IEEE Geoscience and Remote Sensing Magazine - September 2022 - 185

information of pansharpened products is exploited the
most, e.g., in photogrammetry.
On the other hand, it is important to recall that the
RQNR employs an MLR between the original Pan and
the fused MS bands, as in (13), on which the spatial
mismatch is measured by means of the coefficient of
determination (i.e., it is related to the residuals of the
multivariate regression). Even though, in the context of
pansharpening, the adoption of a multivariate linear
model is typically considered-see, e.g., the estimation of
spectral weights for the widely used GSA method-some
situations can certainly occur where such a model is not
the most appropriate. For instance, the use of a nonlinear
model explaining the spectral relation between the MS
and the Pan domains could be sometimes more suitable.
In these cases, the spectral mismatch due to the use of
an inappropriate linear model can result in an increase
of the regression residuals, thus reducing the coefficient
of determination for reasons far from a spatial distortion
introduced in a particular fused product. Moreover, even
an error in the estimation of the coefficients of the linear
model in (12) can result in a similar effect on the coefficient
of determination.
Thus, even for this index, a perfect spatiospectral decoupling
cannot be ensured due to possible inaccuracies in the
adopted linear spectral model. However, most of the spectral
distortion is usually captured by the linear regression
model, thus guaranteeing a spatial distortion metric with
a small (or zero) coupling with the spectral counterpart
(different from the spatial distortion index exploited by the
QNR and HQNR).
Another issue of the RQNR, more relevant than the
previous one, involves the distribution of the values of the
spatial distortion index in the dynamic range that theoretically
ranges from zero to one. Indeed, the employment of
the coefficient of determination limits the dynamic of the
expected values showing a compression toward zero of Ds
R
or, equivalently, toward one if the complementary values
1 Ds
-
R are considered (see the " FR Assessment: QNR-Like
Protocols " section for more details). This consideration is
somehow related to another issue that involves the combination
of the spatial and spectral components through a
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
(j)
(k)
(l)
(m)
(n)
(o)
(p)
(q)
(r)
(s)
(t)
(u)
(v)
(w)
(x)
FIGURE 13. The FR fusion products of a close-up view of the IKONOS Toulouse data set, using a true-color representation: (a) PAN, (b) EXP,
(c) GIHS, (d) BT, (e) BT-H, (f) BDSD-PC, (g) GS, (h) GSA, (i) C-GSA, (j) PRACS, (k) AWLP, (l) MTF-GLP-FS, (m) MTF-GLP-HPM-H, (n) MTF-GLPHPM-R,
(o) MTF-GLP-CBD, (p) MF, (q) FE-HPM, (r) SR-D, (s) PWMBF, (t) TV, (u) RRP, (v) PNN, (w) PNN-IDX, and (x) A-PNN-FT.
SEPTEMBER 2022 IEEE GEOSCIENCE AND REMOTE SENSING MAGAZINE
185
IEEE Geoscience and Remote Sensing Magazine - September 2022

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