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for striping. The drift observed on MSS detectors response was attributed in [Horn and
Woodham, 1979] to the degradation of photomultipliers with respect to exposure time.
Despite the calibration system on-board LANDSAT, MSS images still contain stripes and
additional radiometric correction were developped by [Strome and Vishnubhatla, 1973]
and [Sloan and Orth, 1977]. The resulting method is referred to as moment matching and
is based on the assumption of both linear and time invariant behavior of the detectors.
Stripe noise is assumed to be the result of relative uncorrected gain and offset coefficients.
Hereafter, we denote d k the signal acquired by detector number k. In the case of MODIS,
k =1..10 (for FPAs with 1 km resolution), images are formed by interlacing signals from
the 10 detectors. Under the assumption of linear responses, the signal from detector k can
be written as :
d k = G k .d c k + O k (3.1)
where G k and O k are gain and offset parameters, d k is the noisy signal and d c k
is the true
signal for detector k. Once G k and O k are determined, values of detector k are corrected
as :
d c k = d k − O k
(3.2)
G k
Unless calibration targets with known radiance values are used, absolute values for G k and
O k remain undetermined. Nevertheless, destriping only requires relative gain/offset coefficients.
These can be estimated statistically from the entire image. In fact, the acquisition
process of whiskbroom systems makes it reasonnable to assume that signals acquired by
each detector share similar statistical characteristics. The validity of this hypothesis holds
for images with high dimensions. Relative gain/offsets can then be determined from the
mean value and standard deviation of a signal d ref acquired by a predetermined reference
detector. Let us denote µ k and σ k , - respectively µ ref et σ ref - the mean value and standard
deviation of d k , - resp. d ref -. Moment matching adjusts the response of a noisy detector
by forcing its mean value and standard deviation to coincide with those derived from the
reference detector. Using equation (3.1), this translates to :
and gain and offset are obtained as :
µ k = G k .µ ref + O k
σ k = G k .σ ref
(3.3)
G k =
σ k
σ ref
O k = µ k − µ ref . σ k
σ ref
(3.4)
Replacing equations (3.4) in (3.2), the signal from detector k is corrected with :
ˆd c k = σ ref .(d k − µ k )
σ k
− µ ref (3.5)