# Sparse Representing Denoising of Hyperspectral Data for Water Color Remote Sensing
## 1 Introduction  
Hyperspectral techniques have long been utilized in water color remote sensing [1, 2], especially for optically complex water [3, 4, 5]. The main controllers of the optical properties are the absorption and scattering of the water color parameters, such as phytoplankton, particulate matter, and colored, dissolved organic matter [6, 7]. Different pigments also have varied optical characteristics [8]. Therefore, researchers suggested that to accurately capture the concentration of the water color parameters, the spectrometer needs to contain at least 15 bands at specific wavelength in the visible and near infrared spectral ranges [9, 10]. Furthermore, to quantitatively determine the chlorophyll concentration (\(C_{\text{chla}}\)) by remote sensing in systems dominated by suspended sediment, the sensor needs a high spectral resolution (10 to 15 nm band width) at 675 and 705 nm [11]. This determines that the hyperspectral data are urgently needed for the building and refining of water color parameter estimation models [12, 13, 14, 15]. However, the accurate hyperspectral measurement of water surface reflectance (\(R_{\text{rs}}\)) is challenging. In field measurements, the above water method is popular because it is stable and easy to use. During the measurement, we need to strictly obey some geometriesto limit sun glitter, avoid instrument-shading problems, and retrieve the \(R_{\text{rs}}\)[16; 17]. In addition, we always collect several spectra (ten in our study) at each sampling station and calculate their average values as the result, in order to control random errors in the measurement. Even though, the occurrence of noise is inevitable. Focusing on this problem, the researchers tried to utilize denoising methods on the \(R_{\text{rs}}\) curves to improve its quality. These methods can be categorized into three types: 1-D, 2-D, and 3-D methods. The 1-D methods are based only on the spectral, such as kernel regression smoothing (KRS) [18; 19], Savitzky-Golay polynomial smoothing (SG) [20], and mean filter smoothing (Mean) [20]. How to choose a proper denoising level is a problem in the 1-D methods, to avoid over-denoising because the spatial information--that can offer extra constraints--is not involved. The 2-D [21; 22] and 3-D [23; 24; 25] methods are focusing on hyperspectral images. More challenging than field measuring, the hyperspectral image needs to separate the radiated signal from the field of view (FOV) into hundreds of spectra bands in each pixel. Furthermore, the integration time of the sensor is limited under its high orbiting speed. For the hyperspectral remote sensors, achieving high SNR images is more difficult. Therefore, signal processing methods, such as classic principal component analysis [26; 27], wavelet transform [21; 28; 29], and total variation method [30; 31], are widely used. Recently developed sparse representing [32; 33], low rank [23; 34], and deep learning algorithms [35] also showed great potential in hyperspectral data denoising. By comprehensively utilizing the spectral and spatial information, these methods can better retrieve useful signals in the hyperspectral image from the noisy data. Both the 2-D and 3-D methods require spatial information. This means that these methods were limited to denoise hyperspectral images. Thus, in this study, we focus on 1-D methods, which can be applied to both field-measured and remotely sensed hyperspectral \(R_{\text{rs}}\) data. Different optical properties will produce a variety of \(R_{\text{rs}}\) features [36; 37], which bring more challenges to the denoising. In this study, in order to keep the universality with high accuracy of the model, we introduced a bio-optical model--a radiative transfer model in the water body--into the sparse-representing algorithm. The method first generates a comprehensive hyperspectral \(R_{\text{rs}}\) dataset and decomposes the noisy \(R_{\text{rs}}\) signals into sparse signals and noise signals. By recomposing the sparse signals, the denoising is completed.