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In this paper, we review joint sparse recovery based reconstruction approach for inverse scattering problems that can solve the nonlnear inverse scattering probleme without linearization or iterative Green's function update. The main idea is to exploit the common support conditions of anomalies during multiple illumination or current injections, after which unknown potential or field can be estimated using recursive integral equation relationship. Explicit derivation for electric impedance tomography and diffuse optical tomography are discussed.

Localization microscopy such as STORM/PALM can achieve a nanometer scale spatial resolution by iteratively localizing fluorescence molecules. It was shown that imaging of densely activated molecules can accelerate temporal resolution which was considered as major limitation of localization microscopy. However, this higher density imaging needs to incorporate advanced localization algorithms to deal with overlapping point spread functions (PSFs). In order to address this technical challenges, previously we developed a localization algorithm called FALCON1, 2 using a quasi-continuous localization model with sparsity prior on image space. It was demonstrated in both 2D/3D live cell imaging. However, it has several disadvantages to be further improved. Here, we proposed a new localization algorithm using annihilating filter-based low rank Hankel structured matrix approach (ALOHA). According to ALOHA principle, sparsity in image domain implies the existence of rankdeficient Hankel structured matrix in Fourier space. Thanks to this fundamental duality, our new algorithm can perform data-adaptive PSF estimation and deconvolution of Fourier spectrum, followed by truly grid-free localization using spectral estimation technique. Furthermore, all these optimizations are conducted on Fourier space only. We validated the performance of the new method with numerical experiments and live cell imaging experiment. The results confirmed that it has the higher localization performances in both experiments in terms of accuracy and detection rate.

Recently, there has been increased interest in the usage of neuroimaging techniques to investigate what happens in the brain at rest. Functional imaging studies have revealed that the default-mode network activity is disrupted in Alzheimer's disease (AD). However, there is no consensus, as yet, on the choice of analysis method for the application of resting-state analysis for disease classification. This paper proposes a novel compressed sensing based resting-state fMRI analysis tool called Sparse-SPM. As the brain's functional systems has shown to have features of complex networks according to graph theoretical analysis, we apply a graph model to represent a sparse combination of information flows in complex network perspectives. In particular, a new concept of spatially adaptive design matrix has been proposed by implementing sparse dictionary learning based on sparsity. The proposed approach shows better performance compared to other conventional methods, such as independent component analysis (ICA) and seed-based approach, in classifying the AD patients from normal using resting-state analysis.

This paper describes a novel quantitative phase microscopy based on a simple self-referencing scheme using Michelson interferometry. In order to achieve the homogeneous reference field for accurate phase measurement, the imaging field-of-view (FOV) is split onto the sample and homogenous background areas. The reference field can be generated by rotating the relative position of the sample and homogenous background in the object arm. Furthermore, our system is realized using an extended depth-of-field (eDOF) optics, which allows quantitative phase measurement for an increase of the depth-of-field without moving objective lens or specimen. The proposed method is confirmed by experimental results using various samples such as polystyrene beads and red blood cells (RBCs).

Inverse scattering refers the retrieval of the unknown constitutive parameters from measured scattered wave fields, and has many applications such as ultrasound imaging, optics, T-ray imaging, radar, and etc. Two distinct imaging strategies have been commonly used: narrow band inverse scattering approaches using a large number of transmitters and receivers, or wideband imaging approaches with smaller number of transmitters and receivers. In some biomedical imaging applications, the limited accessibility of scattered fields using externally located antenna arrays usually prefers the wideband imaging approaches. The main contribution of this paper is, therefore, to analyze the wideband inverse scattering problem from compressive sensing perspective. Specifically, the mutual coherence of the wideband imaging geometry is analyzed, which reveals a significant advantage to identify the sparse targets from very limited number of measurements.

Single particle reconstruction is often employed for 3-D reconstruction of diverse macromolecules. However, the algorithm requires a good initial guess from a priori information to guarantee the convergence to the correct solution. This paper describes a novel model free 3-D reconstruction algorithm by employing the symmetry and sparsity of unknown structure. Especially, we develop an accurate and fully automatic iterative algorithm for 3D reconstruction of unknown helix structures. Because the macromolecule structure assumes only sparse supports in real space and the helical symmetry provides several symmetric views from a single micrograph, a reasonably quality 3-D reconstruction can be obtained from the limited views using the compressed sensing theory. Furthermore, the correct helix parameters usually provide the maximal variance of the reconstructed volume, facilitating the parameter estimation. Remarkably, the search space of helix parameter can be drastically reduced by exploiting the diffraction pattern. With the estimated helix parameter and additional 3-D registration, the multiple helix segments can be combined for the optimal quality reconstruction. Experimental results using synthetic and real helix data confirm that our algorithm provides superior reconstruction of 3-D helical structure.

This paper describes a novel reconstruction algorithm for microscopy axial tomography, which reconstructs a 3-D volume using multiple tilted views through an off-centered aperture and numerical processing. The main contribution of this paper is a derivation of novel optimization criterion and algorithm for a cost function with L 1 fidelity term and sparsity constraint. A parallel coordinate descent (PCD) algorithm has been derived as an efficient optimization methods, which corresponds to iterative application of projection and nonlinear back-projection using median. Numerical simulation results using synthetic and real microscopy data show that accurate reconstruction can be obtained rapidly, and interference artifacts from high contrast objects in a volume can be removed efficiently. Our algorithm is quite general, and can be used for many other tomosynthesis applications with limited number of views.© (2008) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Even though there exists a powerful statistical parametric mapping (SPM) tool for fMRI, similar public domain tools are not available for near infrared spectroscopy (NIRS). In this paper, we describe a new public domain statistical toolbox called NIRS-SPM for quantitative analysis of NIRS signals. Specifically, NIRS-SPM statistically analyzes the NIRS data using GLM and makes inference as the excursion probability which comes from the random field that are interpolated from the sparse measurement. In order to obtain correct inference, NIRS-SPM offers the pre-coloring and pre-whitening method for temporal correlation estimation. For simultaneous recording NIRS signal with fMRI, the spatial mapping between fMRI image and real coordinate in 3-D digitizer is estimated using Horn's algorithm. These powerful tools allows us the super-resolution localization of the brain activation which is not possible using the conventional NIRS analysis tools.

Sparse object supports are often encountered in many imaging problems. For such sparse objects, recent theory of compressed sensing tells us that accurate reconstruction of objects are possible even from highly limited number of measurements drastically smaller than the Nyquist sampling limit by solving L 1 minimization problem. This paper employs the compressed sensing theory for cryo-electron microscopy (cryo-EM) single particle reconstruction of virus particles. Cryo-EM single particle reconstruction is a nice application of the compressed sensing theory because of the following reasons: 1) in some cases, due to the difficulty in sample collection, each experiment can obtain micrographs with limited number of virus samples, providing undersampled projection data, and 2) the nucleic acid of a viron is enclosed within capsid composed of a few proteins; hence the support of capsid in 3-D real space is quite sparse. In order to minimize the L 1 cost function derived from compressed sensing, we develop a novel L 1 minimization method based on the sliding mode control theory. Experimental results using synthetic and real virus data confirm that the our algorithm provides superior reconstructions of 3-D viral structures compared to the conventional reconstruction algorithms.

This paper is concerned about high resolution reconstruction of projection reconstruction MR imaging from angular under-sampled k-space data. A similar problem has been recently addressed in the framework of compressed sensing theory. Unlike the existing algorithms used in compressed sensing theory, this paper employs the FOCal Underdetermined System Solver(FOCUSS), which was originally designed for EEG and MEG source localization to obtain sparse solution by successively solving quadratic optimization. We show that FOCUSS is very effective for the projection reconstruction MRI, because the medical images are usually sparse in image domain, and the center region of the under-sampled radial k-space data still provides a meaningful low resolution image, which is essential for the convergence of FOCUSS. We applied FOCUSS for projection reconstruction MR imaging using single coil. Extensive experiments confirms that high resolution reconstruction with virtually free of angular aliasing artifacts can be obtained from severely under-sampled k-space data.

A novel support vector machine (SVM) classifier incorporating the complexity of fluorescent spectral data is designed to reliably differentiate normal and malignant human breast cancer tissues. Analysis has been carried out with parallel and perpendicularly polarized fluorescence data using 36 normal and 36 cancerous tissue samples. In order to incorporate the complexity of fluorescence spectral profile into a SVM design, the curvature of phase space trajectory is extracted as a useful complexity feature. We found that the fluorescence intensity peaks at 541nm-620nm as well as the complexity features at 621nm-700nm are important discriminating features. By incorporating both features in SVM design, we can improve both sensitivity and specificity of the classifier.

Optical diffusion imaging is a new imaging modality that promises great potential in applications such as medical imaging, environmental sensing and nondestructive testing. It presents a difficult nonlinear image reconstruction problem however. An inversion algorithm is formulated in Bayesian framework, and an efficient optimization technique that uses iterative coordinate descent is presented. A general multigrid optimization technique for nonlinear image reconstruction problems is developed and applied to the optical diffusion imaging problem. Numerical results show that this approach improves the quality of reconstructions and dramatically decreases computation times.

We present new methods for computing fundamental performance limits for parametric shape estimation in inverse scattering problems, such as passive radar imaging. We evaluate Cramer- Rao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory. The CRB provides an unbeatable performance limit for nay unbiased estimator, and under fairly mild regularity conditions, is asymptotically achieved by the maximum likelihood estimator (MLE). Furthermore, the resultant CRBs are used to define a global confidence region, centered around the true boundary, in which the boundary estimate lies with a prescribed probability. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated target, and facilitate geometric inferences. Numerical simulations are performed using the layer approach and the Nystrom method for computation of domain derivatives, and using Fourier descriptors for target shape parameterization. This analysis demonstrates the accuracy and generality of the proposed methods.

Frequency-domain diffusion imaging is a new imaging modality which uses the magnitude and phase of modulated light propagation through a highly scattering medium to reconstruct an image of the scattering and/or the absorption coefficient in the medium. In this paper, the inversion algorithm is formulated in a Bayesian framework and an efficient optimization technique is presented for calculating the maximum a posteriori image. Numerical result show that the Bayesian framework with the new optimization scheme out-performs conventional approaches in both speed and reconstruction quality.

A weighted distorted Born iterative method is presented for reconstruction optical diffusion images from scattering data. A generalization of the distorted Born iterative method that uses a preconditioned cost function and an elliptical constraint allows a weighting matrix to be applied to the gradient term in the iterative algorithm according to the reconstruction history. The proposed algorithm shows stable and fast convergence for reconstruction of high contrast inhomogeneities.