Signal restoration

Lanteri, H., Roche, M., Cuevas, O., Aime, C., 2001, A general method to devise maximum-likelihood signal restoration multiplicative algorithms with nonnegativity constraints. Signal Processing 81, 945 Lucy, L.B., 1974, An iterative technique for the rectification of observed distributions, ApJ 79, 745... 

In this chapter we discuss techniques both for signal enhancement and signal restoration. Techniques to model or to reconstruct the deterministic part of a digital signal in the presence of noise are discussed in Chapter 41. 

As said before, there are two main applications of Fourier transforms the enhancement of signals and the restoration of the deterministic part of a signal. Signal enhancement is an operation for the reduction of the noise leading to an improved signal-to-noise ratio. By signal restoration deformations of the signal introduced by imperfections in the measurement device are corrected. These two operations can be executed in both domains, the time and frequency domain. 

When the maximum entropy approach is used for signal restoration a step has to be included between steps (1) and (2) in which the trial spectrum is first convoluted (see Section 40.4) with the point-spread function before calculating and testing the differences with the measured spectrum. The entropy of the trial spectrum before convolution is evaluated as usual. 

The chapter is organized as follows. We firstly describe models which are suitable for audio signal restoration, in particular those which are used in later work. Subsequent sections describe individual restoration problems separately, considering the alternative methods available to the restorer. A concluding section summarizes the work and discusses future trends. 

J. Lundstedt, S. Strom, and S. He, Time-domain signal restoration and parameter reconstruction on an LCRG transmission hne, in URSI International Symposium on Signals, Systems, and Electronics, ISSSE 95, Proceedings, IEEE, 1995, pp. 323-326. 

Discrete stat and steady-state methods, whether automatic or semiautomatic, are frequently used for monitoring catalyzed reactions. Stat methods involve addition of a small amount of one of the reaction ingredients until a given value of the monitored parameter (pH, absorbance, luminescence, etc.) is reached. Any deviation from this state as a result of reaction development is immediately compensated for by the automatic addition of such an ingredient, the speed of signal restoration being proportional to the catalyst concentration. The procedure is referred to as pH-stat or absorptiostat method, according to whether the pH or absorbance is the continuously monitored parameter. Alternative techniques used to monitor the catalyzed reaction include biamperometry. 

Lifetimes between a few nanoseconds and some microseconds can readily be deconvoluted. By applying simulations based on a theoretical treatment of the signal, restoration limits have been derived for amplitudes and lifetimes in the case of a sum of two single-exponential decays. The influences of variable geometry, energy distribution and different deconvolution methods, as well as that of the signal-to-noise... 

Tasks of the USCT IT are restoring of SD of the certain acoustic parameter of material in product volume on the base of measured parameters of US signals, but afterwards determination of necessary PMF. It is defined strong factors basically on the grounds of their correlation with acoustic features. 

The function h(t) to be restored is the impulse response of the medium x(t) is the transmitted pulse measured by reflection on a perfect plane reflector, for example the interface between air and water and y(t) is the observed signal. 

The image without treatment (Fig lb) should be compared with the deconvolved image of the rod (Fig. 2b). The dimension of the rod is well restored and the contour is reinforced by the signal processing. 

To restore resolution, we proposed a signal processing method based on Papoulis deconvolution. We implemented this algorithm and tried to operate an improvement from an aluminum rod smaller than the wavelength. 

When the energy flows in and out of a compartment do not balance, the energy difference accumulates and the temperature increases or decreases. The changes in core and skin temperature then in turn alter the physiological control signals to restore balance and thermal stability. 

It is important to avoid saturation of the signal during pulse width calibration. The Bloch equations predict that a delay of 5 1] will be required for complete restoration to the equilibrium state. It is therefore advisable to determine the 1] values an approximate determination may be made quickly by using the inversion-recovery sequence (see next paragraph). The protons of the sample on which the pulse widths are being determined should have relaxation times of less than a second, to avoid unnecessary delays in pulse width calibration. If the sample has protons with longer relaxation times, then it may be advisable to add a small quantity of a relaxation reagent, such as Cr(acac) or Gkl(FOD)3, to induce the nuclei to relax more quickly. 

It is still possible to enhance the resolution also when the point-spread function is unknown. For instance, the resolution is improved by subtracting the second-derivative g x) from the measured signal g x). Thus the signal is restored by ag x) - (7 - a)g Xx) with 0 < a < 1. This llgorithm is called pseudo-deconvolution. Because the second-derivative of any bell-shaped peak is negative between the two inflection points (second-derivative is zero) and positive elsewhere, the subtraction makes the top higher and narrows the wings, which results in a better resolution (see Fig. 40.30). Pseudo-deconvolution methods can correct for sym-... 

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