Wavelet Operators and Multiplicative Observation Models -Application to SAR Image Time Series Analysis

International audienceThis paper first provides statistical properties of wavelet operators when the observation model can be seen as the product of a deterministic piece-wise regular function (signal) and a stationary random field (noise). This multiplicative observation model is analyzed in two standard frameworks by considering either (1) a direct wavelet transform of the model or (2) a log-transform of the model prior to wavelet decomposition. The paper shows that, in Framework (1), wavelet coefficients of the time series are affected by intricate correlation structures which blur signal singularities. Framework (2) is shown to be associated with a multiplicative (or geometric) wavelet transform and the multiplicative interactions between wavelets and the model highlight both sparsity of signal changes near singularities (dominant coefficients) and decorre-lation of speckle wavelet coefficients. The paper then derives that, for time series of synthetic aperture radar data, geometric wavelets represent a more intuitive and relevant framework for the analysis of smooth earth fields observed in the presence of speckle. From this analysis, the paper proposes a fast-and-concise geometric wavelet based method for joint change detection and regularization of synthetic aperture radar image time series. In this method, geometric wavelet details are first computed with respect to the temporal axis in order to derive generalized-ratio change-images from the time series. The changes are then enhanced and speckle is attenuated by using spatial block sigmoid shrinkage. Finally, a regularized time series is reconstructed from the sigmoid shrunken change-images. Some applications highlight relevancy of the method for the analysis of SENTINEL-1A and TerraSAR-X image time series over Chamonix-Mont-Blanc

Wavelet Operators and Multiplicative Observation Models - Application to Change-Enhanced Regularization of SAR Image Time Series

This paper first provides statistical properties of wavelet operators when the observation model can be seen as the product of a deterministic piecewise regular function (signal) and a stationary random field (noise). This multiplicative observation model is analyzed in two standard frameworks by considering either (1) a direct wavelet transform of the model or (2) a log-transform of the model prior to wavelet decomposition. The paper shows that, in Framework (1), wavelet coefficients of the time series are affected by intricate correlation structures which affect the signal singularities. Framework (2) is shown to be associated with a multiplicative (or geometric) wavelet transform and the multiplicative interactions between wavelets and the model highlight both sparsity of signal changes near singularities (dominant coefficients) and decorrelation of speckle wavelet coefficients. The paper then derives that, for time series of synthetic aperture radar data, geometric wavelets represent a more intuitive and relevant framework for the analysis of smooth earth fields observed in the presence of speckle. From this analysis, the paper proposes a fast-and-concise geometric wavelet based method for joint change detection and regularization of synthetic aperture radar image time series. In this method, geometric wavelet details are first computed with respect to the temporal axis in order to derive generalized-ratio change-images from the time series. The changes are then enhanced and speckle is attenuated by using spatial bloc sigmoid shrinkage. Finally, a regularized time series is reconstructed from the sigmoid shrunken change-images. An application of this method highlights the relevancy of the method for change detection and regularization of SENTINEL-1A dual-polarimetric image time series over Chamonix-Mont-Blanc test site

"Rewiring" Filterbanks for Local Fourier Analysis: Theory and Practice

This article describes a series of new results outlining equivalences between certain "rewirings" of filterbank system block diagrams, and the corresponding actions of convolution, modulation, and downsampling operators. This gives rise to a general framework of reverse-order and convolution subband structures in filterbank transforms, which we show to be well suited to the analysis of filterbank coefficients arising from subsampled or multiplexed signals. These results thus provide a means to understand time-localized aliasing and modulation properties of such signals and their subband representations--notions that are notably absent from the global viewpoint afforded by Fourier analysis. The utility of filterbank rewirings is demonstrated by the closed-form analysis of signals subject to degradations such as missing data, spatially or temporally multiplexed data acquisition, or signal-dependent noise, such as are often encountered in practical signal processing applications

Multiplicative Noise Removal Using Variable Splitting and Constrained Optimization

Multiplicative noise (also known as speckle noise) models are central to the study of coherent imaging systems, such as synthetic aperture radar and sonar, and ultrasound and laser imaging. These models introduce two additional layers of difficulties with respect to the standard Gaussian additive noise scenario: (1) the noise is multiplied by (rather than added to) the original image; (2) the noise is not Gaussian, with Rayleigh and Gamma being commonly used densities. These two features of multiplicative noise models preclude the direct application of most state-of-the-art algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (log-likelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or wavelet-based regularizer/prior). In this paper, we address these difficulties by: (1) converting the multiplicative model into an additive one by taking logarithms, as proposed by some other authors; (2) using variable splitting to obtain an equivalent constrained problem; and (3) dealing with this optimization problem using the augmented Lagrangian framework. A set of experiments shows that the proposed method, which we name MIDAL (multiplicative image denoising by augmented Lagrangian), yields state-of-the-art results both in terms of speed and denoising performance.Comment: 11 pages, 7 figures, 2 tables. To appear in the IEEE Transactions on Image Processing

Image Restoration for Remote Sensing: Overview and Toolbox

Remote sensing provides valuable information about objects or areas from a distance in either active (e.g., RADAR and LiDAR) or passive (e.g., multispectral and hyperspectral) modes. The quality of data acquired by remotely sensed imaging sensors (both active and passive) is often degraded by a variety of noise types and artifacts. Image restoration, which is a vibrant field of research in the remote sensing community, is the task of recovering the true unknown image from the degraded observed image. Each imaging sensor induces unique noise types and artifacts into the observed image. This fact has led to the expansion of restoration techniques in different paths according to each sensor type. This review paper brings together the advances of image restoration techniques with particular focuses on synthetic aperture radar and hyperspectral images as the most active sub-fields of image restoration in the remote sensing community. We, therefore, provide a comprehensive, discipline-specific starting point for researchers at different levels (i.e., students, researchers, and senior researchers) willing to investigate the vibrant topic of data restoration by supplying sufficient detail and references. Additionally, this review paper accompanies a toolbox to provide a platform to encourage interested students and researchers in the field to further explore the restoration techniques and fast-forward the community. The toolboxes are provided in https://github.com/ImageRestorationToolbox.Comment: This paper is under review in GRS

Unsupervised multi-scale change detection from SAR imagery for monitoring natural and anthropogenic disasters

Thesis (Ph.D.) University of Alaska Fairbanks, 2017Radar remote sensing can play a critical role in operational monitoring of natural and anthropogenic disasters. Despite its all-weather capabilities, and its high performance in mapping, and monitoring of change, the application of radar remote sensing in operational monitoring activities has been limited. This has largely been due to: (1) the historically high costs associated with obtaining radar data; (2) slow data processing, and delivery procedures; and (3) the limited temporal sampling that was provided by spaceborne radar-based satellites. Recent advances in the capabilities of spaceborne Synthetic Aperture Radar (SAR) sensors have developed an environment that now allows for SAR to make significant contributions to disaster monitoring. New SAR processing strategies that can take full advantage of these new sensor capabilities are currently being developed. Hence, with this PhD dissertation, I aim to: (i) investigate unsupervised change detection techniques that can reliably extract signatures from time series of SAR images, and provide the necessary flexibility for application to a variety of natural, and anthropogenic hazard situations; (ii) investigate effective methods to reduce the effects of speckle and other noise on change detection performance; (iii) automate change detection algorithms using probabilistic Bayesian inferencing; and (iv) ensure that the developed technology is applicable to current, and future SAR sensors to maximize temporal sampling of a hazardous event. This is achieved by developing new algorithms that rely on image amplitude information only, the sole image parameter that is available for every single SAR acquisition. The motivation and implementation of the change detection concept are described in detail in Chapter 3. In the same chapter, I demonstrated the technique's performance using synthetic data as well as a real-data application to map wildfire progression. I applied Radiometric Terrain Correction (RTC) to the data to increase the sampling frequency, while the developed multiscaledriven approach reliably identified changes embedded in largely stationary background scenes. With this technique, I was able to identify the extent of burn scars with high accuracy. I further applied the application of the change detection technology to oil spill mapping. The analysis highlights that the approach described in Chapter 3 can be applied to this drastically different change detection problem with only little modification. While the core of the change detection technique remained unchanged, I made modifications to the pre-processing step to enable change detection from scenes of continuously varying background. I introduced the Lipschitz regularity (LR) transformation as a technique to normalize the typically dynamic ocean surface, facilitating high performance oil spill detection independent of environmental conditions during image acquisition. For instance, I showed that LR processing reduces the sensitivity of change detection performance to variations in surface winds, which is a known limitation in oil spill detection from SAR. Finally, I applied the change detection technique to aufeis flood mapping along the Sagavanirktok River. Due to the complex nature of aufeis flooded areas, I substituted the resolution-preserving speckle filter used in Chapter 3 with curvelet filters. In addition to validating the performance of the change detection results, I also provide evidence of the wealth of information that can be extracted about aufeis flooding events once a time series of change detection information was extracted from SAR imagery. A summary of the developed change detection techniques is conducted and suggested future work is presented in Chapter 6

Multiplicative Noise Removal with a Sparsity-Aware Optimization Model

Restoration of images contaminated by multiplicative noise (also known as speckle noise) is a key issue in coherent image processing. Notice that images under consideration are often highly compressible in certain suitably chosen transform domains. By exploring this intrinsic feature embedded in images, this paper introduces a variational restoration model for multiplicative noise reduction that consists of a term reflecting the observed image and multiplicative noise, a quadratic term measuring the closeness of the underlying image in a transform domain to a sparse vector, and a sparse regularizer for removing multiplicative noise. Being different from popular existing models which focus on pursuing convexity, the proposed sparsity-aware model may be nonconvex depending on the conditions of the parameters of the model for achieving the optimal denoising performance. An algorithm for finding a critical point of the objective function of the model is developed based on coupled fixed-point equations expressed in terms of the proximity operator of functions that appear in the objective function. Convergence analysis of the algorithm is provided. Experimental results are shown to demonstrate that the proposed iterative algorithm is sensitive to some initializations for obtaining the best restoration results. We observe that the proposed method with SAR-BM3D filtering images as initial estimates can remarkably outperform several state of-art methods in terms of the quality of the restored images

A Fast Level Set Method for Synthetic Aperture Radar Ocean Image Segmentation

Segmentation of high noise imagery like Synthetic Aperture Radar (SAR) images is still one of the most challenging tasks in image processing. While level set, a novel approach based on the analysis of the motion of an interface, can be used to address this challenge, the cell-based iterations may make the process of image segmentation remarkably slow, especially for large-size images. For this reason fast level set algorithms such as narrow band and fast marching have been attempted. Built upon these, this paper presents an improved fast level set method for SAR ocean image segmentation. This competent method is dependent on both the intensity driven speed and curvature flow that result in a stable and smooth boundary. Notably, it is optimized to track moving interfaces for keeping up with the point-wise boundary propagation using a single list and a method of fast up-wind scheme iteration. The list facilitates efficient insertion and deletion of pixels on the propagation front. Meanwhile, the local up-wind scheme is used to update the motion of the curvature front instead of solving partial differential equations. Experiments have been carried out on extraction of surface slick features from ERS-2 SAR images to substantiate the efficacy of the proposed fast level set method

Information Extraction and Modeling from Remote Sensing Images: Application to the Enhancement of Digital Elevation Models

To deal with high complexity data such as remote sensing images presenting metric resolution over large areas, an innovative, fast and robust image processing system is presented. The modeling of increasing level of information is used to extract, represent and link image features to semantic content. The potential of the proposed techniques is demonstrated with an application to enhance and regularize digital elevation models based on information collected from RS images