Hopfield neural network and pareto optimal algorithms for retrieving sea surface current from TanDEM-X data

This is first work is done on the application of TanDEM-X data satellite data for the Malaysian coastal waters. This study aims at comparison between Hopfield neural network and Pareto optimal algorithms for modelling sea surface current using TanDEM-X satellite data. In fact, X-band data have a great potential for retrieving sea surface parameters such as sea surface current movement and ocean wave spectra. Therefore, TanDEM-X is the term of the satellite operation hovering the two satellites in a strictly controlled foundation with regular distances between 250 and 500 m. The study of ocean surface current is important for understanding the coastal water circulation. The set of TanDEM-X satellite data are examined by using Hopfield neural network algorithm. The sea surface current is retrieved based on the energy function. Therefore, the Pareto optimal algorithm is used to determine the optimal solution for nonlinearity problem which is raised due to the Doppler frequency shift impact. The study shows that the Pareto optimum resolution has highest performance than Hopfield neural network rule with lowest RMSE of ±0.08. Further, Pareto optimum resolution can verify the ocean surface current pattern variation on coastal water from TanDEMX data. Last, TanDEMX data reveals a superb guarantees for retrieving ocean surface current with X-band.


Introduction
Complexity of ocean nature needs standard instruments and procedures to comprehend. Despite advance technology of ocean in situ measurements, large ocean area cannot survey with effortless [1]. In reality, whether circumstances induce storms, which cause disasters in coastal zone that do not allow oceanographers and researchers to acquire timeless and effortless in situ measurements. Recently, researchers have shown an increased interest in ocean studies using remote sensing technology, which can image large-scale ocean area and provides precisely information on air-sea surface interactions [2][3][4][5][6][7][8][9]. Synthetic aperture radar (SAR) is recognized as the potential radar sensor for monitoring the dynamic ocean surface. One of an attention-grabbing topic is current flow that is needed short go back satellite cycle and high resolution. These will provide precisely data concerning current dynamic flow [10] [12]. In fact, current is very important for ship navigation, fishing, waste matter substances transport and sediment transport [2] [11]. Respectively optical and microwave sensors are enforced to monitor the current flows. Indeed, the ocean surface dynamic options of sea surface current is vital parameters for atmospheric-sea surface interactions. In this regard, the global climate change, marine pollution and coastal risky are preponderantly dominated by current speed and direction [12].
The measurements of ocean current from space relies on the electromagnetic signal. Truly, associate degree of an electromagnetic signal of optical and microwave reflects from the ocean carrying records concerning one among the first discernible quantities that are the colour, the beamy 2 1234567890 ''"" temperature, the roughness, and also the height of the ocean [13]. The principal conception to retrieve the ocean surface current from SAR information is perform of the Doppler frequency shift theory [14]. Incidentally, the orbital quality of the ocean wave and surface current dynamic interactions will cause shifting of the radiolocation signal within the angle direction i.e. the flight direction that is thought because the Doppler frequency shift [11]. In truth, the surface current dynamic is virtual to the orbital movement and an antenna rotation of the synthetic aperture radar. Consequently, the Doppler frequency shift, reckon the SAR antenna angle of view that is virtual to the orbital mechanical phenomenon rotation [15]. Consequently, the connection between the ocean surface dynamic orbital movement and also the SAR satellite orbital motion would be nonlinear attributable to the Doppler influence [16]. In literature, there are many mathematical algorithms that are supported physical models to retrieve ocean surface current from SAR information. In other words, these algorithms area unit enforced to map the Doppler frequency spectra into the important ocean surface current speed. However, these techniques are restricted attributable to the nonlinear quality of ocean surface dynamic behaviours and radar signal [3]. In this regard, the Doppler rate has coarser resolution than radar cross section on the angle direction [17].
In this paper, we have a tendency to address the question of retrieving ocean surface current pattern from TanDEM-X data. This is often verified an exploitation of neural network technique. Hypotheses examined are: (i) Hopfield neural network based mostly multi-objective optimisation via Pareto dominance algorithmic rule is executed to TanDEM-X data; (ii) multi-objective optimisation via Pareto dominance is used as procedures for eliminating inherent speckle from TanDEM-X data; and (iii); the nonlinearity of the physicist frequency shift is reduced multi-objective optimisation via Pareto dominance.
The novelty of this work is to optimize the lapses occurring on retrieving sea surface current parameters from TanDEM-X satellite data. Hypotheses examined are: (i) Hopfield neural network based mostly multi-objective optimisation via Pareto dominance algorithmic rule is executed to TanDEM-X data; (ii) multi-objective optimisation via Pareto dominance is used as procedures for eliminating inherent speckle from TanDEM-X data; and (iii); the nonlinearity of the physicist frequency shift is reduced multi-objective optimisation via Pareto dominance.

Data Acquisitions
Two styles of knowledge area unit needed to retrieve sea surface current parameters: TanDEM-X of SAR; (ii) and therefore the real unaltered sea surface current measuring throughout TanDEM-X satellite overpassed.

TanDEM-X Data
Pair of Terra-SAR satellite data is acquired by the TanDEM-X satellite on May 6 2017. The first image was acquired 7:27:17 am while the second image acquired at 19:20:06 pm. The data are in spotlight mode with X-band and HH and VV polarization. These data are single look complex formatted data.
The TanDEM-X operational consequence involves the coordinated operation of 2 satellites flying in adjacent configuration. The alteration constraints for the formation are: (i) the orbits ascending nodes, (ii) the angle between the perigees, (iii) the orbit eccentricities and (iv) the phasing between the satellites. The observance of ocean currents is a vital facet of assessing climate changes. Space borne SAR along-track interferometry (ATI) has the promise to considerably contribute to the present field. It will offer large-area, world-wide surface current measurements. The matter of mapping relatively low velocities are often resolved by formations of SAR satellites that yield sufficiently sensitive ATI measurements [18]].
In this study, the Hopfield algorithm relies on the TanDEMX information. The TerraSAR-X and TanDEM-X satellites transmit identical SAR instruments working at 9.65 GHz frequency (X-band). Throughout some devoted operations, both satellites are placed associate exceedingly in a very special orbit configuration with a brief along track baseline providing a probability for current measurements. The data utilized in this study were uninheritable in stripmap (SM), bistatic (TS-X active / TD-X passive) mode and VV polarization [

In situ ocean wave measurement
Following Marghany [19] sea surface current speed and direction are collected by Aquadopp® 2MHz current meter (Figure 1). For the surface current knowledge acquisition, the Aquadopp® 2MHz current meter factory-made by Nortek AS (Figure1), Scandinavian country was used. The instrumentality could be a standalone instrumentation exploitation Doppler based mostly technology to measure surface currents at the deployment web site. The instrumentation is intended with intrinsically memory and internal battery pack wherever it may be designed to record and store information internally for self-deployment [19].

Hopfield Neural Network Algorithm
Marghany [19] has implemented Hopfield neural networks for RADARSAT-2 SAR data to retrieve sea surface current. This section has been retrieved from Marghany [11] work. Therefore, Hopfield neural networks is used with TanDEM-X data. Consistent with Côté and Tatnall [20], Hopfield neural networks is considered as a promising method for determining a minimum of energy of function. For instance, motion analysis and object pattern recognitions might be coded into an energy function [21]. Furthermore, the actual physical constraint, heuristics, or prior knowledge of sea surface features, nonlinearity and the Doppler frequency shift [11] can be coded into the energy function.
A pattern, in the context of the N node Hopfield neural network is an N-dimensional vectors ) ,....... , ( and k is exemplar pattern where K k   1 [19]. The Hopfield net associates a vector from S with an exemplar pattern in E. Following Marghany [19], Hopfield net is involved that The Hopfield algorithm has consisted of (i) assign weights to synaptic connections; (ii) initialize the net with unknown pattern; and (iii) iterate until convergence and continue features tracking (equation 2) [5]. First step of assign weight ij w to synaptic connection can be achieved as understands: Hopfield neural network could be identified current pattern features by mathematical comparing to each other in order to build an energy function [19]. According to Côté and Tatnall [20] the difference function to determine the discriminations between different features where, " L is curvature shape of current feature,  are the minimum acceptable distance and the maximum acceptable rotation angle, respectively before energy function [19][20][21].

Pareto Algorithm
Following Atashkari et al., [22], the Multi-objective optimization (MOB) which is also termed the multi-criteria optimization or vector optimization. In this regard, it has been defined as finding a vector of decision variables satisfying constraints to give acceptable values to all objective functions.
In other words, the solution * Ƥ‫.}٭‬ In other words, the Pareto front ƤŦ‫٭‬ is a set of the vectors of objective functions mapped from Ƥ‫٭‬ [19].

Results and Discussion
The sea surface current velocities are simulated and modelled from the TanDEM-X data spotlight with VV polarization. The simulation has been done along the range direction. The simulated velocity is taken across the location of The Aquadopp® 2MHz current meter (Figure 3). The test area is shown in Figure 1 which is inshore the coastal water of the Malacca Straits, Malaysia. Figure 4 shows TanDEM-X data cross section values increased with the increasing of the incidence angle where the backscatter value is raised to -10 dB. The second curve is the result of the Doppler shift frequency. The curve shows that the Doppler shift frequency values were fluctuated with value decreasing in the onshore 2km to 5 km. The frequency value in the nearshore area was extremely low with 0.1 m/s. The spectra peak of Doppler frequency is 0.04 with range frequency of -200 Hz. The average of the Doppler shift frequency in the onshore area was 0.01 Hz. This could be due to low tide level of 0.3 m which was observed during in-situ data collection. The TanDEM-X data with X-band of the spotlight product which derived from the strip-map mode has utilized in this study. The Figure 4 indicates the results that are retrieved from Hopfield rule and Pareto rule. It is attention-grabbing realize that Pareto algorithmic rule has found the most effective solution for sea surface current pattern as compared to Hopfield neural network (Figure 4b). The morphology of ocean surface current structures are well known exploitation Pareto algorithmic rule. Indeed, random generation of 1000 iterations at intervals 3 min are needed to realize the performance of the Pareto algorithmic program. Clearly, Pareto algorithm delivered a spatial variation of surface current from onshore to offshore. Onshore surface current is dominated by maximum value of 0.12 m/s while the offshore surface currents have maximum value of 0.2 m/s.  Figure 5 illustrates how the correlation coefficient changes as the linear relationship between the two variables is altered. While in regression the emphasis is on predicting one variable from the other, in correlation the emphasis is on the degree to which a linear model may describe the relationship between two variables. Clearly, there is a good relationship between the two variables with R² of 0.75. However, this relationship is not perfect, but seems to have a positive linear relationship, and corresponds to what one would expect when considering two variables correlated and following the assumption of normality. Table 1 delivers the accuracy of this study. Clearly, the Pareto optimal solution has an excellent performance than Hopfield algorithm, with lowest P value of 0.00006 and RMSE of ±0.009 and highest r² of 0.75. Consistent with Marghany and Mansor [12] and Marghany [19], the Hopfield neural network is anticipated as optimization tool to reduce the impact of the Doppler nonlinearity in the SAR data. Subsequently, multi-objective optimization is fairly deliberated as attaining a vector of verdict variables satisfying constraints to offer precise to all objective functions. This confirms study of Marghany and Mansor [12]. Additionally, the multi-objective optimisation via Pareto dominance acquires a particular curve that reduces the inconsistency between the certain ocean surface current from TanDEMX data and in situ measurements. In this understanding, the new approach supported TanDEMX data and as a result the multi-objective optimisation via Pareto Dominance, know how to minimalize the number of the residual faults for retrieving ocean surface current from TanDEMX data and delivers precise ocean surface current pattern spatial variation. This work recommends the work done by Atashkari et al., [22] and Marghany [19]. Moreover, it is suggested to exploit the time series of TanDEMX satellite data for watching the daily coastal current and its seasonal variations. This work initiated a new approach for sea surface current studies along Malaysian coastal waters. This is first experimental operated TanDEM-X satellite not only in Malaysia but in all the South-east Asian coastal waters. Two approaches are prescribed: (i) Hopfield neural network rule; and (ii) Pareto optimum resolution. The study shows that the Pareto optimum resolution has highest performance than Hopfield neural network rule with lowest RMSE of ±0.08. Further, Pareto optimum resolution can verify the ocean surface current pattern variation using TanDEMX data. In conclusion, TanDEMX data reveals a superb guarantees for retrieving ocean surface current with X-band with VV polarization.