A full-plane block Kalman filter for image restoration

Abstract

Abstract-A new two-dimensional (2-D) block Kalman filtering method is presented which uses a full-plane image model to generate a more accurate filtered estimate of an image that has been corrupted by additive noise and full-plane blur. Causality is maintained within the filtering process by employing multiple concurrent block estimators. In addition, true state dynamics are preserved, resulting in an accurate Kalman gain matrix. Simulation results on a test image corupted by additive white Gaussian noise are presented for various image models and compared to those of the previous block Kalman filtering methods.

Fast and Stable Bayesian Image Expansion Using Sparse Edge Priors

“…Using the SVD of , we have , and . Thus (12) In absence of variable weights, is diagonalized by the DFT because is Toeplitz:…”

“…Since and both contain aliased DFT vectors, it is the case (see Appendix B) that all matrices in (12) are, in fact, diagonal in the absence of . Thus, (12) becomes a bidiagonal system and is speedily solved in linear time.…”

“…Some principled model-based approaches have also been reported. Wiener [11], Kalman [12], and adaptive-filter-based [13] methods achieve spatial adaptation, but at the cost of processing time. However, the value of these essentially causal/temporal techniques is unproven on images, whose statistics are liable to change abruptly and noncausally.…”

Regularization Parameter Selection for Total Variation Model Based on Local Spectral Response

“…To date a variety of image denoising methods using smoothing constraint have been introduced, such as the Gaussian smoothing model [2,3], the anisotropic filtering model [4][5][6][7], the total variation (TV) model [8], the Yaroslavsky [12] neighbourhood filter, the Winner filter [13,14], the Kalman filter [15,16], and so on. Among these methods, the TV method has drawn much attention, which is widely used over the past decades, probably because of its low time consumption and well-understood behaviour.…”

“…Numerous image denoising approaches have been presented, such as smoothness constraint based method [10][11][12][13][14][15][16], the self-similarity based non-local method [17][18][19][20][21][22], the sparse representation based method [23][24][25][26][27][28], and so on. With the observation that similar structures are frequently distributed over the whole image, the self-similarity based non-local method has been widely studied for image regularization.…”