The signal-to-noise ratio (SNR), the ratio of signal power to the noise power, is a key parameter of satellite sensors. It quantifies how much the signal has been corrupted by noise. Users require data and images with high SNRs to better serve their analysis needs. However, to build a satellite sensor with a high SNR is challenging, potentially expensive, and often constrained by the available technology. For satellites already in orbit, users have to live with the low SNRs in the images acquired.
To achieve a high SNR, we normally need to adopt excessive measures in building a satellite. These include increasing the aperture or lens size to capture as much signal as possible, choosing much more sensitive detectors with a larger pixel size to gather more signal, cooling the detectors to extremely low temperatures to lower the noise, and allocating longer integration times to accumulate more signal. They all have a negative impact on the satellite's mass, power, and cost. Sometimes, the ultimately achievable SNR still does not meet users' needs. To get around these challenges, we have developed a signal-processing-based technology to improve the SNR by removing the noise in the observed images.
Wavelet transforms are often used to separate noise from signal.1 The signal in the observed images is transformed to a few coefficients with large amplitudes in the wavelet domain, while the noise transforms to a large number of coefficients with small amplitudes (close to zero). Removing the small and shrinking the large coefficients, a process known as wavelet shrinking, eliminates most of the noise contribution in the wavelet domain. Several algorithms have been proposed to estimate threshold values that are optimal in different senses. We use a global minimax threshold,2 in combination with the SURE3 and BayesShrink data-driven thresholds.4
Figure 1.Signal-to-noise ratio (SNR) of a satellite datacube before and after enhancement using our new signal-processing-based technology.
We have developed our noise-reduction technology for multidimensional satellite images.5,6 The images used comprised a 3D ‘datacube,’ of which two dimensions correspond to spatial directions and one dimension represents the spectral wavelength. Because of the low noise level in typical satellite datacubes, with SNRs of 100:1 or better, the noise can be difficult to see and remove. Our solution is to elevate and, thus, emphasize the noise temporarily by taking the spectral derivative of the datacube.5 We can then perform denoising in the wavelet domain.
To better accommodate the dissimilarity between the spatial and spectral dimensions of the datacubes, we developed a hybrid spatial-spectral two-step noise-reduction process. We operate in the spectral-derivative domain (for elevating the noise level) and also in the wavelet domain (for separation of signal and noise). After spatial denoising in the wavelet domain, we go back to the derivative domain. Finally, after the two-step denoising, we go back to the original time domain by spectral integration.
In the inverse derivative, the spectral-integration operation on the denoised datacube can accumulate a significant amount of low-frequency errors. These grow with the number of spectral bands. Normally, hyperspectral datacubes contain a large number of spectral bands, which may result in an accumulated error that can be significantly larger than the initial noise. To overcome this problem, we apply a simple and efficient solution to correct the accumulated errors by replacing them with the low-frequency components of the observed signal.
The experimental results show that our noise-reduction technology can improve the overall SNR of hyperspectral datacubes by a factor of two (see Figure 1). We have evaluated the impact on remote-sensing products (e.g., narrow-band vegetation indices, red-edge positions).7 Evaluation results indicate that our technique successfully preserved scientific information for remote-sensing applications. We conducted a simplified, application-based evaluation of target-detection performance using a spectral-angle mapper.8 We also examined the effectiveness of the technology using a military target-detection application. The targets, which could not be detected from the original datacube, were detected after applying our noise-reduction approach (see Figure 2).9
Figure 2.(left) The target of size 6×6m2(inside the red granule) cannot be derived from the original hyperspectral datacube. (right) Target derived after the SNR of the datacube is enhanced using our wavelet approach.
Our hybrid two-step wavelet method is a feasible and cost-effective solution to improving or complementing the SNR of satellite sensors by removing noise from observed images while retaining the signal. Experimental results have confirmed that our technique can achieve up to a factor of two enhancement in SNR. Our next step will be to apply this technology to a new Canadian mission—Polar Communication and Weather—and possibly to other missions.
Canadian Space Agency
Shen-En Qian is a senior scientist and the scientific authority for Canadian government contracts in the development of space technologies and satellite missions. He heads a research and development team, holds six patents, and is author or co-author of more than 100 papers.
7. H. Othman, S.-E. Qian, Evaluation of wavelet denoised hyperspectral data for remote sensing, Can. J. Rem. Sens. 34, no. 1pp. 59-67, 2008.
8. S.-E. Qian, H. Othman, J. Lévesque, Spectral angle mapper based assessment of detectability of man-made targets from hyperspectral imagery after SNR enhancement, Proc. SPIE
6361, pp. 63611H, 2006. doi:10.1117/12.689113
9. S.-E. Qian, J. Lévesque, Target detection from noise-reduced hyperspectral imagery using spectral unmixing approach, Opt. Eng.
48, no. 2pp. 026401.1-11, 2009. doi:10.1117/1.3077179