This paper describes numerical estimation techniques for coded aperture snapshot spectral imagers (CASSI). In
a snapshot, a CASSI captures a two-dimensional (2D) array of measurements that is an encoded representation
of both spectral information and 2D spatial information of a scene. The spatial information is modulated by
a coded aperture and the spectral information is modulated by a dispersive element. The estimation process
decodes the 2D measurements to render a three-dimensional spatio-spectral estimate of the scene, and is therefore
an indispensable component of the spectral imager. Numerical estimation results are presented.
A hybrid method is presented which allows the acceleration of parallel MR imaging through combining the ideas
of compressed sensing with inversion of the imaging matrix. A novel data reordering is employed to enhance the
sparsity inherent in the image transform. Simulation results with actual head scan data are presented.
With this work we propose spatio-temporal sampling strategies for video using a lenslet array computational imaging system and explore the opportunities and challenges in the design of compressive video sensors and corresponding processing algorithms. The redundancies in video streams are exploited by (a) sampling the sub-apertures of a multichannel (TOMBO) camera, and (b) by the computational reconstruction to achieve low power and low complexity video sensors. A spatial and a spatio-temporal sampling strategy are considered, taking into account the feasibility for implementation in the focal-plane readout hardware. The algorithms used to reconstruct the video frames from measurements are also presented.
Intensity diffraction tomography (I-DT) is a non-interferometric imaging method for reconstructing the complex-valued
refractive index distribution of a weakly scattering object. The original formulation of I-DT requires
measurement of two in-line intensity measurements on parallel detector planes at each tomographic view angle.
In this work, a reconstruction theory for multi-spectral is established and investigated for use with single material
objects whose dispersion characteristics are known a priori. Unlike other I-DT methods, the temporal frequency
of the illuminating plane-wave represents the degree-of-freedom of the imaging system that is varied to acquire
two independent intensity measurements on a fixed detector-plane. Moreover, the proposed method accounts for
Reconstructing an object from scattered field data has always been very challenging, especially when dealing with strong
scatterers scatterers. Several techniques have been proposed to address this problem but either they fail to provide a good estimate
. of the object or they are computationally very expensive. We have proposed a straightforward non non-linear signal
processing method in which we fir first process the scattered field data to generate a minimum phase function in the object
st domain. This is accomplished by adding a reference wave whose amplitude and phase satisfy certain conditions.
Minimum Minimum-phase functions are causal transforms and their ph phase is continuous in the interval -π and +π i.e. it is always
unwrapped. Following this step, we compute the Fourier transform of the logarithm of this minimum phase function,
referred to as its cepstrum. In this domain one can filter cepstral frequencie frequencies arising from the object from those of the
s scattered field. Cepstral data are meaningless for non non-minimum phase functions because of phase wraps. We apply low
pass filters in the cepstral domain to isolate information about the object and then perform an inverse transform and
exponentiation. We have applied this technique to measured data provided by Institut Fresnel (Marseille, France) and
investigated in a systematic way the dependence of the approach on the properties of the reference wave and filter. We
show that while being a robust method, one can identify optimal parameters for the reference wave that result in a good
reconstruction of a penetrable, strongly scattering permittivity distribution.
In this work different surrogate data strategies to reduce metal artifacts in reconstructed CT images are tested.
Inconsistent sinogram projection data caused by e.g. beam hardening are the origin of metal artifacts in the
reconstructed images. The goal of this work is to replace this inconsistent projection data by artificially generated data.
Therefore, here, two 1D interpolation strategies, a directional interpolation based upon the sinogram 'flow' and a 1D
interpolation by means of the non-equispaced fast Fourier transform are compared to a fully 2D method based upon the
idea of image inpainting. Due to the fact that the artificially generated data never perfectly fit the gap inside the
projection data caused by the inconsistencies, those repaired sinogram data are reconstructed using a weighted
Maximum Likelihood Expectation Maximization algorithm called λ-MLEM algorithm. In this way, the artificially
generated data, still contaminated with residual inconsistencies, are weighted less during reconstruction.
Diffuse Optical Tomography (DOT) is a functional medical imaging modality which can determine the spatial optical parameters' distributions inside a medium. The forward model of DOT is described by the diffusion approximation of radiative transform equation (RTE) while the DOT is to recover optical parameters of a medium from the boundary measurements induced by external near-infared (NIR) light. In this paper, we propose a mathematic model of DOT and then give a novel iterative reconstruction method of the proposed model. The new iterative reconstruction method is based on the assumption that the measurement noise is Poissonian while previous iterative reconstruction methods are mostly base on the assumption that the measurement noise is Gaussian, and are of least-squares type. The proposed algorithm is a variant of the well-known EM algorithm. It can also be used to deal with the incomplete boundary measurements. The performance of the reconstruction algorithm including spatial resolution and contrast are investigated with 2-dimensional numerical experiments.
Extracting quantitative image information from coherent diffraction measurements remains challenging due to
problems such as slow convergence of iterative phase retrieval algorithms, questionable uniqueness of the resulting
images, and common requirements of compactness of the specimens. These difficulties are overcome by combining
iterative phase retrieval with ptychography, i.e., the use of multiple diffraction measurements probing several
overlapping regions of the specimen. While promising results of ptychographical coherent diffractive imaging have
been achieved the technique has been limited by requiring precise knowledge of the illumination. We present
advances of the reconstruction algorithm, which allow unsupervised deconvolution of the illuminating probe and
the complex-valued optical transmission function of the specimen. We have performed measurements using both
visible light and x-rays, demonstrating sub-50nm resolution.
Measuring a series of far-field intensity patterns from an object, taken after a transverse translation of the object with respect to a known illumination pattern, has been shown to make the problem of image reconstruction by phase retrieval much more robust. However, previously reported reconstruction algorithms [Phys. Rev. Lett. 93, 023903 (2004)] rely on an accurate knowledge of the translations and illumination pattern for a successful reconstruction. We developed a nonlinear optimization algorithm that allows optimization over the translations and illumination pattern, dramatically improving the reconstructions if the system parameters are inaccurately known [Opt. Express 16, 7264 (2008)]. In this paper we compare reconstructions obtained with these algorithms under realistic experimental scenarios.
An algorithm is described for reconstructing compact binary images from limited Fourier amplitude data. This
problem arises in macromolecular crystallography where one wishes to reconstruct the molecular envelope from
crystal x-ray diffraction amplitudes using a solvent contrast series. Such data are the amplitude of the Fourier
transform of an object that has a constant electron density within the boundary of the molecule and zero outside.
The image is thus binary and compact, but the data are available only within a limited resolution range in Fourier
space and are undersampled. The problem is solved using an iterative projection algorithm; a class of algorithm
used to solve inverse problems for which the solution is subject to a number of constraints that represent a priori
information and the data. Unfortunately, these algorithms experience convergence difficulties if one or more of
the constraints are non-convex, which is the case for all the constraints in this problem. We solve the problem
by constructing appropriate projection operators and implementing the difference map projection algorithm.
Simulations are used to study convergence behaviour of the algorithm.
X-ray phase-retrieval algorithms are widely exploited in contemporary diffraction techniques to image at the nanoscale.
Often reconstruction of the sample shape (image) suffices for the purpose of experiment. Identification of specimen
composition requires a quantitative profiling of the complex refractive index. We show that the diffraction effects from
the experimental setup and artifacts from the phase-retrieval algorithms themselves are comparable with the diffraction
contrast that is experimentally observable from thin specimens with very low electron density. We show that, based on
the analysis of application of the relevant phase-retrieval methods, there is a lower limit in optical density, which can be
reconstructed using the existing phase-retrieval methods. This limit appears to be imposed by real-life experimental
conditions and the intrinsic artifacts of the phase-retrieval techniques.
We report a test of the turbulence found in real-world, horizontal imaging under high magnification. The experiment
creates a double "star" on a test chart for use both with a SLODAR turbulence profiling instrument, and simultaneously
imaged using a very fast camera to determine traditional seeing parameters. Effects on a similarly located image are
investigated to determine the observed effects on the imagery as a function of turbulence location.
We present a simple theoretical model for dewarped imaging through a turbulent medium, and calculate the degree of superresolution that can be attained by dewarping of the distorted instantaneous images registered through a turbulent atmosphere. Our estimates show that on 1 km near the ground propagation path spatial frequencies of the dewarped image can exceed the diffraction limit three times with a probability up to 10%.
In our previous work we have demonstrated that the perceived wander of image intensities as seen through the
"windows" of each pixel due to atmospheric turbulence can be modelled as a simple oscillator pixel-by-pixel and a linear
Kalman filter (KF) can be finetuned to predict to a certain extent short term future deformations. In this paper, we are
expanding the Kalman filter into a Hybrid Extended Kalman filter (HEKF) to fine tune itself by relaxing the oscillator
parameters at each individual pixel. Results show that HEKF performs significantly better than linear KF.
Maximum likelihood statistical algorithms are described for estimating the 3-D variation of the electron scattering
intensity of biological objects from cryo electron microscopy images of multiple instances of the object.
Three virus objects, two spherical and one helical, are considered. Solution of the maximum likelihood problem
by expectation maximization algorithms or by direct maximization of the log likelihood requires large scale computing
and end-to-end codesign of biological problem formulation, statistical models, algorithms, and software
design and implementation have contributed to achieving practical results.
Bulk motion occurring during the acquisition of data in magnetic resonance imaging (MRI) causes serious artifacts
in the reconstructed images. The paper presents an extension to TRELLIS, a recently developed method of
detecting and correcting for bulk motion. While TRELLIS detects and corrects for bulk translation and rotation,
only rotation is considered here. Accurate determination of the relative orientations of overlapping strips of kspace
is demonstrated using a robust statistical approach to aid least squares estimation. Reconstructions for
both simulated and actual MRI acquisitions are presented.
Recently, a model based dynamic imaging algorithm called k-t BLAST/SENSE has drawn significant attentions from MR imaging community due to its improved spatio-temporal resolution for dynamic MR imaging. In our previous work, we proved that k-t BLAST/SENSE can be derived as the first step of FOCal Underdetermined System Solver (FOCUSS) that exploits the sparsity of x-f support. Furthermore, the newly derived algorithm called k-t FOCUSS can be shown optimal from compressed sensing perspective. In this paper, the k-t FOCUSS algorithm is extended to radial trajectory. More specifically, the
radial data are transformed to Cartesian domain implicitly during
the FOCUSS iterations without explicit gridding to prevent error propagation. Thanks to the implicit gridding that allows fast Fourier transform, we can reduce the computational burden
significantly. Additionally, a novel concept of motion estimation and compensation (ME/MC) is proposed to
improve the performance of the algorithm significantly. In our ME/MC framework, we additionally obtain one reference sinogram with the full view, then the reference signogram is subtracted from all the radial data. Then, we can apply motion estimation/ motion compensation (ME/MC) to improve the final reconstruction. The experimental results show that our new method can provide very high resolution even from very limited radial data set.
We analyze a Fourier-domain Wiener filter for the reconstruction of aliased imagery. The filter is designed to minimize the expected mean square error for the unaliased portion of the object Fourier transform. This analysis yields a net system transfer function, which characterizes the combined effects of the imaging system, sampling, and the reconstruction process, that is valid at both aliased and unaliased spatial frequencies. This transfer function provides insight into how aliasing artifacts are modified by the reconstruction process. Additionally, the net transfer function is useful for characterizing the combined performance of the imaging system and post processing. For example, the net system transfer function can be used to calculate the edge response for reconstructed imagery even in the presence of aliasing. Examples are used to illustrate these aspects of using the Wiener filter with aliased imagery.
Multichannel sampling strategies have been considered for a number of applications including feature specific
imaging, and digital superresolution. Typically, channel coding is accomplished with a thin modulating mask,
either in the focal plane, or in the aperture of the imaging system. In this contribution, we extend the concept
of multichannel imaging to systems by suggesting the use of 3D structures for channel coding. A single pixel
camera design and the single scattering approximation are used to obtain a Fourier space interpretation of 3D
filters. The k-space analysis indicates that the dispersion relation of propagating plane wave modes set severe
constraints if 3D filters are used for channel coding. We relate this to the broader questions about the fundamental
limits of optical and computational imaging and propose 3D filters for wavelength coding and superresolution
This paper deals with simulation and modeling of the optical systems used in astronomy and their transfer characteristics. It is especially focused to the WFC (Wide-Field Camera) and UWFC (Ultra Wide-Field Camera) SV (Space Variant) optical systems. The properties of UWFC astronomical systems along with specific visual data in astronomical images contribute to complicated evaluation of acquired image data. There is an experiment for estimate the optical aberration
of optical systems described in this paper. The results of different deconvolution algorithms, which are used with partially variant model of UWFC optical system, are demonstrated in this paper.
Proc. SPIE 7076, The iterative detection network based suppression of the thermal noise and blurring due to object moving in black and white pictures shot by a camera with CCD/CMOS sensor, 70760M (5 September 2008); doi: 10.1117/12.794224
The paper deals with elimination of blurring caused by the object moving and thermal noise in black & white pictures captured by a CCD/CMOS camera. This problem can be also interpreted like image passage through some kind of ISI channel with specific 2D impulse response. Hence for purposes of image recovery we can use the MAP criterion based iterative detection network (IDN) containing a number of mutually concatenated functional blocks so-called soft inversions (SISOs). This cellular structure makes IDN suboptimal but also numerically very simple and practically applicable in contrast to an unviable optimal (single-stage) MAP detector. Firstly we focus closer to parameters determination of the image blurring hypothetical model (misrepresenting ISI channel). Consequently we are going to deal with the SISO entities and the synthesis of entire IDN, specifically the synthesis of so-called distributed IDN marginalizing at the symbol level because this structure presents the best solution for the mentioned issue. At the end, the image reconstruction example will be presented (using this type of IDN).