Results 1 
9 of
9
Image restoration subject to a total variation constraint
 IEEE Transactions on Image Processing
, 2004
"... Abstract—Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective to be minimized under constraints. In this paper, we propose an alternative formulation in which ..."
Abstract

Cited by 26 (2 self)
 Add to MetaCart
Abstract—Total variation has proven to be a valuable concept in connection with the recovery of images featuring piecewise smooth components. So far, however, it has been used exclusively as an objective to be minimized under constraints. In this paper, we propose an alternative formulation in which total variation is used as a constraint in a general convex programming framework. This approach places no limitation on the incorporation of additional constraints in the restoration process and the resulting optimization problem can be solved efficiently via blockiterative methods. Image denoising and deconvolution applications are demonstrated. I. PROBLEM STATEMENT THE CLASSICAL linear restoration problem is to find the original form of an image in a real Hilbert space from the observation of a degraded image where
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, ..."
Abstract

Cited by 9 (3 self)
 Add to MetaCart
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.
Discrete Analytical Ridgelet Transform
 Signal Processing
, 2004
"... In this paper, we propose an implementation of the 3D ridgelet transform: The 3D Discrete Analytical Ridgelet Transform (3D DART). This transform uses the Fourier strategy for the computation of the associated 3D discrete Radon transform. The innovative step is the definition of a discrete 3D t ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
In this paper, we propose an implementation of the 3D ridgelet transform: The 3D Discrete Analytical Ridgelet Transform (3D DART). This transform uses the Fourier strategy for the computation of the associated 3D discrete Radon transform. The innovative step is the definition of a discrete 3D transform with the discrete analytical geometry theory by the construction of 3D discrete analytical lines in the Fourier domain. We propose two types of 3D discrete lines: 3D discrete radial lines going through the origin defined from their orthogonal projections and 3D planes covered with 2D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3D DART adapted to a specific application. Indeed, the 3D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3D DART and its extension to the LocalDART (with smooth windowing) to the denoising of 3D image and colour video. These experimental results show that the simple thresholding of the 3D DART coefficients is efficient.
Ultrasound Tomography Calibration Using Structured Matrix Completion
"... Calibration of ultrasound tomography devices is a challenging problem and of highly practical interest in medical and seismic imaging. This work addresses the position calibration problem in circular apertures where sensors are arranged on a circular ring and act both as transmitters and receivers. ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
Calibration of ultrasound tomography devices is a challenging problem and of highly practical interest in medical and seismic imaging. This work addresses the position calibration problem in circular apertures where sensors are arranged on a circular ring and act both as transmitters and receivers. We introduce a new method of calibration based on the timeofflight (ToF) measurements between sensors when the enclosed medium is homogeneous. Knowing all the pairwise ToFs, one can find the positions of the sensors using multidimensional scaling (MDS) method. In practice, however, we are facing two major sources of loss. One is due to the transitional behaviour of the sensors, which makes the ToF measurements for closeby sensors unavailable. The other is due to the random malfunctioning of the sensors, that leads to random missing ToF measurements. On top of the missing entries, since in practice the impulse response of the piezoelectric and the time origin in the measurement procedure are not present, a time mismatch is also added to the measurements. In this work, we first show that a matrix defined from all the ToF measurements is of rank at most four. In order to estimate the structured and random missing entries, utilizing the fact that the matrix in question is shown to be lowrank, we apply a stateoftheart lowrank matrix completion algorithm. Then we use MDS in order to find the correct positions of the sensors. To confirm the functionality of our method in practice, simulations mimicking the measurements of an ultrasound tomography device are performed.
A Convex Programming Algorithm for Noisy Discrete Tomography
"... Summary. A convex programming approach to discrete tomographic image reconstruction in noisy environments is proposed. Conventional constraints are mixed with noisebased constraints on the sinogram and a binaritypromoting total variation constraint. The noisebased constraints are modeled as confi ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Summary. A convex programming approach to discrete tomographic image reconstruction in noisy environments is proposed. Conventional constraints are mixed with noisebased constraints on the sinogram and a binaritypromoting total variation constraint. The noisebased constraints are modeled as confidence regions that are constructed under a Poisson noise assumption. A convex objective is then minimized over the resulting feasibility set via a parallel blockiterative method. Applications to binary tomographic reconstruction are demonstrated. 1
Index Terms
"... We study the calibration problem in circular ultrasound tomography devices for breast imaging, where the sensor positions deviate from the circumference of a perfect circle. We introduce a new method of calibration based on the timeofflight (ToF) measurements between sensors when the enclosed medi ..."
Abstract
 Add to MetaCart
We study the calibration problem in circular ultrasound tomography devices for breast imaging, where the sensor positions deviate from the circumference of a perfect circle. We introduce a new method of calibration based on the timeofflight (ToF) measurements between sensors when the enclosed medium is homogeneous. In the presence of all the pairwise ToFs, one can estimate the sensor positions using multidimensional scaling (MDS) method. In practice, however, we are facing two major sources of loss. One is due to the transitional behaviour of the sensors and the beam form of the transducers, which makes the ToF measurements for closeby sensors unavailable. The other is due to the random malfunctioning of the sensors, that leads to random missing ToF measurements. On top of the missing entries, in practice an unknown time delay is also added to the measurements. In this work, we show that a matrix defined from all the ToF measurements is of rank at most four. In order to estimate the missing ToFs, we apply a stateoftheart lowrank matrix completion algorithm, OPTSPACE. Then we use MDS in order to find the correct positions of the sensors. To confirm the functionality of our method in practice, simulations mimicking the measurements of a circular ultrasound tomography device are performed.
WEIGHTED FOURIER IMAGE ANALYSIS AND MODELING
, 2008
"... A novel systematic framework of medical image analysis, weighted Fourier series (WFS) analysis is introduced. WFS is a combination of Fourier series and heat kernel smoothing. WFS effectively reduces the Gibbs phenomenon, improves the signal to noise ratio, and increases normality of the estimated ..."
Abstract
 Add to MetaCart
A novel systematic framework of medical image analysis, weighted Fourier series (WFS) analysis is introduced. WFS is a combination of Fourier series and heat kernel smoothing. WFS effectively reduces the Gibbs phenomenon, improves the signal to noise ratio, and increases normality of the estimated errors in the WFSbased generalized linear models. In estimating the parameters of WFS, the least squares estimation of WFS has been widely used but it is computationally inefficient. To address the computational inefficiency in the least squares estimation, much faster but less accurate iterative residual fitting (IRF) method has been proposed. The proposed adaptive iterative regression (AIR) technique inherits the computational efficiency of IRF and improves accuracy of IRF. AIR partitions the function space into a set of subspaces, and performs an extra orthogonalization procedure to reduce the bias of IRF estimation. A complimentary tool, the fast weighted
COMPRESSED SENSING FOR SYNTHETIC APERTURE RADAR IMAGING
"... In this paper, we introduce a new Synthetic Aperture Radar (SAR) imaging modality that provides a high resolution map of the spatial distribution of targets and terrain based on a significant reduction in the number of transmitted and/or received electromagnetic waveforms. This new imaging scheme, w ..."
Abstract
 Add to MetaCart
In this paper, we introduce a new Synthetic Aperture Radar (SAR) imaging modality that provides a high resolution map of the spatial distribution of targets and terrain based on a significant reduction in the number of transmitted and/or received electromagnetic waveforms. This new imaging scheme, which requires no new hardware components, allows the aperture to be compressed and presents many important applications and advantages among which include resolving ambiguities, strong resistance to countermesasures and interception, and reduced onboard storage constraints. Index Terms — compressed sensing, SAR 1.