Regularizing kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval using smoothness constraint

[1] In this paper, we consider the problem how to solve the kernel-based bidirectional reflectance distribution function (BRDF) models for the retrieval of land surface albedos. The above problem is an ill-posed inverse problem. We will employ a new regularization technique to alleviate the ill-posedness. The Tikhonov regularization has been discussed for BRDF model inversion, however, much study has to be done before applying it in practice (Wang et al., 2007). In this paper, we thoroughly investigate this method, and propose a discrepancy method for a posteriori choice of the regularization parameter and several options for choosing the regularizing stabilizer. The proposed method can alleviate difficulties in numerical computation when the discrete kernel is badly conditioned and the number of observations is poor. Applying the proposed method can always find a set of suitable BRDF coefficients for poorly sampled data. The proposed method is an improvement of the traditional least squares error algorithm in AMBRALS (Algorithm for MODIS (Moderate Resolution Imaging Spectroradiometer) Bidirectional Reflectance Anisotropies of the Land Surface), see Strahler et al. (1999), and is comparable to the regularized singular value decomposition method developed by Wang et al. (2007). Hence the proposed method can be considered as a supplemental algorithm for the robust estimation of the land surface BRDF/albedos. Numerical performance is given in this paper for the widely used field-based 18 data sets among the 73 data sets (see Li et al., 2001) and for the satellite data.

[1]  Thomas F. Eck,et al.  Reflectance anisotropy for a spruce-hemlock forest canopy , 1994 .

[2]  Michel M. Verstraete,et al.  Potential and limitations of information extraction on the terrestrial biosphere from satellite remote sensing , 1996 .

[3]  Alan H. Strahler,et al.  Validation of Kernel-Driven Semiempirical Models for the Surface Bidirectional Reflectance Distribution Function of Land Surfaces , 1997 .

[4]  Yanning Guan,et al.  Regularized kernel-based BRDF model inversion method for ill-posed land surface parameter retrieval , 2007 .

[5]  Compton J. Tucker,et al.  Directional reflectance factor distributions for cover types of Northern Africa , 1985 .

[6]  A. Tikhonov,et al.  Numerical Methods for the Solution of Ill-Posed Problems , 1995 .

[7]  Retrieving albedo in small sample size , 1998, IGARSS '98. Sensing and Managing the Environment. 1998 IEEE International Geoscience and Remote Sensing. Symposium Proceedings. (Cat. No.98CH36174).

[8]  Yanfei Wang,et al.  Regularized inversion method for retrieval of aerosol particle size distribution function in W(1,2) space. , 2006, Applied optics.

[9]  D. W. Deering,et al.  Spectral Bidirectional and Hemispherical Reflectance Characteristics of Selected Sites in the Streletskaya Steppe , 1992, [Proceedings] IGARSS '92 International Geoscience and Remote Sensing Symposium.

[10]  J. Privette,et al.  Estimating spectral albedo and nadir reflectance through inversion of simple BRDF models with AVHRR/MODIS‐like data , 1997 .

[11]  A. Strahler,et al.  On the derivation of kernels for kernel‐driven models of bidirectional reflectance , 1995 .

[12]  Shiqian Ma,et al.  BRDF Model Inversion of Multiangular Remote Sensing : Ill-posedness and the Interior Point Solution Method , 2005 .

[13]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[14]  J. Roujean,et al.  A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data , 1992 .

[15]  C. Atzberger.  Object-based retrieval of biophysical canopy variables using artificial neural nets and radiative transfer models , 2004 .

[16]  Jindi Wang,et al.  A priori knowledge accumulation and its application to linear BRDF model inversion , 2001 .

[17]  Yanfei Wang,et al.  Fast realization algorithms for determining regularization parameters in linear inverse problems , 2001 .

[18]  Jean-Louis Roujean,et al.  Land surface albedo retrieval via kernel-based BRDF modeling: II. An optimal design scheme for the angular sampling , 2003 .

[19]  Thomas F. Eck,et al.  Temporal attributes of the bidirectional reflectance for three boreal forest canopies , 1995, 1995 International Geoscience and Remote Sensing Symposium, IGARSS '95. Quantitative Remote Sensing for Science and Applications.

[20]  Jean-Louis Roujean,et al.  Development of an operational procedure to estimate surface albedo from the SEVIRI/MSG observing system by using polder BRDF measurements. II. Comparison of several inversion techniques and uncertainty in albedo estimates , 2003 .

[21]  Jean-Louis Roujean,et al.  Data quality control and accumulation of information corresponding to the IGBP land cover classes , 2003 .

[22]  Jean-Louis Roujean,et al.  Land surface albedo retrieval via kernel-based BRDF modeling: I. Statistical inversion method and model comparison , 2003 .

[23]  Donald W. Deering,et al.  Shinnery oak bidirectional reflectance properties and canopy model inversion , 1992, IEEE Trans. Geosci. Remote. Sens..

[24]  Ross Nelson,et al.  Directional Reflectance Distributions of a Hardwood and Pine Forest Canopy , 1986, IEEE Transactions on Geoscience and Remote Sensing.

[25]  A. Tarantola.  Inverse problem theory : methods for data fitting and model parameter estimation , 1987 .