Fabrizio Argenti

Speckle removal from SAR images in the undecimated wavelet domain

Speckle reduction is approached as a minimum mean-square error (MMSE) filtering performed in the undecimated wavelet domain by means of an adaptive rescaling of the detail coefficients, whose amplitude is divided by the variance ratio of the noisy coefficient to the noise-free one. All the above quantities are analytically calculated from the speckled image, the variance and autocorrelation of the fading variable, and the wavelet filters only, without resorting to any model to describe the underlying backscatter. On the test image Lena corrupted by synthetic speckle, the proposed method outperforms Kuans local linear MMSE filtering by almost 3-dB signal-to-noise ratio. When true synthetic aperture radar (SAR) images are concerned, empirical criteria based on distributions of multiscale local coefficient of variation, calculated in the undecimated wavelet domain, are introduced to mitigate the rescaling of coefficients in highly heterogeneous areas where the speckle does not obey a fully developed model, to avoid blurring strong textures and point targets. Experiments carried out on widespread test SAR images and on a speckled mosaic image, comprising synthetic shapes, textures, and details from optical images, demonstrate that the visual quality of the results is excellent in terms of both background smoothing and preservation of edge sharpness, textures, and point targets. The absence of decimation in the wavelet decomposition avoids typical impairments often introduced by critically subsampled wavelet-based denoising.

A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images

Speckle is a granular disturbance, usually modeled as a multiplicative noise, that affects synthetic aperture radar (SAR) images, as well as all coherent images. Over the last three decades, several methods have been proposed for the reduction of speckle, or despeckling, in SAR images. Goal of this paper is making a comprehensive review of despeckling methods since their birth, over thirty years ago, highlighting trends and changing approaches over years. The concept of fully developed speckle is explained. Drawbacks of homomorphic filtering are pointed out. Assets of multiresolution despeckling, as opposite to spatial-domain despeckling, are highlighted. Also advantages of undecimated, or stationary, wavelet transforms over decimated ones are discussed. Bayesian estimators and probability density function (pdf) models in both spatial and multiresolution domains are reviewed. Scale-space varying pdf models, as opposite to scale varying models, are promoted. Promising methods following non-Bayesian approaches, like nonlocal (NL) filtering and total variation (TV) regularization, are reviewed and compared to spatial- and wavelet-domain Bayesian filters. Both established and new trends for assessment of despeckling are presented. A few experiments on simulated data and real COSMO-SkyMed SAR images highlight, on one side the costperformance tradeoff of the different methods, on the other side the effectiveness of solutions purposely designed for SAR heterogeneity and not fully developed speckle. Eventually, upcoming methods based on new concepts of signal processing, like compressive sensing, are foreseen as a new generation of despeckling, after spatial-domain and multiresolution-domain methods.

Multiresolution MAP Despeckling of SAR Images Based on Locally Adaptive Generalized Gaussian pdf Modeling

In this paper, a new despeckling method based on undecimated wavelet decomposition and maximum a posteriori (MAP) estimation is proposed. Such a method relies on the assumption that the probability density function (pdf) of each wavelet coefficient is generalized Gaussian (GG). The major novelty of the proposed approach is that the parameters of the GG pdf are taken to be space-varying within each wavelet frame. Thus, they may be adjusted to spatial image context, not only to scale and orientation. Since the MAP equation to be solved is a function of the parameters of the assumed pdf model, the variance and shape factor of the GG function are derived from the theoretical moments, which depend on the moments and joint moments of the observed noisy signal and on the statistics of speckle. The solution of the MAP equation yields the MAP estimate of the wavelet coefficients of the noise-free image. The restored SAR image is synthesized from such coefficients. Experimental results, carried out on both synthetic speckled images and true SAR images, demonstrate that MAP filtering can be successfully applied to SAR images represented in the shift-invariant wavelet domain, without resorting to a logarithmic transformation

Segmentation-Based MAP Despeckling of SAR Images in the Undecimated Wavelet Domain

In this paper, a novel despeckling algorithm based on undecimated wavelet decomposition and maximum a posteriori estimation is proposed. Such a method represents an improvement with respect to the filter presented by the authors, and it is based on the same conjecture that the probability density functions (pdfs) of the wavelet coefficients follow a generalized Gaussian (GG) distribution. However, the approach introduced here presents two major novelties: 1) theoretically exact expressions for the estimation of the GG parameters are derived: such expressions do not require further assumptions other than the multiplicative model with uncorrelated speckle, and hold also in the case of a strongly correlated reflectivity; 2) a model for the classification of the wavelet coefficients according to their texture energy is introduced. This model allows us to classify the wavelet coefficients into classes having different degrees of heterogeneity, so that ad hoc estimation approaches can be devised for the different sets of coefficients. Three different implementations, characterized by different approaches for incorporating into the filtering procedure the information deriving from the segmentation of the wavelet coefficients, are proposed. Experimental results, carried out on both artificially speckled images and true synthetic aperture radar images, demonstrate that the proposed filtering approach outperforms the previous filters, irrespective of the features of the underlying reflectivity.

Fast MAP Despeckling Based on Laplacian–Gaussian Modeling of Wavelet Coefficients

The undecimated wavelet transform and the maximum a posteriori probability (MAP) criterion have been applied to the problem of synthetic-aperture-radar image despeckling. The MAP solution is based on the assumption that wavelet coefficients have a known distribution. In previous works, the generalized Gaussian (GG) function has been successfully employed. Furthermore, despeckling methods can be improved by using a classification of wavelet coefficients according to their texture energy. A major drawback of using the GG distribution is the high computational cost since the MAP solution can be found only numerically. In this letter, a new modeling of the statistics of wavelet coefficients is proposed. Observations of the estimated GG shape parameters relative to the reflectivity and to the speckle noise suggest that their distributions can be approximated as a Laplacian and a Gaussian function, respectively. Under these hypotheses, a closed form solution of the MAP estimation problem can be achieved. As for the GG case, classification of wavelet coefficients according to their texture content may be exploited also in the proposed method. Experimental results show that the fast MAP estimator based on the Laplacian-Gaussian assumption and on the classification of coefficients reaches almost the same performances as the GG version in terms of speckle removal, with a gain in computational cost of about one order of magnitude.

Filterbanks design for multisensor data fusion

In this letter, we investigate the problem of fusion of data collected by sensors having different ground and wavelength resolutions. This is a typical problem encountered in the interpretation of remotely sensed images. The approach that is proposed here is based on the use of cosine-modulated uniform filter banks. We assume that the ratio of the sampling periods of the input data is not integer and show how to design the filter banks so that spectra from different signals can be integrated with a minimum distortion.

Identification of spatially filtered stimuli as function of the semantic category.

The different weight of spatial frequency content in the identification of visual objects was investigated. Subjects were required to identify spatially filtered pictures of animals, vegetables and nonliving objects, displayed at 9 resolution levels of filtering following a coarse-to-fine order. Results showed that spatial frequency content differentially affected the three categories of stimuli. Data suggested a different involvement of low and high spatial frequency channels in visual processing of objects in relation to the semantic category.

Wavelet and pyramid techniques for multisensor data fusion: a performance comparison varying with scale ratios

Goal of this paper is to provide a quantitative performance evaluation of multiresolution schemes capable to carry out feature-based fusion of data collected by multispectral and panchromatic imaging sensors having different spectral and ground resolutions. To this aim a set of quantitative parameters has been recently proposed. Both visual quality, regarded as contrast, presence of fine details, and absence of impairments and artifacts (e.g., blur, ringing), and spectral fidelity (i.e., preservation of spectral signatures) are concerned and embodied in the measurements. Out of the three methods compared, respectively based on highpass filtering (HPF), wavelet transform (WT), and generalized Laplacian pyramid (GLP), the latter two are far more efficient than the former, thus establishing the advantages for data fusion of a formally multiresolution analysis.

MMSE Filtering of generalised signal-dependent noise in spatial and shift-invariant wavelet domains

This paper addresses the topic of filtering digital images corrupted by signal-dependent additive white noise. The noise model is fully parametric to take into account different noise generation processes, like speckle and film-grain noise. Noise reduction is first approached as a linear minimum mean square error estimation in the spatial domain, thus extending previous results to the most general signal-dependent white noise model. The same type of estimation is performed in a shift-invariant wavelet domain, in which the absence of decimation of the decomposition avoids the typical ringing/aliasing impairments of critically subsampled wavelet-based denoising schemes. In the former case, filtered pixel values are obtained as adaptive combinations of raw and of local average values, driven by locally computed statistics. In the latter case, detail wavelet coefficients of the noisy image are adaptively shrunk by using local statistics derived from the noisy image and the noise model, before the denoised image is synthesised. Experimental results demonstrate that the proposed approaches take full advantage of the knowledge of the underlying noise model. Furthermore, the multiresolution algorithm steadily outperforms the spatial counterpart in terms of both SNR increment and of enhancement in visual quality.

Design of pseudo-QMF banks with rational sampling factors using several prototype filters

A method is presented for designing filter banks that allow the spectrum of a signal to be split into nonuniform width subbands. The filters of the banks are obtained by the cosine modulation of more than one prototype. The method uses the cancellation of the main aliasing component of the reconstructed signal. This imposes constraints on the prototypes that become dependent on each other. The procedure can be applied to banks with both integer and rational decimation factors. Numerical examples are presented to show the effectiveness of the design procedure.