18,813 research outputs found
Sparse image reconstruction for molecular imaging
The application that motivates this paper is molecular imaging at the atomic
level. When discretized at sub-atomic distances, the volume is inherently
sparse. Noiseless measurements from an imaging technology can be modeled by
convolution of the image with the system point spread function (psf). Such is
the case with magnetic resonance force microscopy (MRFM), an emerging
technology where imaging of an individual tobacco mosaic virus was recently
demonstrated with nanometer resolution. We also consider additive white
Gaussian noise (AWGN) in the measurements. Many prior works of sparse
estimators have focused on the case when H has low coherence; however, the
system matrix H in our application is the convolution matrix for the system
psf. A typical convolution matrix has high coherence. The paper therefore does
not assume a low coherence H. A discrete-continuous form of the Laplacian and
atom at zero (LAZE) p.d.f. used by Johnstone and Silverman is formulated, and
two sparse estimators derived by maximizing the joint p.d.f. of the observation
and image conditioned on the hyperparameters. A thresholding rule that
generalizes the hard and soft thresholding rule appears in the course of the
derivation. This so-called hybrid thresholding rule, when used in the iterative
thresholding framework, gives rise to the hybrid estimator, a generalization of
the lasso. Unbiased estimates of the hyperparameters for the lasso and hybrid
estimator are obtained via Stein's unbiased risk estimate (SURE). A numerical
study with a Gaussian psf and two sparse images shows that the hybrid estimator
outperforms the lasso.Comment: 12 pages, 8 figure
Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization
We present a reconstruction method involving maximum-likelihood expectation
maximization (MLEM) to model Poisson noise as applied to fluorescence molecular
tomography (FMT). MLEM is initialized with the output from a sparse
reconstruction-based approach, which performs truncated singular value
decomposition-based preconditioning followed by fast iterative
shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation
for this approach is that sparsity information could be accounted for within
the initialization, while MLEM would accurately model Poisson noise in the FMT
system. Simulation experiments show the proposed method significantly improves
images qualitatively and quantitatively. The method results in over 20 times
faster convergence compared to uniformly initialized MLEM and improves
robustness to noise compared to pure sparse reconstruction. We also
theoretically justify the ability of the proposed approach to reduce noise in
the background region compared to pure sparse reconstruction. Overall, these
results provide strong evidence to model Poisson noise in FMT reconstruction
and for application of the proposed reconstruction framework to FMT imaging
Phase Retrieval with Application to Optical Imaging
This review article provides a contemporary overview of phase retrieval in
optical imaging, linking the relevant optical physics to the information
processing methods and algorithms. Its purpose is to describe the current state
of the art in this area, identify challenges, and suggest vision and areas
where signal processing methods can have a large impact on optical imaging and
on the world of imaging at large, with applications in a variety of fields
ranging from biology and chemistry to physics and engineering
Hierarchical Bayesian sparse image reconstruction with application to MRFM
This paper presents a hierarchical Bayesian model to reconstruct sparse
images when the observations are obtained from linear transformations and
corrupted by an additive white Gaussian noise. Our hierarchical Bayes model is
well suited to such naturally sparse image applications as it seamlessly
accounts for properties such as sparsity and positivity of the image via
appropriate Bayes priors. We propose a prior that is based on a weighted
mixture of a positive exponential distribution and a mass at zero. The prior
has hyperparameters that are tuned automatically by marginalization over the
hierarchical Bayesian model. To overcome the complexity of the posterior
distribution, a Gibbs sampling strategy is proposed. The Gibbs samples can be
used to estimate the image to be recovered, e.g. by maximizing the estimated
posterior distribution. In our fully Bayesian approach the posteriors of all
the parameters are available. Thus our algorithm provides more information than
other previously proposed sparse reconstruction methods that only give a point
estimate. The performance of our hierarchical Bayesian sparse reconstruction
method is illustrated on synthetic and real data collected from a tobacco virus
sample using a prototype MRFM instrument.Comment: v2: final version; IEEE Trans. Image Processing, 200
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
Variational semi-blind sparse deconvolution with orthogonal kernel bases and its application to MRFM
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM)
X-ray luminescence computed tomography using a focused X-ray beam
Due to the low X-ray photon utilization efficiency and low measurement
sensitivity of the electron multiplying charge coupled device (EMCCD) camera
setup, the collimator based narrow beam X-ray luminescence computed tomography
(XLCT) usually requires a long measurement time. In this paper, we, for the
first time, report a focused X-ray beam based XLCT imaging system with
measurements by a single optical fiber bundle and a photomultiplier tube (PMT).
An X-ray tube with a polycapillary lens was used to generate a focused X-ray
beam whose X-ray photon density is 1200 times larger than a collimated X-ray
beam. An optical fiber bundle was employed to collect and deliver the emitted
photons on the phantom surface to the PMT. The total measurement time was
reduced to 12.5 minutes. For numerical simulations of both single and six fiber
bundle cases, we were able to reconstruct six targets successfully. For the
phantom experiment, two targets with an edge-to-edge distance of 0.4 mm and a
center-to-center distance of 0.8 mm were successfully reconstructed by the
measurement setup with a single fiber bundle and a PMT.Comment: 39 Pages, 12 Figures, 2 Tables, In submission (under review) to JB
Iterative CT reconstruction using shearlet-based regularization
In computerized tomography, it is important to reduce the image noise without increasing the acquisition dose. Extensive research has been done into total variation minimization for image denoising and sparse-view reconstruction. However, TV minimization methods show superior denoising performance for simple images (with little texture), but result in texture information loss when applied to more complex images. Since in medical imaging, we are often confronted with textured images, it might not be beneficial to use TV. Our objective is to find a regularization term outperforming TV for sparse-view reconstruction and image denoising in general. A recent efficient solver was developed for convex problems, based on a split-Bregman approach, able to incorporate regularization terms different from TV. In this work, a proof-of-concept study demonstrates the usage of the discrete shearlet transform as a sparsifying transform within this solver for CT reconstructions. In particular, the regularization term is the 1-norm of the shearlet coefficients. We compared our newly developed shearlet approach to traditional TV on both sparse-view and on low-count simulated and measured preclinical data. Shearlet-based regularization does not outperform TV-based regularization for all datasets. Reconstructed images exhibit small aliasing artifacts in sparse-view reconstruction problems, but show no staircasing effect. This results in a slightly higher resolution than with TV-based regularization
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