  Since asymptotic giant branch (AGB) stars are bright and extended infrared
objects, most Galactic AGB stars saturate the Wide-field Infrared Survey
Explorer (WISE) detectors and therefore the WISE magnitudes that are restored
by applying point-spread-function fitting need to be verified. Statistical
properties of circumstellar envelopes around AGB stars are discussed on the
basis of a WISE AGB catalog verified in this way. We cross-matched an AGB star
sample with the WISE All-Sky Source Catalog and the Two Mircon All Sky Survey
catalog. Infrared Space Observatory (ISO) spectra of a subsample of WISE AGB
stars were also exploited. The dust radiation transfer code DUSTY was used to
help predict the magnitudes in the W1 and W2 bands, the two WISE bands most
affected by saturation, for calibration purpose, and to provide physical
parameters of the AGB sample stars for analysis. DUSTY is verified against the
ISO spectra to be a good tool to reproduce the spectral energy distributions of
these AGB stars. Systematic magnitude-dependent offsets have been identified in
WISE W1 and W2 magnitudes of the saturated AGB stars, and empirical calibration
formulas are obtained for them on the basis of 1877 (W1) and 1558 (W2) AGB
stars that are successfully fit with DUSTY. According to the calibration
formulae, the corrections for W1 at 5 mag and W2 at 4 mag are $-0.383$ and
0.217 mag, respectively. In total, we calibrated the W1/W2 magnitudes of
2390/2021 AGB stars. The model parameters from the DUSTY and the calibrated
WISE W1 and W2 magnitudes are used to discuss the behavior of the WISE
color-color diagrams of AGB stars. The model parameters also reveal that O-rich
AGB stars with opaque circumstellar envelopes are much rarer than opaque C-rich
AGB stars toward the anti-Galactic center direction, which we attribute to the
metallicity gradient of our Galaxy.
