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sholding) can be tuned to regulate the amount of distortion introduced in the restored
image. A rigourous comparison of these methods requires additional criteria other than
visual interpretation. In this section, we recall the definition of several qualitative indexes
used to evaluate the destriping quality.
3.8.1 Noise Reduction Ratio and Image Distortion
The spectral analysis conducted in section 3.5.1, takes advantage of the unidirectional
aspect of striping to highlight its spectral signature. Periodic stripes related to detectorto-detector
and mirror banding introduces peaks, clearly visible in the ensemble averaged
power spectrum down the columns. A reliable destriping should reduce the stripe peaks
without interfering with the global shape of the original signal’s power spectrum. Let us
denote P 0 -resp. P 1 - the power spectrum obtained as an average of the periodograms of
the noisy image -resp. the destriped image- columns. We define :
N 0 =
∑
P 0 (f)
f∈BW N
N 1 =
∑
P 1 (f)
f∈BW N
(3.52)
where BW N is the noisy part of the frequency spectrum (f ∈ BW N corresponds to f ∈
{0.1, 0.2, 0.3, 0.4, 0.5} in the case of detector-to-detector stripes). N 0 and N 1 contain the
spectral components of stripes in both the noisy image and the restored one. The Noise
Reduction ratio (NR) is then defined as :
NR = N 0
N 1
(3.53)
The NR index measures the attenuation of the frequency peaks in the power spectrum and
hence can only be used for images affected with periodic stripes. Furthermore, evaluation
of a destriping techniques with the NR index has to be imperatively completed with a
distortion index that quantifies the blur introduced in the destriped result. Denoting :
S 0 =
∑
P 0 (f)
f∈BW S
S 1 =
∑
P 1 (f)
f∈BW S
(3.54)
where BW S is the noise-free portion of the spectrum, the image distortion index used in
[Pan and Chang, 1992] is defined as :
ID = N 0
N 1
(3.55)