Bayesian Techniques in Remote Sensing

Pierdicca, Nazzareno

doi:10.1007/0-306-48150-2_4

Cited by 4 publications

(5 citation statements)

References 10 publications

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“…The Bayesian theory of parameter estimation [14, 15] has been considered in this work to infer u 19 and φ . It focuses on the probability density function (pdf) p ( x | Y ) of a certain parameter x conditioned to the vector of measurements Y .…”

Section: Wind Vector Retrievalmentioning

confidence: 99%

“…It is well known that, if we compute the expected value of p ( u 19 | Y ) we obtain a MV estimator, which minimizes the root mean square (rms) retrieval error (and is also called Minimum Mean Square Estimator) [14, 15]. The wind speed estimate is therefore given by:

{\overset{u}{true}}_{19} = \int_{D} u_{19} p (u_{19} ∣ Y) d u_{19} = \frac{\int_{D} u_{19} p (Y ∣ u_{19}) p (u_{19}) d u_{19}}{\int_{D} p (Y ∣ u_{19}) p (u_{19}) d u_{19}}

where Y =[ T Bh 10 T Bv 10 T Bh 18 T Bv 18 T Bh 23 T Bv 23 T Bh 37 T Bv 37 ] T (superscript T indicates transposition) and D is the integral domain of u 19 , that we have chosen equal to [0-25 m/s], thus assuming that the pdf of wind speed p ( u 19 ) is zero outside this interval.…”

Section: Wind Vector Retrievalmentioning

confidence: 99%

“…It is worth noting that, since the Weibull distribution is not a symmetric pdf, the MAP estimate differs from the MV one. Using the pdf s represented by equations (3) and (4), the MAP criterion reduces to minimize the following cost function with respect to u 19 [14, 15]:

d_{MAP} (u_{19}) = {[{boldY}_{meas} - Y (u_{19})]}^{T} {boldC}_{normalY}^{- 1} [{boldY}_{meas} - Y (u_{19})] - 2 (k - 1) ln (u_{19} / c) + 2 {(u_{19} / c)}^{k}

…”

Section: Wind Vector Retrievalmentioning

confidence: 99%

“…Different Bayesian techniques [14, 15], such as Minimum Variance (MV), Maximum Likelihood (ML) and Maximum Posterior Probability (MAP) criteria have been used. Furthermore, for the latter two methods, an iterative inversion of the trained NN-based forward model has been performed and different methods to minimize the cost function, such as the common Gradient Descent and the more sophisticated Simulated Annealing, have been used.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Coupling a Neural Network-Based forward Model and a Bayesian Inversion Approach to Retrieve Wind Field from Spaceborne Polarimetric Radiometers

Pulvirenti

Pierdicca

Marzano

2008

Sensors

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A simulation study to assess the potentiality of sea surface wind vector estimation based on the approximation of the forward model through Neural Networks and on the Bayesian theory of parameter estimation is presented. A polarimetric microwave radiometer has been considered and its observations have been simulated by means of the two scale model. To perform the simulations, the atmospheric and surface parameters have been derived from ECMWF analysis fields. To retrieve wind speed, Minimum Variance (MV) and Maximum Posterior Probability (MAP) criteria have been used while, for wind direction, a Maximum Likelihood (ML) criterion has been exploited. To minimize the cost function of MAP and ML, conventional Gradient Descent method, as well as Simulated Annealing optimization technique, have been employed. Results have shown that the standard deviation of the wind speed retrieval error is approximately 1.1 m/s for the best estimator. As for the wind direction, the standard deviation of the estimation error is less than 13° for wind speeds larger than 6 m/s. For lower wind velocities, the wind direction signal is too weak to ensure reliable retrievals. A method to deal with the non-uniqueness of the wind direction solution has been also developed. A test on a case study has yielded encouraging results.

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Section: Wind Vector Retrievalmentioning

confidence: 99%

{\overset{u}{true}}_{19} = \int_{D} u_{19} p (u_{19} ∣ Y) d u_{19} = \frac{\int_{D} u_{19} p (Y ∣ u_{19}) p (u_{19}) d u_{19}}{\int_{D} p (Y ∣ u_{19}) p (u_{19}) d u_{19}}

Section: Wind Vector Retrievalmentioning

confidence: 99%

d_{MAP} (u_{19}) = {[{boldY}_{meas} - Y (u_{19})]}^{T} {boldC}_{normalY}^{- 1} [{boldY}_{meas} - Y (u_{19})] - 2 (k - 1) ln (u_{19} / c) + 2 {(u_{19} / c)}^{k}

…”

Section: Wind Vector Retrievalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Coupling a Neural Network-Based forward Model and a Bayesian Inversion Approach to Retrieve Wind Field from Spaceborne Polarimetric Radiometers

Pulvirenti

Pierdicca

Marzano

2008

Sensors

Self Cite

View full text Add to dashboard Cite

show abstract

“…Pixel-based classification methods mainly analyze differences in the spectral information of pixels for classification. Some simpler machine-learning methods are being trialed that do not require many input features [5][6][7]; they are suitable for low-and medium-resolution remote-sensing images. For example, Fei Yuan et al used the maximum likelihood method to classify most of the Minnesota urban area pixel by pixel in tandem with multi-temporal Landsat series data, and quantified the land-cover change patterns of the city with an overall classification accuracy between 80% and 90% [8].…”

Section: Introductionmentioning

confidence: 99%

Production–Living–Ecological Spatial Function Identification and Pattern Analysis Based on Multi-Source Geographic Data and Machine Learning

Bu,

Fu,

Jiang

et al. 2023

Land

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Land use cannot be simply understood as land cover. The same land may carry different functions, such as production, living, and ecological applications; the dominant function of land will affect and restrict other uses. Disorderly urbanization and industrialization have led to an intensification of conflicts among the production, living, and ecological functions of land, which is a major constraint on regional sustainable development. This paper took the perspective of land-use function and used multi-source data such as Sentinel remote-sensing imagery, VIIRS night-time light data, and POIs to classify land-use functions on a large scale in the Beijing–Tianjin–Hebei (BTH) urban agglomeration. The specific research process was as follows. Firstly, the BTH region was multi-scale-segmented based on Sentinel remote-sensing data. Then, the spectral, texture, shape, and socio-economic features of each small area after segmentation were extracted. Moreover, a PLES land-use classification system oriented towards land-use function was established, and a series of representative samples were selected. Subsequently, a random forest model was trained using these samples; then, the trained model was used for the large-scale analysis of land use in the entire BTH region. Finally, the spatial distribution patterns and temporal–spatial evolution characteristics of PLES in the BTH region from 2016 to 2021 were analyzed from the macro level to the micro level.

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Intercomparison of inversion algorithms to retrieve rain rate from SSM/I by using an extended validation set over the Mediterranean area

Pierdicca

Pulvirenti

Marzano

et al. 2004

IEEE Trans. Geosci. Remote Sensing

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The capability of some inversion algorithms to estimate surface rain rate at the midlatitude basin scale from the Special Sensor Microwave Imager (SSM/I) data is analyzed. For this purpose, an extended database has been derived from coincident SSM/I images and half-hourly rain rate data obtained from a rain gauge network, placed along the Tiber River basin in Central Italy, during nine years (from 1992 to 2000). The database has been divided in a training set, to calibrate the empirical algorithms, and in a validation one, to compare the results of the considered techniques. The proposed retrieval methods are based on both empirical and physical approaches. Among the empirical methods, a regression, an artificial feedforward neural network, and a Bayesian maximum a posteriori (MAP) inversion have been considered. Three algorithms available in the literature are also included as benchmarks. As physical algorithms, the MAP method and the minimum mean square estimator have been used. Moreover, in order to test the behavior of the algorithms with different kinds of precipitation, a classification of rainy events, based on some statistical parameters derived from rain gauge measurements, has been performed. From this classification, an attempt to identify the type of event from radiometric data has been carried out. The purposes of this paper are to determine whether the use of an extended training set, referred to a limited geographical area, can improve the SSM/I skill in rain detection and estimation and, mainly, to confirm the validity of the physical approach adopted in previous works. It will be shown that, among all the estimators, the neural network presents the best performances and that the physical techniques provide results only slightly worse than those given by empirical methods, but with the well-known advantage of an easy application to different geographical zones and different sensors

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Bayesian Techniques in Remote Sensing

Cited by 4 publications

References 10 publications

Coupling a Neural Network-Based forward Model and a Bayesian Inversion Approach to Retrieve Wind Field from Spaceborne Polarimetric Radiometers

Coupling a Neural Network-Based forward Model and a Bayesian Inversion Approach to Retrieve Wind Field from Spaceborne Polarimetric Radiometers

Production–Living–Ecological Spatial Function Identification and Pattern Analysis Based on Multi-Source Geographic Data and Machine Learning

Intercomparison of inversion algorithms to retrieve rain rate from SSM/I by using an extended validation set over the Mediterranean area

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