This paper provides the derivation of speckle reducing anisotropic diffusion (SRAD), a diffusion method tailored to ultrasonic and radar imaging applications. SRAD is the edge-sensitive diffusion for speckled images, in the same way that conventional anisotropic diffusion is the edge-sensitive diffusion for images corrupted with additive noise. We first show that the Lee and Frost filters can be cast as partial differential equations, and then we derive SRAD by allowing edge-sensitive anisotropic diffusion within this context. Just as the Lee (1980, 1981, 1986) and Frost (1982) filters utilize the coefficient of variation in adaptive filtering, SRAD exploits the instantaneous coefficient of variation, which is shown to be a function of the local gradient magnitude and Laplacian operators. We validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery. We also demonstrate the algorithm performance with real SAR data. The performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes. In the presence of speckle noise, speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation, variance reduction, and edge localization.

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Speckle reducing anisotropic diffusion

Diffraction characteristics of general dielectric planar (slab) gratings and surface-relief (corrugated) gratings are reviewed. Applications to laser-beam deflection, guidance, modulation, coupling, filtering, wavefront reconstruction, and distributed feedback in the fields of acoustooptics, integrated optics, holography, and spectral analysis are discussed. An exact formulation of the grating diffraction problem without approximations (rigorous coupled-wave theory developed by the authors) is presented. The method of solution is in terms of state variables and this is presented in detail. Then, using a series of fundamental assumptions, this rigorous theory is shown to reduce to the various existing approximate theories in the appropriate limits. The effects of these fundamental assumptions in the approximate theories are quantified and discussed.

Analysis and applications of optical diffraction by gratings

We present a novel automatic and unsupervised change-detection approach specifically oriented to the analysis of multitemporal single-channel single-polarization synthetic aperture radar (SAR) images. This approach is based on a closed-loop process made up of three main steps: (1) a novel preprocessing based on a controlled adaptive iterative filtering; (2) a comparison between multitemporal images carried out according to a standard log-ratio operator; and (3) a novel approach to the automatic analysis of the log-ratio image for generating the change-detection map. The first step aims at reducing the speckle noise in a controlled way in order to maximize the discrimination capability between changed and unchanged classes. In the second step, the two filtered multitemporal images are compared to generate a log-ratio image that contains explicit information on changed areas. The third step produces the change-detection map according to a thresholding procedure based on a reformulation of the Kittler-Illingworth (KI) threshold selection criterion. In particular, the modified KI criterion is derived under the generalized Gaussian assumption for modeling the distributions of changed and unchanged classes. This parametric model was chosen because it is capable of better fitting the conditional densities of classes in the log-ratio image. In order to control the filtering step and, accordingly, the effects of the filtering process on change-detection accuracy, we propose to identify automatically the optimal number of despeckling filter iterations [Step 1] by analyzing the behavior of the modified KI criterion. This results in a completely automatic and self-consistent change-detection approach that avoids the use of empirical methods for the selection of the best number of filtering iterations. Experiments carried out on two sets of multitemporal images (characterized by different levels of speckle noise) acquired by the European Remote Sensing 2 satellite SAR sensor confirm the effectiveness of the proposed unsupervised approach, which results in change-detection accuracies very similar to those that can be achieved by a manual supervised thresholding.

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An unsupervised approach based on the generalized Gaussian model to automatic change detection in multitemporal SAR images

Active, optical range imaging systems collect three-dimensional coordinate data from object surfaces. These systems can be useful in a wide variety of automation applications, including shape acquisition, bin picking, assembly, inspection, gauging, robot navigation, medical diagnosis, cartography, and military tasks. The range-imaging sensors in such systems are unique imaging devices in that the image data points explicitly represent scene surface geometry in a sampled form. At least six different optical principles have been used to actively obtain range images: (1) radar, (2) triangulation, (3) moire, (4) holographic interferometry, (5) lens focusing, and (6) diffraction. The relative capabilities of different sensors and sensing methods are evaluated using a figure of merit based on range accuracy, depth of field, and image acquisition time.

Active optical range imaging sensors

Automated breast cancer detection and classification using ultrasound images: A survey

Speckle is a granular noise that inherently exists in all types of coherent imaging systems. The presence of speckle in an image reduces the resolution of the image and the detectability of the target. Many speckle reduction algorithms assume speckle noise is multiplicative. We instead model the speckle according to the exact physical process of coherent image formation. Thus, the model includes signal-dependent effects and accurately represents the higher order statistical properties of speckle that are important to the restoration procedure. Various adaptive restoration filters for intensity speckle images are derived based on different model assumptions and a nonstationary image model. These filters respond adaptively to the signal-dependent speckle noise and the nonstationary statistics of the original image.

Adaptive restoration of images with speckle

Speckle is a granular noise that inherently exists in all types of coherent imaging systems. The presence of speckle in an image reduces the resolution of the image and the detectability of the target. Many speckle reduction algorithms assume speckle noise is multiplicative. We instead model the speckle according to the exact physical process of coherent image formation. Thus, the model includes signal-dependent effects and accurately represents the higher order statistical properties of speckle that are important to the restoration procedure. Various adaptive restoration filters for intensity speckle images are derived based on different speckle model assumptions and a nonstationary image model. These filters respond adaptively to the signal-dependent speckle noise and the nonstationary statistics of the original image.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Adaptive Restoration Of Images With Speckle

A general technique is described for implementing sequential logic circuits optically. In contrast with semiconductor integrated circuitry, optical logic systems allow very flexible interconnections between gates and between subsystems. Because of this, certain processing algorithms which do not map well onto semiconductor architectures can be implemented on the optical structure. The algorithms and processor architectures which can be implemented on the optical system depend on the interconnection technique. We describe three interconnection methods and analyze their advantages and limitations.

Architectural implications of a digital optical processor.

An optical system that performs sequential binary logic operations is described. The system consists of a spatial light modulator (SLM) used to provide a nonlinear threshold response and a computer-generated hologram to provide interconnections between logic gates. A 2-D array of logic gates with binary inputs and outputs is formed on the active surface of the SLM. These gates are interconnected by a 2-D array of subholograms, one for each gate. Arbitrary logic circuits consisting of NOR gates and inverters can be implemented, and the system can be reconfigured by changing a single holographic element. The system is demonstrated using a twisted-nematic liquid crystal light valve as the SLM. A test circuit is implemented that includes a synchronous master–slave flip-flop and an oscillator consisting of five inverters in a feedback loop. Experimental results of this test circuit are presented.

Sequential optical logic implementation

A range measurement technique is presented which allows real-time range data acquisition for all points in an image. The technique relies upon the systematic variation in the Fresnel diffraction pattern of a grating as a function of propagation distance. The technique uses a single view of the volume in question so there are no hidden points. Furthermore, there is no need for beam scanning or is any off-line processing required. An extensive theory of operation is presented along with grating and illumination design methods which allow one to tailor the technique to specific measurement requirements. Qualitative experimental results are given along with quantitative results.

T. C. Strand

Papers

Adaptive restoration of images with speckle

Adaptive Restoration Of Images With Speckle

Architectural implications of a digital optical processor.

Sequential optical logic implementation

Range measurement using Talbot diffraction imaging of gratings.