# HYPSO-1 CubeSat: First Images and In-Orbit Characterization
## 3 In-Orbit Payload Performance
### Spectral Signal-to-Noise Ratio
Following the notation found in [28], the noise estimation from [51] can be performed as  
\[\mathbf{X}_{o}^{T} =\mathbf{Y} \tag{2}\] \[\mathbf{Y}_{(-k)} =\big{[}\mathbf{y}_{1},\ \ \mathbf{y}_{2},\ \ \cdots,\ \ \mathbf{y}_{k-1},\ \ \mathbf{y}_{k+1},\ \ \cdots,\ \ \mathbf{y}_{L}\big{]}\] \[\mathbf{\tilde{n}}_{k} =\mathbf{y}_{(k)}-\mathbf{Y}_{(-k)}\big{(}\mathbf{Y}_{(-k)}^{T} \mathbf{Y}_{(-k)}\big{)}^{-1}\mathbf{Y}_{(-k)}^{T}\mathbf{y}_{(k)}\] \[\mathbf{X}_{nspectral}^{T} =\big{[}\mathbf{\tilde{n}}_{1},\ \ \ \mathbf{\tilde{n}}_{2},\ \ \cdots,\ \ \ \mathbf{\tilde{n}}_{N}\big{]}\ \ \ \forall k\in\{1,2,\cdots,N\}.\]  
Secondly, [PERSON]'s method is also used to estimate noise [50]. The resulting noise vector set \(\mathbf{X}_{n}\) is computed by taking the difference between neighboring pixels in a spatial area that is spectrally uniform, as follows:  
\[\mathbf{X}_{n,spatial} =\big{[}\mathbf{x}_{1}-\mathbf{x}_{2},\ \ \mathbf{x}_{2}-\mathbf{x}_{3},\ \ \cdots,\ \ \ \mathbf{x}_{N-1}-\mathbf{x}_{N}\big{]} \tag{3}\] \[=\big{[}\mathbf{\tilde{n}}_{1},\ \ \ \mathbf{\tilde{n}}_{2},\ \ \cdots,\ \ \ \mathbf{\tilde{n}}_{N-1}\big{]}.\]  
These methods give a relative estimate of the SNR dependent on the statistics of a specified region of the image cube. The noise estimation is performed on raw uncalibrated data from HYPSO-1. The application of the calibration coefficient to convert the digital counts to radiance values is most commonly a linear transformation between the underlying noise and the measured signal, i.e., SNR should be unaffected by this linear scaling with these estimation approaches. Regions that appear to be homogeneous and stable, both spectrally and spatially, are selected to fit best the underlying assumptions for noise estimation, illustrated in Figure 14. The results are given in Figure 16.  
The shape of the curves in Figure 16 originates from the wavelength-dependence of water reflectance. Over water, the measured signals are mainly due to scattering in the atmosphere, and water is strongly absorbent in the longer wavelengths given in Figure 16. In addition, the variation in the shape of the curves between sensors originates from the wavelength-dependence of the quantum efficiency, i.e., the sensor's sensitivity to different parts of the spectrum. The SNR estimate is expected to be higher in those parts of the spectrum with the highest signal. The comparison is complex because each sensor undergoes different types of pre-processing, in addition to the variance between scenes. The HICO data are preprocessed using a Gaussian smoothing filter. In the range of 400 nm to 745 nm, the filter size is 10 nm. For wavelengths 746 nm to 900 nm, a filter size of 20 nm is used. Data from the HICO instrument that is not preprocessed are not freely available. This preprocessing gives an artificially high SNR performance when estimated by Equation (2). This artificially high SNR performance is evident from the counter-intuitive and significant increase in SNR from 746 nm to 900 nm, as well as the much poorer performance when estimating the noise spatially by Equation (3). When using Equation (3), the noise for HICO corresponds with the numbers given in [7,8]. This result is \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sensor** & **Scene ID** & **Area** & **Pixel Extent** & **Label** \\ \hline
**HYPSO-1** & 20220419 Frohavet & Frohavet, Norway & \(350\times 100\) & a \\
**HICO** & H2014218021732 & Dunedin, New Zealand & \(350\times 300\) & b \\
**AVIRIS-NG** & 20210728201553 & Santa Catalina Is., USA & \(300\times 200\) & c \\
**PRISMA** & PRS_1L1_20220427122725 & Jan Mayen, Norway & \(100\times 180\) & d \\
**SeaHawk** & 20220212T143933 & Bermuda & \(800\times 500\) & e \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The sensor and accompanying scene identification string alongside the area name of the scenes used for SNR estimation. The Pixel Extent is the spatial picture element dimensions of the homogeneous area.