Digital Signal Processing Reference
In-Depth Information
Figure 10.21. (top) Spherical map obtained by subtracting the coarse-scale map of Fig. 10.20
(right) from the initial map of Fig. 10.20 (left). (bottom) Component maps separated by the
MCA method on the sphere: (left) interference patterns and measurement artifacts were
caught by the local cosine functions on the sphere, whereas (right) the isolated bumps
were caught using the undecimated wavelet on the sphere. Adding back the coarse scale of
Fig. 10.20 (right) to the latter map results in a clean map of the surface structures of an ICF
spherical shell with the interference patterns and artifacts removed. (
See color plates.
)
easily. The resulting bumps, added to the coarsest scale, comprise the clean data
with the interference patterns and artifacts removed, as shown in Fig. 10.21. The
spherical harmonic decomposition of the cleaned image gives rise to coefficients of
various
modes, which will be amplified by the implosion process.
The implosion process can now be assessed correctly using numerical hydro-
dynamic simulation-generated growth factors. If the bumps are clustered and not
randomly distributed, then systematic errors in the manufacturing process can be
tracked down. For more details, see Afeyan et al. (2006).
10.8.2 Application in Cosmology
A major issue in modern cosmology is the measurement and the statistical char-
acterization (spatial power spectrum, Gaussianity) of the slight fluctuations in the
cosmic microwave background (CMB) radiation field. These are strongly related
to the cosmological scenarios describing the properties and evolution of our uni-
verse. Some 370,000 years after the big bang, when the temperature of the universe
was around 3,000 K, thermal energy was no longer sufficient to keep electrons and
positively charged particles apart, so they combined. Photons were then set free in
a nearly transparent universe. Since the universe further expanded, these photons
are now in the microwave range, but they should still be distributed according to a
blackbody emission law. Indeed, before recombination, the universe was a highly
homogeneous opaque plasma in near-thermal equilibrium, in which photons and
