We propose a novel despeckling algorithm for synthetic aperture radar (SAR) images based on the concepts of nonlocal filtering and wavelet-domain shrinkage. It follows the structure of the block-matching 3-D algorithm, recently proposed for additive white Gaussian noise denoising, but modifies its major processing steps in order to take into account the peculiarities of SAR images. A probabilistic similarity measure is used for the block-matching step, while the wavelet shrinkage is developed using an additive signal-dependent noise model and looking for the optimum local linear minimum-mean-square-error estimator in the wavelet domain. The proposed technique compares favorably w.r.t. several state-of-the-art reference techniques, with better results both in terms of signal-to-noise ratio (on simulated speckled images) and of perceived image quality.

A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage

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.

A Tutorial on Speckle Reduction in Synthetic Aperture Radar Images

Speckle noise is an inherent problem in coherent imaging systems like synthetic aperture radar. It creates strong intensity fluctuations and hampers the analysis of images and the estimation of local radiometric, polarimetric or interferometric properties. SAR processing chains thus often include a multi-looking (i.e., averaging) filter for speckle reduction, at the expense of a strong resolution loss. Preservation of point-like and fine structures and textures requires to adapt locally the estimation. Non-local means successfully adapt smoothing by deriving data-driven weights from the similarity between small image patches. The generalization of non-local approaches offers a flexible framework for resolution-preserving speckle reduction. We describe a general method, NL-SAR, that builds extended non-local neighborhoods for denoising amplitude, polarimetric and/or interferometric SAR images. These neighborhoods are defined on the basis of pixel similarity as evaluated by multi-channel comparison of patches. Several non-local estimations are performed and the best one is locally selected to form a single restored image with good preservation of radar structures and discontinuities. The proposed method is fully automatic and handles single and multi-look images, with or without interferometric or polarimetric channels. Efficient speckle reduction with very good resolution preservation is demonstrated both on numerical experiments using simulated data, airborne and spaceborne radar images. The source code of a parallel implementation of NL-SAR is released with the paper.

/pdf/nl-sar-a-unified-nonlocal-framework-for-resolution-3baw4qqdee.pdf

NL-SAR: A Unified Nonlocal Framework for Resolution-Preserving (Pol)(In)SAR Denoising

1. Introduction.- 1 Fundamentals of the Theory of Digital Signal Processing.- 2. Elements of Signal Theory.- 2.1 Signals as Mathematical Functions.- 2.2 Signal Space.- 2.3 The Most Common Systems of Basis Functions.- 2.3.1 Impulse Basis Functions.- 2.3.2 Harmonic Functions.- 2.3.3 Walsh Functions.- 2.3.4 Haar Functions.- 2.3.5 Sampling Functions.- 2.4 Continuous Representations of Signals.- 2.5 Description of Signal Transformations.- 2.5.1 Linear Transformations.- 2.5.2 Nonlinear Element-by-Element Transforms.- 2.6 Representation of Linear Transformations with Respect to Discrete Bases.- 2.6.1 Representation Using Vector Responses.- 2.6.2 Matrix Representations.- 2.6.3 Representation of Operators by Means of Their Eigenfunctions and Eigenvalues.- 2.7 Representing Operator with Respect to Continuous Bases.- 2.7.1 Operator Kernel.- 2.7.2 Description in Terms of Impulse Responses.- 2.7.3 Description Using Frequency Transfer Functions.- 2.7.4 Description with Input and Output Signals Referred to Different Bases.- 2.7.5 Description Using Eigenfunctions.- 2.8 Examples of Linear Operators.- 2.8.1 Shift-Invariant Filters.- 2.8.2 The Identity Operator.- 2.8.3 Shi ft Operator.- 2.8.4 Sampling Oparator.- 2.8.5 Gating Operator (Multiplier).- 3. Discretization and Quantization of Signals.- 3.1 Generalized Quantization.- 3.2 Concepts of Discretization and Element-by-Element Quantization.- 3.2.1 Discretization.- 3.2.2 Element-by-Element Quantization.- 3.3 The Sampling Theorem.- 3.4 Sampling Theory for Two-Dimensional Signals.- 3.5 Errors of Discretization and Restoration of Signals in Sampling Theory.- 3.6 Other Approaches to Discretization.- 3.7 Optimal Discrete Representation and Dimensionality of Signals.- 3.8 Element-by-Element Quantization.- 3.9 Examples of Optimum Quantization.- 3.9.1 Example: The Threshold Metric.- 3.9.2 Example: Power Criteria for the Absolute Value of the Quantization Error.- 3.9.3 Example: Power Criteria for the Relative Quantization Error.- 3.10 Quantization in the Presence of Noise. Quantization and Representation of Numbers in Digital Processors.- 3.11 Review of Picture-Coding Methods.- 4. Discrete Representations of Linear Transforms.- 4.1 Problem Formulation and General Approach.- 4.2 Discrete Representation of Shift-Invariant Filters for Band-Limited Signals.- 4.3 Digital Filters.- 4.4 Transfer Functions and Impulse Responses of Digital Filters.- 4.5 Boundary Effects in Digital Filtering.- 4.6 The Discrete Fourier Transform (DFT).- 4.7 Shifted, Odd and Even DFTs.- 4.8 Using Discrete Fourier Transforms.- 4.8.1 Calculating Convolutions.- 4.8.2 Signal Interpolation.- 4.9 Walsh and Similar Transforms.- 4.10 The Haar Tansform. Addition Elements of Matrix Calculus.- 4.11 Other Orthogonal Tansforms. General Representations. Review of Applications.- 5. Linear Transform Algorithms.- 5.1 Fast Algorithms of Discrete Orthogonal Transforms.- 5.2 Fast Haar Transform (FHT) Algorithms.- 5.3 Fast Walsh Transform (FWT) Algorithms.- 5.4 Fast Discrete Fourier Transform (FFT) Algorithms.- 5.5 Review of Other Fast Algorithms. Features of Two-Dimensional Transforms.- 5.5.1 Truncated FFT and FWT Algorithms.- 5.5.2 Transition Matrices Between Various Transforms.- 5.5.3 Calculation of Two-Dimensional Transforms.- 5.6 Combined DFT Algorithms.- 5.6.1 Combined DFT Algorithms of Real Sequences.- 5.6.2 Combined SDFT (1/2, 0) Algorithms of Even and Real Even Sequences.- 5.7 Recursive DFT Algorithms.- 5.8 Fast Algorithms for Calculating the DFT and Signal Convolution with Decreased Multiplication.- 6. Digital Statistical Methods.- 6.1 Principles of the Statistical Description of Pictures.- 6.2 Measuring the Grey-Level Distribution.- 6.2.1 Step Smoothing.- 6.2.2 Smoothing by Sliding Summation.- 6.2.3 Smoothing with Orthogonal Transforms.- 6.3 The Estimation of Correlation Functions and Spectra.- 6.3.1 Averaging Local Spectra.- 6.3.2 Masking (Windowing) the Process by Smooth Functions.- 6.3.3 Direct Smoothing of Spectra.- 6.4 Generating Pseudorandom Numbers.- 6.5 Measuring Picture Noise.- 6.5.1 The Prediction Method.- 6.5.2 The Voting Method.- 6.5.3 Measuring the Variance and the Auto-Correlation Function of Additive Wideband Noise.- 6.5.4 Evaluation of the Intensity and Frequency of the Harmonic Components of Periodic Interference and Other Types of Interference with Narrow Spectra.- 6.5.5 Evaluation of the Parameters of Pulse Noise, Quantization Noise and Strip-Like Noise.- 2 Picture Processing.- 7. Correcting Imaging Systems.- 7.1 Problem Formulation.- 7.2 Suppression of Additive Noise by Linear Filtering.- 7.3 Filtering of Pulse Interference.- 7.4 Correction of Linear Distortion.- 7.5 Correction of Amplitude Characteristics.- 8. Picture Enhancement and Preparation.- 8.1 Preparation Problems and Visual Analysis of Pictures.- 8.1.1 Feature Processing.- 8.1.2 Geometric Transformations.- 8.2 Adaptive Quantization of Modes.- 8.3 Preparation by Nonlinear Transformation of the Video Signal Scale.- 8.4 Linear Preparation Methods.- 8.5 Methods of Constructing Graphical Representation: Computer Graphics.- 8.6 Geometric Picture Transformation.- 8.6.1 Bilinear Interpolation.- 8.6.2 Interpolation Using DFT and SDFT.- 9. Measuring the Coordinates of Objects in Pictures.- 9.1 Problem Formulation.- 9.2 Localizing a Precisely Known Object in a Spatially Homogeneous Picture.- 9.3 Uncertainty in the Object and Picture Inhomogeneity. Localization in "Blurred" Pictures.- 9.3.1 "Exhaustive" Estimator.- 9.3.2 Estimator Seeking an Averaged Object.- 9.3.3 Adjustable Estimator with Fragment-by Fraament Optimal Fi1tering.- 9.3.4 Non-Adjustable Estimator.- 9.3.5 Localization in Blurred and Noisy Pictures.- 9.4 Optimal Localization and Picture Contours. Choice of Reference Objects.- 9.5 Algorithm for the Automatic Detection and Extraction of Bench-Marks in Aerial and Space Photographs.- 10-Conclusion.- References.

Digital picture processing : an introduction

Synthetic aperture radar (SAR) images are often contaminated by a multiplicative noise known as speckle Speckle makes the processing and interpretation of SAR images difficult We propose a deep-learning-based approach called, image despeckling convolutional neural network (ID-CNN), for automatically removing speckle from the input noisy images In particular, ID-CNN uses a set of convolutional layers along with batch normalization and rectified linear unit activation function and a componentwise division residual layer to estimate speckle and it is trained in an end-to-end fashion using a combination of Euclidean loss and total variation loss Extensive experiments on synthetic and real SAR images show that the proposed method achieves significant improvements over the state-of-the-art speckle reduction methods

SAR Image Despeckling Using a Convolutional Neural Network

Objective performance assessment is a key enabling factor for the development of better and better image processing algorithms. In synthetic aperture radar (SAR) despeckling, however, the lack of speckle-free images precludes the use of reliable full-reference measures, leaving the comparison among competing techniques on shaky bases. In this paper, we propose a new framework for the objective (quantitative) assessment of SAR despeckling techniques, based on simulation of SAR images relevant to canonical scenes. Each image is generated using a complete SAR simulator that includes proper physical models for the sensed surface, the scattering, and the radar operational mode. Therefore, in the limits of the simulation models, the employed simulation procedure generates reliable and meaningful SAR images with controllable parameters. Through simulating multiple SAR images as different instances relevant to the same scene we can therefore obtain, a true multilook full-resolution SAR image, with an arbitrary number of looks, thus generating (by definition) the closest object to a clean reference image. Based on this concept, we build a full performance assessment framework by choosing a suitable set of canonical scenes and corresponding objective measures on the SAR images that consider speckle suppression and feature preservation. We test our framework by studying the performance of a representative set of actual despeckling algorithms; we verify that the quantitative indications given by numerical measures are always fully consistent with the rationale specific of each despeckling technique, strongly agrees with qualitative (expert) visual inspections, and provide insight into SAR despeckling approaches.

Benchmarking Framework for SAR Despeckling

Speckle reduction is a key step in several SAR image processing procedures. In this paper, a new despeckling technique based on the “nonlocal” denoising filter BM3D [1] is presented. The filter has been modified in order to take into account SAR image characteristics. The experimental results, conducted on both synthetic and real SAR images, confirm the potential of the proposed approach.

/pdf/a-nonlocal-approach-for-sar-image-denoising-47t9v8fq80.pdf

A nonlocal approach for SAR image denoising

In this work we propose a modified version of the BM3D algorithm recently introduced by Dabov et al. [1] for the denoising of images corrupted by additive white Gaussian noise. The original technique performs a multipoint filtering, where the nonlocal approach is combined with the wavelet shrinkage of a 3D cube composed by similar patches collected by means of block-matching. Our improvement concerns the thresholding of wavelet coefficients, which are subject to a different shrinkage depending on their level of sparsity. The modified algorithm is more robust with respect to block matching errors, especially when noise is high, as proved by experimental results on a large set of natural images.

Sigmoid shrinkage for BM3D denoising algorithm

We propose a new framework for the quantitative assessment of SAR despeckling techniques, based on physical-level simulation of SAR images corresponding to canonical scenes. Thanks to the simulator, we can generate multiple SAR images of the same scene which differ only in the speckle content, and, hence, a true multilook SAR image, with an arbitrarily large number of looks, to use as “speckle-free” reference. Based on this concept, we select a small set of canonical scenes and, for each of them, a suitable set of objective measures which account for speckle suppression and image feature preservation. We gain insight into the system reliability by comparing the indications it gives for some sample despeckling filters with those obtained by expert visual inspection of the filtered images.

/pdf/sar-image-simulation-for-the-assessment-of-despeckling-k2r6breqbm.pdf

Mariana Poderico

Papers

A Nonlocal SAR Image Denoising Algorithm Based on LLMMSE Wavelet Shrinkage

Benchmarking Framework for SAR Despeckling

A nonlocal approach for SAR image denoising

Sigmoid shrinkage for BM3D denoising algorithm

SAR image simulation for the assessment of despeckling techniques