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72
Phase unwrapping via graph cuts
 IEEE Transactions on Image Processing
, 2007
"... Abstract — Phase unwrapping is the inference of absolute phase from modulo2π phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are firstorder Markov random fields. We provide an exact energy minimization algorithm, whenever th ..."
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Cited by 18 (6 self)
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Abstract — Phase unwrapping is the inference of absolute phase from modulo2π phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are firstorder Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical L p norm, with p ≥ 1. Its complexity is KT(n, 3n), where K is the length of the absolute phase domain measured in 2π units and T (n, m) is the complexity of a maxflow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NPhard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems, by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrapping maxflow/mincut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with stateoftheart phase unwrapping algorithms. Index Terms — Phase unwrapping, energy minimization, integer optimization, submodularity, graph cuts, image
The ZπM algorithm: A method for interferometric image reconstruction in sar/sas
 IEEE Transactions on Image Processing
, 2002
"... Abstract—This paper presents an effective algorithm for absolute phase (not simply modulo2) estimation from incomplete, noisy and modulo2 observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical inter ..."
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Cited by 14 (2 self)
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Abstract—This paper presents an effective algorithm for absolute phase (not simply modulo2) estimation from incomplete, noisy and modulo2 observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging and diffraction tomography. The Bayesian viewpoint is adopted; the observation density is 2periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modeled by a compound Gauss–Markov random field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) absolute phase estimate. Each iteration embodies a discrete optimization step (step), implemented by network programming techniques and an iterative conditional modes (ICM) step (step). Accordingly, the algorithm is termed, where the letter stands for maximization. An important contribution of the paper is the simultaneous implementation of phase unwrapping (inference of the 2multiples) and smoothing (denoising of the observations). This improves considerably the accuracy of the absolute phase estimates compared to methods in which the data is lowpass filtered prior to unwrapping. A set of experimental results, comparing the proposed algorithm with alternative methods, illustrates the effectiveness of our approach. Index Terms—Bayesian estimation, compound Gauss–Markov random, interferometry, iterative conditioonal modes (ICM), network
Unwrapping Phase Images By Propagating Probabilities Across Graphs
, 2001
"... Phase images are derived from source images by applying a modulus operation to each pixel value. Phase unwrapping is the problem of inferring the original, unwrapped values from the wrapped values, using prior knowledge about the smoothness of the image. One approach to solving this problem is to i ..."
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Cited by 10 (4 self)
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Phase images are derived from source images by applying a modulus operation to each pixel value. Phase unwrapping is the problem of inferring the original, unwrapped values from the wrapped values, using prior knowledge about the smoothness of the image. One approach to solving this problem is to infer the gradient vector field of the unwrapped image and then integrate the gradient field. The gradient in a particular direction at a pixel is equal to the observed pixel difference plus an unknown integer number of shifts. We introduce a technique for inferring these shifts using the lowcomplexity probability propagation algorithm, applied in a graphical model that prefers shifts that match the phase image and that constrains the shifts to satisfy the properties of a gradient field. We present results for a phase image from the region of the Sandia National Laboratories.
The ZπM Algorithm for Interferometric Image Reconstruction in SAR/SAS
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2002
"... The paper presents an effective algorithm for absolute phase (not simply modulo2#) estimation from incomplete, noisy, and modulo2# observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferomet ..."
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Cited by 10 (0 self)
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The paper presents an effective algorithm for absolute phase (not simply modulo2#) estimation from incomplete, noisy, and modulo2# observations in interferometric aperture radar and sonar (InSAR/InSAS). The adopted framework is also representative of other applications such as optical interferometry, magnetic resonance imaging, and di#=143/z tomography. The Bayesian viewpoint is adopted; the observation density is 2#periodic and accounts for the interferometric pair decorrelation and system noise; the a priori probability of the absolute phase is modelled by a Compound Gauss Markov rand field (CGMRF) tailored to piecewise smooth absolute phase images. We propose an iterative scheme for the computation of the maximum a posteriori probability (MAP) phase estimate. Each iteration embodies a discrete optimization step (Zstep), implemented by network programming techniques, and an iterative cond mod (ICM) step (#step). Accordingly, the algorithm is termed where the letter M stands for maximization. A set of experimental results, comparing the proposed algorithm with alternative approaches, illustrates the effectiveness of the proposed method.
Multiplicative noise removal using variable splitting and constrained optimization
 IEEE Transactions on Image Processing
, 2010
"... Abstract—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 ad ..."
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Cited by 10 (1 self)
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Abstract—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 stateoftheart algorithms, which are designed for solving unconstrained optimization problems where the objective has two terms: a quadratic data term (loglikelihood), reflecting the additive and Gaussian nature of the noise, plus a convex (possibly nonsmooth) regularizer (e.g., a total variation or waveletbased 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 stateoftheart results both in terms of speed and denoising performance. Index Terms—Augmented Lagrangian, Douglas–Rachford splitting, multiplicative noise, speckled images, synthetic aperture
DirectFourier Reconstruction In Tomography And Synthetic Aperture Radar
 Intl. J. Imaging Sys. and Tech
, 1998
"... We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR ..."
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Cited by 9 (0 self)
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We investigate the use of directFourier (DF) image reconstruction in computerized tomography and synthetic aperture radar (SAR). One of our aims is to determine why the convolutionbackprojection (CBP) method is favored over DF methods in tomography, while DF methods are virtually always used in SAR. We show that the CBP algorithm is equivalent to DF reconstruction using a Jacobianweighted 2D periodic sinckernel interpolator. This interpolation is not optimal in any sense, which suggests that DF algorithms utilizing optimal interpolators may surpass CBP in image quality. We consider use of two types of DF interpolation: a windowed sinc kernel, and the leastsquares optimal Yen interpolator. Simulations show that reconstructions using the Yen interpolator do not possess the expected visual quality, because of regularization needed to preserve numerical stability. Next, we show that with a concentricsquares sampling scheme, DF interpolation can be performed accurately and efficiently...
Compressed Synthetic Aperture Radar
, 2010
"... In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a highresolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, ..."
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Cited by 9 (3 self)
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In this paper, we introduce a new synthetic aperture radar (SAR) imaging modality which can provide a highresolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. This new imaging scheme, requires no new hardware components and allows the aperture to be compressed. It also presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced onboard storage requirements.
An Experimental Study Of A New EntropyBased SAR Autofocus Technique
 Proc. of the Int. Conf. on Image Processing 2
, 2002
"... The Stage By Stage Approaching (SSA) entropy minimization approach to synthetic aperture radar (SAR) autofocus is a modern and innovative technique, which has not been compared with other approaches, to date. We provide such a comparison and show that SSA is a most promising autofocus method. In thi ..."
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Cited by 7 (1 self)
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The Stage By Stage Approaching (SSA) entropy minimization approach to synthetic aperture radar (SAR) autofocus is a modern and innovative technique, which has not been compared with other approaches, to date. We provide such a comparison and show that SSA is a most promising autofocus method. In this paper, we evaluate the merit of this algorithm through comparison with the established Phase Gradient Autofocus (PGA) algorithm on both simulated and real SAR data.
Test Results from a MultiFrequency Bathymetric Synthetic Aperture Sonar
, 2001
"... This paper describes the implementation of a bathymetric synthetic aperture sonar and presents preliminary results from sea trials of the sonar. The sonar is designed for high resolution seafloor imaging in a shallow water environment. This is achieved through coherent summation of successive echo s ..."
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Cited by 6 (6 self)
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This paper describes the implementation of a bathymetric synthetic aperture sonar and presents preliminary results from sea trials of the sonar. The sonar is designed for high resolution seafloor imaging in a shallow water environment. This is achieved through coherent summation of successive echo signals to synthesise an aperture many times longer than the towfish. Provided the motion of the towfish is accurately estimated and compensated, the application of aperture synthesis can result in a range independent resolution over the operating swath.
Noncoherent 2D and 3D SAR reconstruction from wideangle measurements
 in 13th Annual Adaptive Sensor Array Processing Workshop, MIT Lincoln Laboratory
, 2005
"... This paper considers processing and visualization of radar scattering measurements from one or more wideangle synthetic apertures. We consider both twodimensional imaging and threedimensional interferometric reconstructions. A pointscattering assumption is poorly suited to wideangle scattering; ..."
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Cited by 6 (1 self)
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This paper considers processing and visualization of radar scattering measurements from one or more wideangle synthetic apertures. We consider both twodimensional imaging and threedimensional interferometric reconstructions. A pointscattering assumption is poorly suited to wideangle scattering; scattering objects within a target typically have narrow beam patterns, resulting in limited angles of persistence. We revisit traditional imaging in 2D or 3D to propose image formation techniques that use nonlinear, noncoherent combinations of subaperture data. The proposed techniques can be interpreted as approximations to a generalized likelihood ratio test. For sufficiently high resolutions, individual reflectors are resolved, and hence the phase and amplitude of their responses are stable under small changes in viewing angle. This stability is in contrast to the scintillation observed in lowresolution data. Three processing techniques benefit as a result: interferometric measurement of 3D location is possible without widearea averaging; polarimetric features may be used to describe local geometry; and, bandwidth enhancement is possible. We illustrate processing and visualization techniques using Xband scattering predictions of a backhoe computed using Xpatch. The reconstructions permit an approximation to the literal interpretation afforded by optical imaging, but with millimeter wave sensing. In addition, angledependent and polarizationdependent behaviors are displayed for enhanced recognition. 1.