Noise removal on ocean scalars by means of singularity-based fusion

Abstract

Thanks to new remote sensing platforms as SMOS and Aquarius we have now access to synoptic maps of Sea Surface Salinity (SSS) at global scale. Both missions require a non-negligible amount of development in order to meet pre-launch requirements on the quality of the retrieved variables. Development efforts have been so far mainly concentrated in improving the accuracy of the acquired signals from the radiometric point of view, which is a point-wise characteristic, that is, the qualities of each point in the snapshot or swath are considered separately. However, some spatial redundancy (i.e., spatial correlation) is implicit in geophysical signals, and particularly in SSS. This redundancy is known since the beginning of the remote sensing age: eddies and fronts are visually evident in images of different variables, including Sea Surface Temperature (SST), Sea Surface Height (SSH), Ocean Color (OC), Synthetic Aperture Radars (SAR) and Brightness Temperatures (BT) at different bands. An assessment on the quality of SSS products accounting for this kind of spatial redundancy would be very interesting. So far, the structure of those correlations have been evidenced using correlation functions, but correlation functions vary from one variable to other; additionally, they are not characteristic to the points of the image but to a given large enough area. The introduction of singularity analysis for remote sensing maps of the ocean has shown that the correspondence among different scalars can be rigorously stated in terms of the correspondence of the values of their associated singularity exponents. The singularity exponents of a scalar at a given point is a unitless measure of the degree of regularity or irregularity of this function at that given point. Hence, singularity exponents can be directly compared disregarding the physical meaning of the variable from which they were derived. Using singularity analysis we can assess the quality of any scalar, as singularity exponents align in fronts following the streamlines of the flow, while noise breaks up the coherence of singularity fronts. The analysis of the output of numerical models show that up to the numerical accuracy singularity exponents of different scalars take the same values at every point. Taking the correspondence of the singularity exponents into account, it can be proved that two scalars having the same singularity exponents have a relation of functional dependence (a matricial identity involving their gradients). That functional relation can be approximated by a local linear regression under some hypothesis, which simplifies and speeds up the calculations and leads to a simple algorithm to reduce noise on a given ocean scalar using another higher- quality variable as template. This simple algorithm has been applied to SMOS data with a considerable quality gain. As a template, high-level SST maps from different sources have been used, while SMOS L2 and L3 SSS maps, and even brightness temperature maps play the role of the noisy data to be corrected. In all instances the noise level is divided by a factor of two at least. This quality gain opens the use of SMOS data for new applications, including the instant identification of ocean fronts, rain lenses, hurricane tracks, etc