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Comments and concluding remarks
Published in Bertero Mario, Boccacci Patrizia, Introduction to Inverse Problems in Imaging, 2020
Bertero Mario, Boccacci Patrizia
We briefly discuss now the various steps mentioned above. Step 1 is obvious; it is the basic point for the formulation of the problem of image formation. In some cases, as in X-ray tomography, this step may be rather easy while it may be very difficult in others (for instance, in the case of emission tomography). In image deconvolution this step is equivalent to the identification of the PSF by means of measurements or of computations based on a sufficiently accurate model of the imaging system. If one has only a poor knowledge of the PSF one can attempt to improve it by means of methods of blind deconvolution, a term introduced by Stockham, Cannon and Ingebretsen [1] to denote problems where both the PSF and the object are unknown. One has now at one's disposal many methods of blind-deconvolution: spectral methods [1], iterative methods [2] or maximum likelihood methods [3].
Basic Signal Processing Operations
Published in Nassir H. Sabah, Electric Circuits and Signals, 2017
Deconvolution is important in many signal processing applications. A communication channel, such as a telephone line, can introduce frequency distortion, for example, because of its limited bandwidth. An equalizer circuit can be inserted in series with the telephone line to reverse the distortion in the line. If the channel introduces some time delay because of phase lag, as explained in Section 17.1, the inverse system will have to compensate this delay with an advance in time, which makes the inverse system noncausal. What is done is to make the channel and the equalizer distortionless, as discussed in Section 17.1. This gives: Hch(jω)Heq(jω)=e−jωτ(17.3.3)
Signal Processing
Published in Leslie Hogben, Richard Brualdi, Anne Greenbaum, Roy Mathias, Handbook of Linear Algebra, 2006
Depending on specific relations that may be imposed on y and x, the Wiener filtering problem specializes in several important ways: The Wiener prediction problem for which y(k) = x(k+l) where l ≥ 1 and w is assumed causal; the Wiener smoothing problem for which y is arbitrary and x is a noise corrupted version of y given by x = y + n where n is the noise; and the Wiener deconvolution problem for which we have arbitrary desired signals y and x obtained from y by convolution and the addition of noise, x = h * y + n. For the Wiener prediction problem, the goal is to predict future values of x from past values. For the Wiener smoothing problem, the goal is to recover an approximation to a signal y from a noise corrupted version of the signal x. For the Wiener deconvolution, the goal is to invert a filter in the presence of noise to obtain the signal y from the filtered and noise corrupted version x.
A knowledge augmented image deblurring method with deep learning for in-situ quality detection of yarn production
Published in International Journal of Production Research, 2023
Chuqiao Xu, Junliang Wang, Jing Tao, Jie Zhang, Ray Y. Zhong
Reconstruction module: the reconstruction module is composed of reconstruction channels. The th probabilistic feature map is fed into th reconstruction channels. Each reconstruction channel is composed of 3 deconvolutional layers to reconstruct the clear features by deconvolving the feature maps. Where denotes the reconstructed clear features at th channel. denotes the deconvolution operation, which is the reverse of convolution .
Degradation modeling based on the gamma process with random initial degradation level and random threshold
Published in Quality Technology & Quantitative Management, 2023
Luis Alberto Rodríguez-Picón, Luis Carlos Méndez-González, Víctor Hugo Flores-Ochoa, Iván JC Pérez Olguín, Vicente García
It can be noted that in the second term in the incomplete gamma function in (3) considers the subtraction . Since both terms are random quantities, a deconvolution approach is proposed in this paper to obtain the random variable . In general terms, the deconvolution consists of the inverse process of the convolution operation, which considers the distribution of sums of independent random variables. For example, consider the random independent variables and , which denote the operation . If the PDF of and are known to be and respectively. Then, the PDF of can be obtained by considering the characteristic functions (CF) of and , which in general terms, for any random variable with PDF are obtained as,
Performance Improvement of Bistatic Baseline Detection
Published in IETE Journal of Research, 2023
Xueli Sheng, Dian Lu, Yingsong Li, Mengfei Mu, Jinghan Sun
Let , the received signal is obtained by convolving the channel impulse response (CIR) with the source signal , s the noise component. Deconvolution is a method to estimate the source signal from the received data given that is known. For a specific case where both the received data and CIR are positive definite functions [28], we can estimate the source signal using the Richardson-Lucy (R-L) algorithm [27], which is given byWhere, , i denotes the iteration number. After a certain number of iterations, the iterative sequence converges into a unique solution [27] Where, , denotes Csiszar discrimination [28,29]. We usually apply the R-L algorithm in image processing, where the CIR is regarded as the point scattering function (PSF) and assumed to be position independent (shift invariant), namely, . Image processing aims to recover the original image smeared by the PSF. Hence, deconvolution is known as (image) deblurring.