Abstract
Regularization methods play an important role in solving linear equations of the form
with prior knowledge about the solution. The corresponding regularization results in minimization of
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Notes
- 1.
In order to determine boundary samples of output signal, we assumed circularly symmetric or periodic input with period N.
- 2.
Most one-dimensional filters have a causal impulse response because the future input is not available for convolution with the filter. In this case, the filtered output comes with a certain amount of delay. On the other hand, in two-dimensional image processing, noncausal filters are used in order to avoid a shifted output image, caused by the two-dimensional delay.
- 3.
The impulse response of a two-dimensional filter is called the point spread function if each coefficient has a nonnegative value.
- 4.
A sample procedure to make the periodically extended PSF is illustrated in Fig. 6.2.
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Additional References and Further Readings
A.D. Hillery, R.T. Chin, Iterative Wiener filters for image restoration. IEEE Trans. Signal Process. 39(8), 1892–1899 (1991)
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Abidi, M.A., Gribok, A.V., Paik, J. (2016). Frequency-Domain Implementation of Regularization. In: Optimization Techniques in Computer Vision. Advances in Computer Vision and Pattern Recognition. Springer, Cham. https://doi.org/10.1007/978-3-319-46364-3_6
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