6]. By and large, these attempts have yielded small improvements in the restorations at the expense of greater complexity.…”

Nonlinear image restoration using a segmentation-oriented expert system

“…The algebraic approach, such as the iterative [4l, 43] or recursive [42,44,48] method, has been successfully applied to the problem of spatially-varying image degradation. The locally adaptive method is another way of solving the space-variant problem [45].…”