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The conjugated null space method of blind deconvolution
Published in Waldemar Wójcik, Andrzej Smolarz, Information Technology in Medical Diagnostics, 2017
R.N. Kvyetnyy, O.Yu. Sofina, Y.A. Bunyak, W. Wόjcik, P. Komada, A. Kalizhanova, N.A. Orshubekov
When the PSF is known, the problem of deblurring can be considered as an inverse filtration of the observed image. Methods of inverse filter implementation are direct, mainly in spectral domain, and indirect, by using maximum likelihood, Bayesian and variational approaches. The Wiener spectral method (Biemond et al. 1990, Kundur & Hatzinakos 1996) lies at the base of most methods of inverse filtration (Carasso et al. 2006, Michailovich & Tannenbaum 2007, Ng et al. 2000). The designed methods are intended for regularisation of spectrum inversion and optimisation of the PSF spectrum shape with the aim of eliminating the noise influence.
The Devil’s in the Details
Published in S. Merrill Weiss, Issues in Advanced Television Technology, 1996
By finding the differences between the transmitted reference signal and the internal copy of the reference pattern, a description of the transmission channel in the form of a filter response can be calculated. The second part of the adaptive equalizer uses the channel model to construct a filter that is the inverse of the filter found to be in the channel. When the inverse filter is applied to the incoming signal, most or all of the effects of the channel can be removed, permitting the signal to be accurately recovered.
Image Restoration
Published in Jiří Jan, Medical Image Processing, Reconstruction and Analysis, 2019
so the blur is really convolutional. Knowing its frequency transfer function, we can, in principle, easily design the corresponding inverse filter. Note that when the motion is unidirectional with a constant speed V, the PSF is a short abscissa of length VT with the same direction, and the corresponding frequency response has the sinc(…) shape (Figure 12.4), which is rather unpleasant in inverse filtering because of the presence of zeros (see Section 12.3).
Inferring decelerated land subsidence and groundwater storage dynamics in Tianjin–Langfang using Sentinel-1 InSAR
Published in International Journal of Digital Earth, 2022
Xuguo Shi, Tongtong Zhu, Wei Tang, Mi Jiang, Houjun Jiang, Chen Yang, Wei Zhan, Zutao Ming, Shaocheng Zhang
To retrieve the aquifer parameters further, InSAR time series deformations and hydraulic head measurements can be decomposed into seasonal and long-term trend signals. Wavelet transform is a useful tool when dealing with natural nonstationary signals (Torrence and Compo 1998). CWT can separate frequency features at different times and frequencies from time series signals (Miller and Shirzaei 2015). In this study, we utilize CWT to separate the seasonal components from time series deformations and hydraulic heads. We first remove the linear trend by assuming a constant rate (Jiang et al. 2018). Then, time series residuals are decomposed into a series of signals with different time and frequency scales. The short-term signal is reconstructed using signals with time scales between 0.5 and 1 year through inverse filter. The amplitude is half of the difference between the maximum value and the minimum value within a year. The long-term trend is then retrieved by subtracting the short-term seasonal signal from the original time series signals.
Decoupled reference governors: a constraint management technique for MIMO systems
Published in International Journal of Control, 2022
Yudan Liu, Joycer Osorio, Hamid R. Ossareh
In this paper, we study two structures for , which lead to the following two decoupling methods: Diagonal Method: We find such that . The filter and the inverse filter are defined as: Identity Method: We find such that equals the identity matrix. The filter and the inverse filter are defined as:
Pre-study for facilitating the discovery of microfluidic properties in blood vessels using retinal fundus images
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2022
Adel Elamari, Amine Ben Slama, Hedi Trabelsi, Ezeddine Sediki
where T(u,v) presents the degradation function and is the complex conjugate of T(u,v). Note that the power spectrum of the noise and the power spectrum of the original image are respectively introduced as follows: and . The noise to signal power ratio is noted by . In fact, we sign that if the noise to signal power ratio is zero, then the Wiener filter is reduced to the inverse filter. The average noise power and the average image power are correspondingly defined as follows..