Recent developments in medical treatment put challenging demands on ultrasound imaging systems. These demands typically imply increasing the number of transducer elements involved in each imaging cycle. Confined to traditional sampling methods, the inevitable result is a significant growth in the amount of raw data that needs to be transmitted from the system front end, and then processed by the processing unit, effecting machinery size and power consumption. In this paper, we derive a scheme which reduces the amount of transmitted data, by applying Compressed Sensing (CS) techniques to analog ultrasound signals detected in the transducer elements. We follow the spirit of Xampling, which combines classic methods from sampling theory with recent developments in CS, aimed at sampling analog signals far below the Nyquist rate. Our scheme enhances SNR, by integrating low-rate samples extracted from multiple transducer elements. We refer to this process as “beamforming in the compressed domain”, or “compressed beamforming”.

In this work, we propose a novel method for the regularization of blind deconvolution algorithms. The proposed method employs example-based machine learning techniques for modeling the space of point spread functions. During an iterative blind deconvolution process, a prior term attracts the point spread function estimates to the learned point spread function space. We demonstrate the usage of this regularizer within a Bayesian blind deconvolution framework and also integrate into the latter a method for noise reduction, thus creating a complete blind deconvolution method. The application of the proposed algorithm is demonstrated on synthetic and real-world three-dimensional images acquired by a wide-field fluorescence microscope, where the need for blind deconvolution algorithms is indispensable, yielding excellent results.

This paper presents novel results on the joint problem of sampling and quantization of non bandlimited signals. Existing literature typically focuses either on sampling in the absence of quantization, or, conversely, studies quantization for already sampled signals. Our emphasis here is on the issues that arise al the intersection of these two design problems. We argue that the joint problem can be formulated and solved to any desired level of accuracy, using moving horizon optimization methods. We present several examples which show that consideration of the combined sampling and quantization problem gives important performance gains, relative to strategies which don't specifically address the interaction between these two problems

Papoulis' generalized sampling expansion (GSE) can be carried out if a set of linear equations has a solution. This enables the reconstruction of a signal from its filtered and downsampled versions. We show that the existence of this solution is also a necessary condition for the reconstruction of the signal from the available data. Special attention is given to the case of recurrent multidimensional sampling.

In previous work, Elad and Bruckstein (EB) have provided a sufficient condition for replacing an l/sub 0/ optimization by linear programming minimization when searching for the unique sparse representation. We establish here that the EB condition is both sufficient and necessary.

Super-resolution reconstruction algorithms perform a fusion of several low quality images of the same scene into a single improved quality image. As opposed to this STATIC recovery problem, in this paper we define a DYNAMIC super-resolution task: the restoration of a blurred, decimated, and noisy image sequence. We first model this problem through state-space equations, showing that this problem can be viewed as a sequence of STATIC super-resolution problems. Two efficient reconstruction algorithms are proposed, both being adaptive filtering approximations of the Kalman filter; the R-SD and the R-LMS. Computer simulations on synthetic sequences indicate the computational feasibility of these algorithms.

In an earlier work (1999), we introduced the problem of reconstructing a super-resolution image sequence from a given low resolution sequence. We proposed two iterative algorithms, the R-SD and the R-LMS, to generate the desired image sequence. These algorithms assume the knowledge of the blur, the down-sampling, the sequences motion, and the measurements noise characteristics, and apply a sequential reconstruction process. It has been shown that the computational complexity of these two algorithms makes both of them practically applicable. In this paper, we rederive these algorithms as approximations of the Kalman filter and then carry out a thorough analysis of their performance. For each algorithm, we calculate a bound on its deviation from the Kalman filter performance. We also show that the propagated information matrix within the R-SD algorithm remains sparse in time, thus ensuring the applicability of this algorithm. To support these analytical results we present some computer simulations on synthetic sequences, which also show the computational feasibility of these algorithms.

This paper presents a new method based on adaptive filtering theory for superresolution restoration of continuous image sequences. The proposed methodology suggests least squares (LS) estimators which adapt in time, based on adaptive filters, least mean squares (LMS) or recursive least squares (RLS). The adaptation enables the treatment of linear space and time-variant blurring and arbitrary motion, both of them assumed known. The proposed new approach is shown to be of relatively low computational requirements. Simulations demonstrating the superresolution restoration algorithms are presented.

This paper presents a new approach based on the differential framework proposed by Horn and Schunck, to the problem of recursive optical flow estimation from image sequences. The original method of Horn and Schunck is applicable only to the problem of estimating the optical flow between a pair of images from an image sequence. When we aim at estimating the optical flow for long image sequences recursively, the question is whether and how can we gain from previous estimates. In this paper we show that gain is achieved from both computational and accuracy points of view. Incorporation of the time axis into the estimation process is done by assuming temporal smoothness of the optical flow, resulting in simplified spatial–temporal models. The obtained models permit incorporation of the constrained weighted least squares (CWLS) estimator. This estimator is shown to yield RLS and LMS adaptive filter versions for recursive optical flow estimation in time. An interesting and desirable property of the proposed estimation algorithms is their flexibility with respect to performance versus computational requirements. By a simple choice of a parameter these algorithms can be modified to exploit the available time to improve their performance with respect to estimation error. The convergence properties of these estimation algorithms are analyzed. Simulations for various image sequences support the analysis and demonstrate the performance of the estimation algorithms.

The three main tools in the single image restoration theory are the maximum likelihood (ML) estimator, the maximum a posteriori probability (MAP) estimator, and the set theoretic approach using projection onto convex sets (POCS). This paper utilizes the above known tools to propose a unified methodology toward the more complicated problem of superresolution restoration. In the superresolution restoration problem, an improved resolution image is restored from several geometrically warped, blurred, noisy and downsampled measured images. The superresolution restoration problem is modeled and analyzed from the ML, the MAP, and POCS points of view, yielding a generalization of the known superresolution restoration methods. The proposed restoration approach is general but assumes explicit knowledge of the linear space- and time-variant blur, the (additive Gaussian) noise, the different measured resolutions, and the (smooth) motion characteristics. A hybrid method combining the simplicity of the ML and the incorporation of nonellipsoid constraints is presented, giving improved restoration performance, compared with the ML and the POCS approaches. The hybrid method is shown to converge to the unique optimal solution of a new definition of the optimization problem. Superresolution restoration from motionless measurements is also discussed. Simulations demonstrate the power of the proposed methodology.

It is demonstrated that the normalized least mean square (NLMS) algorithm can be viewed as a modification of the widely used LMS algorithm. The NLMS is shown to have an important advantage over the LMS, which is that its convergence is independent of environmental changes. In addition, the authors present a comprehensive study of the first and second-order behavior in the NLMS algorithm. They show that the NLMS algorithm exhibits significant improvement over the LMS algorithm in convergence rate, while its steady-state performance is considerably worse.>