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 Bioautomation , 2005, Abstract: An effective aperture approach is used as a tool for analysis and parameter optimization of mostly known ultrasound imaging systems - phased array systems, compounding systems and synthetic aperture imaging systems. Both characteristics of an imaging system , the effective aperture function and the corresponding two-way radiation pattern, provide information about two the most important parameters of images produced by an ultrasound system - lateral resolution and contrast. Therefore, in the design, optimization of the effective aperture function leads to optimal choice of such parameters of an imaging systems that influence on lateral resolution and contrast of images produced by this imaging system. The numerical results show that Hamming apodization gives the best compromise between the contrast of images and the lateral resolution produced by a conventional phased array imaging system. In compound imaging, the number of transducers and its spatial separation should be chosen in result of optimization of the effective aperture function of a system. It is shown that the effective aperture approach can be also used for optimization of a sparse synthetic transmit aperture (STA) imaging system. A new two-stage algorithm is proposed for optimization of both the positions of the transmit elements and the weights of the receive elements. The proposed system employs a 64- element array with only four active elements used during transmit.
 Computer Science , 2014, Abstract: We consider the analysis operator and synthesis dictionary learning problems based on the the $\ell_1$ regularized sparse representation model. We reveal the internal relations between the $\ell_1$-based analysis model and synthesis model. We then introduce an approach to learn both analysis operator and synthesis dictionary simultaneously by using a unified framework of bi-level optimization. Our aim is to learn a meaningful operator (dictionary) such that the minimum energy solution of the analysis (synthesis)-prior based model is as close as possible to the ground-truth. We solve the bi-level optimization problem using the implicit differentiation technique. Moreover, we demonstrate the effectiveness of our leaning approach by applying the learned analysis operator (dictionary) to the image denoising task and comparing its performance with state-of-the-art methods. Under this unified framework, we can compare the performance of the two types of priors.
 Xiang Gu;Yunhua Zhang PIER B , 2011, DOI: 10.2528/PIERB11040806 Abstract: Super-resolution algorithms used in radar imaging, e.g., MUltiple SIgnal Classification (MUSIC), can help us to get much higher resolution image beyond what is limited by the signal's bandwidth. We focus on MUSIC imaging algorithm in the paper and investigate the uniqueness and effectiveness conditions of the MUSIC algorithm when used in 1-D radar range imaging. Unlike conventional radar resolution analysis, we introduced the concept of resolution threshold from Direction of Arrival (DOA) into the MUSIC radar range imaging, we derive an approximate expression of theoretical resolution threshold for 1-D MUSIC imaging algorithm through the approach of asymptotic and statistical analysis to the null spectrum based on the perturbation theory of algebra and matrix theories. Monte Carlo simulations are presented to verify the work.
 Mihailo Stojnic Mathematics , 2009, Abstract: Recently, \cite{CRT,DonohoPol} theoretically analyzed the success of a polynomial $\ell_1$-optimization algorithm in solving an under-determined system of linear equations. In a large dimensional and statistical context \cite{CRT,DonohoPol} proved that if the number of equations (measurements in the compressed sensing terminology) in the system is proportional to the length of the unknown vector then there is a sparsity (number of non-zero elements of the unknown vector) also proportional to the length of the unknown vector such that $\ell_1$-optimization succeeds in solving the system. In this paper, we provide an alternative performance analysis of $\ell_1$-optimization and obtain the proportionality constants that in certain cases match or improve on the best currently known ones from \cite{DonohoPol,DT}.
 Mathematics , 2013, DOI: 10.1137/130943200 Abstract: We study active array imaging of small but strong scatterers in homogeneous media when multiple scattering between them is important. We use the Foldy-Lax equations to model wave propagation with multiple scattering when the scatterers are small relative to the wavelength. In active array imaging we seek to locate the positions and reflectivities of the scatterers, that is, to determine the support of the reflectivity vector and the values of its nonzero elements from echoes recorded on the array. This is a nonlinear inverse problem because of the multiple scattering. We show in this paper how to avoid the nonlinearity and form images non-iteratively through a two-step process which involves $\ell_1$ norm minimization. However, under certain illuminations imaging may be affected by screening, where some scatterers are obscured by multiple scattering. This problem can be mitigated by using multiple and diverse illuminations. In this case, we determine solution vectors that have a common support. The uniqueness and stability of the support of the reflectivity vector obtained with single or multiple illuminations are analyzed, showing that the errors are proportional to the amount of noise in the data with a proportionality factor dependent on the sparsity of the solution and the mutual coherence of the sensing matrix, which is determined by the geometry of the imaging array. Finally, to filter out noise and improve the resolution of the images, we propose an approach that combines optimal illuminations using the singular value decomposition of the response matrix together with sparsity promoting optimization jointly for all illuminations. This work is an extension of our previous paper [5] on imaging using optimization techniques where we now account for multiple scattering effects.
 Navid Farahi Physics , 2015, Abstract: With the advent of microsphere assisted microscopy in 2011, this technique emerged as a simple and easy way to obtain optical super-resolution. Although the possible mechanisms of imaging by microspheres are debated in the literature, most of the experimental studies established the resolution values well beyond the diffraction limit. It should be noted, however, that there is no standard resolution measurement in this field that researchers can use. The reported resolution has been based on the smallest discernible feature; although it seems logical but it is not based on the standard textbook definition, and so far it has ended to a wide range of resolution reports based on qualitative criteria which can lead to exaggerated resolution values. In addition, this method has another limitation related to its limited field-of-view. In this work, first we fabricated a novel optical component for super-resolution imaging based on an attachable polydimethylsiloxane (PDMS) thin film with embedded high index (n~2) barium titanate glass (BTG) microspheres. It is shown that such films can be translated along the surface of investigated structures to enhance field-of-view. Second, we introduced a method of image treatment which allows determining the super-resolution values consistent with the resolution definition in the conventional diffraction-limited optics. We demonstrated this method for a typical microsphere-assisted image where we measured the super-resolution of ~{\lambda}/5.5. We also developed this technique to measure the resolution of a micro-cylindrical-assisted system.
 Abdul Wahab Mathematics , 2014, Abstract: The aim of this article is to elaborate and rigorously analyze a topological derivative based imaging framework for locating an electromagnetic inclusion of diminishing size from boundary measurements of the tangential component of scattered magnetic field at a fixed frequency. The inverse problem of inclusion detection is formulated as an optimization problem in terms of a filtered discrepancy functional and the topological derivative based imaging functional obtained therefrom. The sensitivity and resolution analysis of the imaging functional is rigorously performed. It is substantiated that the Rayleigh resolution limit is achieved. Further, the stability of the reconstruction with respect to measurement and medium noises is investigated and the signal-to-noise ratio is evaluated in terms of the imaginary part of free space fundamental magnetic solution.
 Computer Science , 2014, Abstract: This work studies the behavior of three elitist multi- and many-objective evolutionary algorithms generating a high-resolution approximation of the Pareto optimal set. Several search-assessment indicators are defined to trace the dynamics of survival selection and measure the ability to simultaneously keep optimal solutions and discover new ones under different population sizes, set as a fraction of the size of the Pareto optimal set.
 Information Technology Journal , 2009, Abstract: Doppler Beam Sharpening (DBS) technique is one of high-resolution radar imaging technique. DBS images are widely used in tactical reconnaissance, terrain matching and navigation, as well as target identification, etc. Range walking correction technique and azimuth dechirping technique can increase the coherent accumulated time of DBS imaging system, which provides greater space for high-resolution DBS Imaging. However, the resolution of DBS images will be limited by frequency source phase noise. This study addresses the effects of frequency source phase noise on the high-resolution DBS imaging. Quantitative estimates are derived analytically based on the second-order statistics characteristic of oscillator phase noise. The research results could further consummate high-resolution DBS imaging theory and provide theory basis for DBS imaging system design.
 Cardiovascular Ultrasound , 2010, DOI: 10.1186/1476-7120-8-22 Abstract: This study performed high-resolution ultrasound imaging of the brachial artery in a healthy adult subject under normal physiologic pressure and the use of external pressure (pressure equalization) to increase strain. These ultrasound results were compared to measurements of arterial strain as determined by finite-element analysis models with and without a surrounding tissue, which was represented by homogenous material with fixed elastic modulus.Use of the pressure equalization technique during imaging resulted in average strain values of 26% and 18% at the top and sides, respectively, compared to 5% and 2%, at the top and sides, respectively, under physiologic pressure. In the artery model that included surrounding tissue, strain was 19% and 16% under pressure equalization versus 9% and 13% at the top and sides, respectively, under physiologic pressure. The model without surrounding tissue had slightly higher levels of strain under physiologic pressure compared to the other model, but the resulting strain values under pressure equalization were > 60% and did not correspond to experimental values.Since pressure equalization may increase the dynamic range of strain imaging, the effect of the surrounding tissue on strain should be incorporated into models of arterial strain, particularly when the pressure equalization technique is used.Arterial stiffness is associated with numerous disease processes, including cardiovascular and renal disease, peripheral vascular occlusive disease, and diabetes. A possible cause of this increased stiffness is a change in the ratio of collagen to elastin in the extracellular matrix of the arterial media [1-3]. A variety of noninvasive techniques have been employed to measure arterial stiffness and vascular elasticity. The pulse-wave velocity (PWV) technique estimates average arterial stiffness on the basis of the travel time of a wave between two measurement sites. PWV is considered one of the best methods of measuring stiffness when t
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