Optical remote sensing in complex waters is challenging because the optically active constituents may vary independently and have a combined and interacting influence on the remote sensing signal. Additionally, the remote sensing signal is influenced by noise and spectral contamination by confounding factors, resulting in ill-posedness and ill-conditionedness in the inversion of the model. There is a need for inversion methods that are less sensitive to these changing or shifting spectral features. We propose WaveIN, a wavelet-enhanced inversion method, specifically designed for complex waters. It integrates wavelet-transformed high-spectral resolution reflectance spectra in a multiscale analysis tool. Wavelets are less sensitive to a bias in the spectra and can avoid the changing or shifting spectral features by selecting specific wavelet scales. This paper applied WaveIN to simulated reflectance spectra for the Scheldt River. We tested different scenarios, where we added specific noise or confounding factors, specifically uncorrelated noise, contamination due to spectral mixing, a different sun zenith angle, and specific inherent optical property (SIOP) variation. WaveIN improved the constituent estimation in case of the reference scenario, contamination due to spectral mixing, and a different sun zenith angle. WaveIN could reduce, but not overcome, the influence of variation in SIOPs. Furthermore, it is sensitive to wavelet edge effects. In addition, it still requires in situ data for the wavelet scale selection. Future research should therefore improve the wavelet scale selection.

This letter presents an application of continuous wavelet analysis, providing a new semi-empirical approach to estimate Chlorophyll-a (Chl-a) in optically complex inland waters. Traditionally spectral narrow band ratios have been used to quantify key diagnostic features in the remote sensing signal to estimate concentrations of optically active water quality constituents. However, they cannot cope easily with shifts in reflectance features caused by multiple interactions between variable absorption and backscattering effects that typically occur in optically complex waters. We use continuous wavelet analysis to detect Chl-a features at various wavelengths and frequency scales. Using the wavelet decomposition, we build a 2-D correlation scalogram between in situ pond reflectance spectra and in situ Chl-a concentration. By isolating the most informative wavelet regions via thresholding, we could relate all five regions to known inherent optical properties. We select the optimal feature per region and compare them to three well-known narrow band ratio models. For this experimental application, the wavelet features outperform the NIR-red models, while fluorescence line height (FLH) yield comparable results. Because wavelets analyze the signal at different scales and synthesize information across bands, we hypothesize that the wavelet features are less sensitive to confounding factors, such as instrument noise, colored dissolved organic matter, and suspended matter.

In the estimation of data with many zeros (sparse data), such as wavelet coefficients, thresholding is a common technique. This letter investigates the behavior of the minimum risk threshold for large values of the noise standard deviation. It finds that the threshold depends quadratically on the noise standard deviation. The relevance of this result is situated in the context of both Bayesian and universal thresholding.

Denoising algorithms based on wavelet thresholding replace small wavelet coefficients by zero and keep or shrink the coefficients with absolute value above the threshold. The optimal threshold minimizes the error of the result as compared to the unknown, exact data. To estimate this optimal threshold, we use generalized cross validation. This procedure does not require an estimation for the noise energy. Originally, this method assumes uncorrelated noise. In this paper, we describe how we can extend it to images with correlated noise.