On the extension of multidimensional speckle noise model from single-look to multilook SAR imagery

Speckle noise represents one of the major problems when synthetic aperture radar (SAR) data are considered. Despite the fact that speckle is caused by the scattering process itself, it must be considered as a noise source due to the complexity of the scattering process. The presence of speckle makes data interpretation difficult, but it also affects the quantitative retrieval of physical parameters. In the case of one-dimensional SAR systems, speckle is completely determined by a multiplicative noise component. Nevertheless, for multidimensional SAR systems, speckle results from the combination of multiplicative and additive noise components. This model has been first developed for single-look data. The objective of this paper is to extend the single-look data model to define a multilook multidimensional speckle noise model. The asymptotic analysis of this extension, for a large number of averaged samples, is also considered to assess the model properties. Details and validation of the multilook multidimensional speckle noise model are provided both theoretically and by means of experimental SAR data acquired by the experimental synthetic aperture radar system, operated by the German Aerospace Center.Peer Reviewe

Coherence estimation in synthetic aperture radar data based on speckle noise modeling

In the past we proposed a multidimensional speckle noise model to which we now include systematic phase variation effects. This extension makes it possible to define what is believed to be a novel coherence model able to identify the different sources of bias when coherence is estimated on multidimensional synthetic radar aperture (SAR) data. On the one hand, low coherence biases are basically due to the complex additive speckle noise component of the Hermitian product of two SAR images. On the other hand, the availability of the coherence model permits us to quantify the bias due to topography when multilook filtering is considered, permitting us to establish the conditions upon which information may be estimated independently of topography. Based on the coherence model, two coherence estimation approaches, aiming to reduce the different biases, are proposed. Results with simulated and experimental polarimetric and interferometric SAR data illustrate and validate both, the coherence model and the coherence estimation algorithms.Peer Reviewe

Dimension in algebraic frames, II: Applications to frames of ideals in C(X)C(X)

summary:This paper continues the investigation into Krull-style dimensions in algebraic frames. Let $L$ be an algebraic frame. $\operatorname{dim}(L)$ is the supremum of the lengths $k$ of sequences $p_0< p_1< \cdots <p_k$ of (proper) prime elements of $L$. Recently, Th. Coquand, H. Lombardi and M.-F. Roy have formulated a characterization which describes the dimension of $L$ in terms of the dimensions of certain boundary quotients of $L$. This paper gives a purely frame-theoretic proof of this result, at once generalizing it to frames which are not necessarily compact. This result applies to the frame \Cal C_z(X) of all $z$-ideals of $C(X)$, provided the underlying Tychonoff space $X$ is Lindelöf. If the space $X$ is compact, then it is shown that the dimension of \Cal C_z(X) is at most $n$ if and only if $X$ is scattered of Cantor-Bendixson index at most $n+1$. If $X$ is the topological union of spaces $X_i$, then the dimension of \Cal C_z(X) is the supremum of the dimensions of the \Cal C_z(X_i). This and other results apply to the frame of all $d$-ideals \Cal C_d(X) of $C(X)$, however, not the characterization in terms of boundaries. An explanation of this is given within, thus marking some of the differences between these two frames and their dimensions