Truncation artifact

For large systems comprising 36,000 atoms FAMUSAMM performs four times faster than SAMM and as fast as a cut-off scheme with a 10 A cut-off distance while completely avoiding truncation artifacts. Here, the speed-up with respect to SAMM is essentially achieved by the multiple-time-step extrapolation of local Taylor expansions in the outer distance classes. For this system FAMUSAMM executes by a factor of 60 faster than explicit evaluation of the Coulomb sum. The subsequent Section describes, as a sample application of FAMUSAMM, the study of a ligand-receptor unbinding process. 

Truncation artifacts are rarely a problem in H NMR, because acquisition times usually are long enough (2-4 s) to permit essentially complete decay of the FID. The... 

Although PET/CT modality is widely employed for diagnostic purpose, CT data acquired either for fusion of PET and CT images or for photon attenuation correction are affected by several factors that cause artifacts in PET/CT images. The factors include patient positioning, metal objects, CT contrast agents, truncation artifacts, and respiratory movement, which are discussed below. 

A simple method of recovering the truncated data is to linearly extrapolate the truncated CT projections to the extent of PET FOV and then setting the values to zero at the edge of the PET FOV. The attenuation correction by this method is adequate to remove the truncation artifacts in PET/CT images (Fig. 3.15). Using the iterative method rather than the filtered back projection technique also has shown to help to eliminate these artifacts. 

While methods of spectrum analysis capable of super-resolution exist, that is, methods that can achieve resolution greater than l/Wx, the most common of these, linear prediction (LP) extrapolation, has substantial drawbacks. LP extrapolation is used to extrapolate signals beyond the measured interval. While this can dramatically suppress truncation artifacts associated with zero-filling as well as improve resolution, because LP extrapolation implicitly assumes exponential decay it can lead to subtle frequency bias when the signal decay is not perfectly exponential [8]. This bias can have detrimental consequences for applications that require the determination of small fi-equency differences, such as measurement of residual dipolar couplings (RDCs). 

As pointed out by Davies and co-workers [91], many high-resolution 2D spectra are not sparse and suffer rather from signal overlap or line shape distortions occurring for several reasons (twisted-shape, truncation artifacts, inhomogeneous broadening). Although these difficulties seem quite different from those in radio astronomy, it became possible to employ essentially the same algorithm to alleviate these problems. 

A similar approach was presented by Keeler in application to heteronuclear J spectra with highly truncated echo modulation [87]. Truncation of signal, used for sensitivity reasons, results in sine wiggles . These artifacts can be suppressed by apodization, although at the expense of resolution. Keeler showed that CLEAN is an inexpensive alternative to the maximum entropy method, which can also remove truncation artifacts without degrading resolution. 

Once the FID has decayed below the noise level there is little more useful information that can be gained. However, increasing the number of data points at the end by filling with zeros can improve spectral resolution. The apparent increased sampling results, after Fourier transform, in a spectrum with more data points consequently improves the visibility of otherwise unresolved peaks. Filtering of the FID is usually applied before zero filling to avoid truncation artifacts. 

Structure and dynamics studies of deuterated peptides and proteins by MAS solid-state NMR have been reviewed by Reif. It has been shown that perdeuteration and back substitution of exchangeable protons in microcrystalline proteins, in combination with recrystallization from D2O-containing buffers, significantly reduce H- H dipolar interactions leading to amide proton line widths on the order of 20 Hz. Aliphatic protons are accessible either via specifically protonated precursors or by using low amounts of H2O in the bacterial growth medium. As emphasised in this article, the labelling scheme enables characterization of structure and dynamics in the solid-state without dipolar truncation artifacts. 

Sury MR, Harker H et al. (2005) The management of infants and children for painless imaging. Clin Radiol 60 731-741 Turner DA, Rapoport MI et al. (1991) Truncation artifact a potential pitfall in MR imaging ofthe menisci of the knee. Radiology 179 629-633... 

Truncation artifacts and density errors can be reduced by applying row-wise extrapolation techniques (Ohnesorge et al. 2000 Starman et al. 2005 Sour-BELLE et al. 2005 Zellerhoee et al. 2005 FIsieh et al. 2004). Since row-wise extrapolation only depends on neighboring data in a horizontal direction, this approach is adaptive, and it can be very effective, as shown in Fig. 3.3d. 

New multi-axis C-arm gantry designs, such as the Artis zeego (Siemens AG, Flealthcare Sector, Forch-heim, Germany) shown in Fig. 3.2b, can be operated in a large-volume scan mode. This approach almost doubles the object size that can be reconstructed without truncation artifacts, because two C-arm runs are performed with the detector positioned such that it captures one half of an X-ray projection in one run while recording the remaining half in the other. 

These functions allow- the nonbonded potential energy Lo turn off smoothly and systematically, removing artifacts caused by a truncated potential. With an appropriate switching function, the potential function is unaffected except m the region of the switch. 

An example of mechanism (1) is given in Section 1.1.2 Essentially, numerical artifacts are due to computational operations that result in a number, the last digits of which were corrupted by numerical overflow or truncation. The following general rules can be set up for simple operations ... 

Many other filter functions can be designed, e.g. an exponential or a trapezoidal function, or a band pass filter. As a rule exponential and trapezoidal filters perform better than cut-off filters, because an abrupt truncation of the Fourier coefficients may introduce artifacts, such as the annoying appearance of periodicities on the signal. The problem of choosing filter shapes is discussed in more detail by Lam and Isenhour [11] with references to a more thorough mathematical treatment of the subject. The expression for a band-pass filter is H v) = 1 for v j < v < else... 

GHJCOSE 1D H GH 013001.FID. Note the baseline artifacts introduced by the truncated FID. In the Linear Prediction (LP) dialog box make sure that the Execute Backward LP option is enabled and the Execute Forward LP option disabled. Set LP backward to Point to 124. Following the rules given above vary the residual parameters First Point used for LP (recommended 196), Last Point used for for LP (recommended 2047) and Number of Coefficients (recommended 128 or larger). Carefully inspect the resulting spectra with respect to spectral resolution and signal shapes and compare it with the spectrum obtained without LP. 

To avoid this phenomenon, as a next truncation scheme we may try a milder truncation for the strong ion-ion interactions the ion-ion potential we cut and shift (to maintain its continuity) while leaving the water-ion and water-water potentials intact. Although the above mentioned artifact becomes less pronounced, it is still large enough to produce wrongly behaving solution. 

---