Reconstruction from incomplete data in cone-beam tomography

A method for reconstruction of an object f(x) x=(x,y,z) from a limited set of cone-beam projection data has been developed. This method uses a modified form of convolution back-projection and projection onto convex sets (POCS) for handling the limited (or incomplete) data problem. In cone-beam tomography, one needs to have a complete geometry to completely reconstruct the original three-dimensional object. While complete geometries do exist, they are of little use in practical implementations. The most common trajectory used in practical scanners is circular, which is incomplete. It is, however, possible to recover some of the information of the original signal f(x) based on a priori knowledge of the nature of f(x). If this knowledge can be posed in a convex set framework, then POCS can be utilized. In this report, we utilize this a priori knowledge as convex set constraints to reconstruct f(x) using POCS. While we demonstrate the effectiveness of our algorithm for circular trajectories, it is essentially geometry independent and will be useful in any limited-view cone-beam reconstruction.

Performance Analysis of Reconstruction Techniques for Frequency-Domain Optical-Coherence Tomography

We address the issue of noise robustness of reconstruction techniques for frequency-domain optical-coherence tomography (FDOCT). We consider three reconstruction techniques: Fourier, iterative phase recovery, and cepstral techniques. We characterize the reconstructions in terms of their statistical bias and variance and obtain approximate analytical expressions under the assumption of small noise. We also perform Monte Carlo analyses and show that the experimental results are in agreement with the theoretical predictions. It turns out that the iterative and cepstral techniques yield reconstructions with a smaller bias than the Fourier method. The three techniques, however, have identical variance profiles, and their consistency increases linearly as a function of the signal-to-noise ratio.

Anterior cruciate ligament reconstruction with special reference to magnetic resonance imaging of the postoperative outcome

Anterior cruciate ligament (ACL) tear is a common sports injury of the knee. Arthroscopic reconstruction using autogenous graft material is widely used for patients with ACL instability. The grafts most commonly used are the patellar and the hamstring tendons, by various fixation techniques. Although clinical evaluation and conventional radiography are routinely used in follow-up after ACL surgery, magnetic resonance imaging (MRI) plays an important role in the diagnosis of complications after ACL surgery. The aim of this thesis was to study the clinical outcome of patellar and hamstring tendon ACL reconstruction techniques. In addition, the postoperative appearance of the ACL graft was evaluated using several MRI sequences. Of the 175 patients who underwent an arthroscopically assisted ACL reconstruction, 99 patients were randomized into patellar tendon (n=51) or hamstring tendon (n=48) groups. In addition, 62 patients with hamstring graft ACL reconstruction were randomized into either cross-pin (n=31) or interference screw (n=31) fixation groups. Follow-up evaluation determined knee laxity, isokinetic muscle performance and several knee scores. Lateral and anteroposterior view radiographs were obtained. Several MRI sequences were obtained with a 1.5-T imager. The appearance and enhancement pattern of the graft and periligamentous tissue, and the location of bone tunnels were evaluated. After MRI, arthroscopy was performed on 14 symptomatic knees. The results revealed no significant differences in the 2-year outcome between the groups. In the hamstring tendon group, the average femoral and tibial bone tunnel diameter increased during 2 years follow-up by 33% and 23%, respectively. In the asymptomatic knees, the graft showed homogeneous and low signal intensity with periligamentous streaks of intermediate signal intensity on T2-weighted MR images. In the symptomatic knees, arthroscopy revealed 12 abnormal grafts and two meniscal tears, each with an intact graft. Among 3 lax grafts visible on arthroscopy, MRI showed an intact graft and improper bone tunnel placement. For diagnosing graft failure, all MRI findings combined gave a specificity of 90% and a sensitivity of 81%. In conclusion, all techniques appeared to improve patients' performance, and were therefore considered as good choices for ACL reconstruction. In follow-up, MRI permits direct evaluation of the ACL graft, the bone tunnels, and additional disorders of the knee. Bone tunnel enlargement and periligamentous tissue showing contrast enhancement were non-specific MRI findings that did not signify ACL deficiency. With an intact graft and optimal femoral bone tunnel placement, graft deficiency is unlikely, and the MRI examination should be carefully scrutinized for possible other causes for the patients symptoms.

Dynamic programming based optimum non-uniform samples for speech reconstruction and coding

Non-uniform sampling of a signal is formulated as an optimization problem which minimizes the reconstruction signal error. Dynamic programming (DP) has been used to solve this problem efficiently for a finite duration signal. Further, the optimum samples are quantized to realize a speech coder. The quantizer and the DP based optimum search for non-uniform samples (DP-NUS) can be combined in a closed-loop manner, which provides distinct advantage over the open-loop formulation. The DP-NUS formulation provides a useful control over the trade-off between bitrate and performance (reconstruction error). It is shown that 5-10 dB SNR improvement is possible using DP-NUS compared to extrema sampling approach. In addition, the close-loop DP-NUS gives a 4-5 dB improvement in reconstruction error.

Exact complex-wave reconstruction in digital holography

We address the problem of exact complex-wave reconstruction in digital holography. We show that, by confining the object-wave modulation to one quadrant of the frequency domain, and by maintaining a reference-wave intensity higher than that of the object, one can achieve exact complex-wave reconstruction in the absence of noise. A feature of the proposed technique is that the zero-order artifact, which is commonly encountered in hologram reconstruction, can be completely suppressed in the absence of noise. The technique is noniterative and nonlinear. We also establish a connection between the reconstruction technique and homomorphic signal processing, which enables an interpretation of the technique from the perspective of deconvolution. Another key contribution of this paper is a direct link between the reconstruction technique and the two-dimensional Hilbert transform formalism proposed by Hahn. We show that this connection leads to explicit Hilbert transform relations between the magnitude and phase of the complex wave encoded in the hologram. We also provide results on simulated as well as experimental data to validate the accuracy of the reconstruction technique. (C) 2011 Optical Society of America

Zero-crossing approach to high-resolution reconstruction in frequency-domain optical-coherence tomography

We address the problem of high-resolution reconstruction in frequency-domain optical-coherence tomography (FDOCT). The traditional method employed uses the inverse discrete Fourier transform, which is limited in resolution due to the Heisenberg uncertainty principle. We propose a reconstruction technique based on zero-crossing (ZC) interval analysis. The motivation for our approach lies in the observation that, for a multilayered specimen, the backscattered signal may be expressed as a sum of sinusoids, and each sinusoid manifests as a peak in the FDOCT reconstruction. The successive ZC intervals of a sinusoid exhibit high consistency, with the intervals being inversely related to the frequency of the sinusoid. The statistics of the ZC intervals are used for detecting the frequencies present in the input signal. The noise robustness of the proposed technique is improved by using a cosine-modulated filter bank for separating the input into different frequency bands, and the ZC analysis is carried out on each band separately. The design of the filter bank requires the design of a prototype, which we accomplish using a Kaiser window approach. We show that the proposed method gives good results on synthesized and experimental data. The resolution is enhanced, and noise robustness is higher compared with the standard Fourier reconstruction. (c) 2012 Optical Society of America

Multidimensional data reconstruction for two color fluorescence microscopy

We propose an iterative data reconstruction technique specifically designed for multi-dimensional multi-color fluorescence imaging. Markov random field is employed (for modeling the multi-color image field) in conjunction with the classical maximum likelihood method. It is noted that, ill-posed nature of the inverse problem associated with multi-color fluorescence imaging forces iterative data reconstruction. Reconstruction of three-dimensional (3D) two-color images (obtained from nanobeads and cultured cell samples) show significant reduction in the background noise (improved signal-to-noise ratio) with an impressive overall improvement in the spatial resolution (approximate to 250 nm) of the imaging system. Proposed data reconstruction technique may find immediate application in 3D in vivo and in vitro multi-color fluorescence imaging of biological specimens. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4769058]

Multiple transmitter localization and communication footprint identification using sparse reconstruction techniques

This paper considers the problem of identifying the footprints of communication of multiple transmitters in a given geographical area. To do this, a number of sensors are deployed at arbitrary but known locations in the area, and their individual decisions regarding the presence or absence of the transmitters' signal are combined at a fusion center to reconstruct the spatial spectral usage map. One straightforward scheme to construct this map is to query each of the sensors and cluster the sensors that detect the primary's signal. However, using the fact that a typical transmitter footprint map is a sparse image, two novel compressive sensing based schemes are proposed, which require significantly fewer number of transmissions compared to the querying scheme. A key feature of the proposed schemes is that the measurement matrix is constructed from a pseudo-random binary phase shift applied to the decision of each sensor prior to transmission. The measurement matrix is thus a binary ensemble which satisfies the restricted isometry property. The number of measurements needed for accurate footprint reconstruction is determined using compressive sampling theory. The three schemes are compared through simulations in terms of a performance measure that quantifies the accuracy of the reconstructed spatial spectral usage map. It is found that the proposed sparse reconstruction technique-based schemes significantly outperform the round-robin scheme.

Taylor series expansion based multidimensional image reconstruction for confocal and 4pi microscopy

We propose and experimentally demonstrate a three-dimensional (3D) image reconstruction methodology based on Taylor series approximation (TSA) in a Bayesian image reconstruction formulation. TSA incorporates the requirement of analyticity in the image domain, and acts as a finite impulse response filter. This technique is validated on images obtained from widefield, confocal laser scanning fluorescence microscopy and two-photon excited 4pi (2PE-4pi) fluorescence microscopy. Studies on simulated 3D objects, mitochondria-tagged yeast cells (labeled with Mitotracker Orange) and mitochondrial networks (tagged with Green fluorescent protein) show a signal-to-background improvement of 40% and resolution enhancement from 360 to 240 nm. This technique can easily be extended to other imaging modalities (single plane illumination microscopy (SPIM), individual molecule localization SPIM, stimulated emission depletion microscopy and its variants).

Photoacoustic and thermoacoustic signal characteristics study

Photoacoustic/thermoacoustic imaging is an emerging hybrid imaging modality combining optical/microwave imaging with ultrasound imaging. The photoacoustic/thermoacoustic signal generated are affected by the nature of excitation pulse waveform, pulse width, target object size, transducer size etc. In this study k-wave was used to simulate various configurations of excitation pulse, transducer types, and target object sizes and to see their effect on the photoacoustic/thermoacoustic signals. Numerical blood vessel phantom was also used to see the effect of various pulse waveform and excitation pulse width on the reconstructed images. This study will help in optimizing transducer design and reconstruction methods to obtain the superior reconstructed image.

Progressive fusion of reconstruction algorithms for low latency applications in compressed sensing

Recently, it has been shown that fusion of the estimates of a set of sparse recovery algorithms result in an estimate better than the best estimate in the set, especially when the number of measurements is very limited. Though these schemes provide better sparse signal recovery performance, the higher computational requirement makes it less attractive for low latency applications. To alleviate this drawback, in this paper, we develop a progressive fusion based scheme for low latency applications in compressed sensing. In progressive fusion, the estimates of the participating algorithms are fused progressively according to the availability of estimates. The availability of estimates depends on computational complexity of the participating algorithms, in turn on their latency requirement. Unlike the other fusion algorithms, the proposed progressive fusion algorithm provides quick interim results and successive refinements during the fusion process, which is highly desirable in low latency applications. We analyse the developed scheme by providing sufficient conditions for improvement of CS reconstruction quality and show the practical efficacy by numerical experiments using synthetic and real-world data. (C) 2013 Elsevier B.V. All rights reserved.

Multispectral Bayesian reconstruction technique for real-time two color fluorescence microscopy

We have developed a real-time imaging method for two-color wide-field fluorescence microscopy using a combined approach that integrates multi-spectral imaging and Bayesian image reconstruction technique. To enable simultaneous observation of two dyes (primary and secondary), we exploit their spectral properties that allow parallel recording in both the channels. The key advantage of this technique is the use of a single wavelength of light to excite both the primary dye and the secondary dye. The primary and secondary dyes respectively give rise to fluorescence and bleed-through signal, which after normalization were merged to obtain two-color 3D images. To realize real-time imaging, we employed maximum likelihood (ML) and maximum a posteriori (MAP) techniques on a high-performance computing platform (GPU). The results show two-fold improvement in contrast while the signal-to-background ratio (SBR) is improved by a factor of 4. We report a speed boost of 52 and 350 for 2D and 3D images respectively. Using this system, we have studied the real-time protein aggregation in yeast cells and HeLa cells that exhibits dot-like protein distribution. The proposed technique has the ability to temporally resolve rapidly occurring biological events.

Optimum Parameter Selection in Sparse Reconstruction of Frequency-Domain Optical-Coherence Tomography Signals

For a multilayered specimen, the back-scattered signal in frequency-domain optical-coherence tomography (FDOCT) is expressible as a sum of cosines, each corresponding to a change of refractive index in the specimen. Each of the cosines represent a peak in the reconstructed tomogram. We consider a truncated cosine series representation of the signal, with the constraint that the coefficients in the basis expansion be sparse. An l(2) (sum of squared errors) data error is considered with an l(1) (summation of absolute values) constraint on the coefficients. The optimization problem is solved using Weiszfeld's iteratively reweighted least squares (IRLS) algorithm. On real FDOCT data, improved results are obtained over the standard reconstruction technique with lower levels of background measurement noise and artifacts due to a strong l(1) penalty. The previous sparse tomogram reconstruction techniques in the literature proposed collecting sparse samples, necessitating a change in the data capturing process conventionally used in FDOCT. The IRLS-based method proposed in this paper does not suffer from this drawback.

A novel three-dimensional imaging array recording and computational method by means of coded cameras reconstruction

In this paper, we propose a novel three-dimensional imaging method by which the object is captured by a coded cameras array (CCA) and computationally reconstructed as a series of longitudinal layered surface images of the object. The distribution of cameras in array, named code pattern, is crucial for reconstructed images fidelity when the correlation decoding is used. We use DIRECT global optimization algorithm to design the code patterns that possess proper imaging property. We have conducted primary experiments to verify and test the performance of the proposed method with a simple discontinuous object and a small-scale CCA including nine cameras. After certain procedures such as capturing, photograph integrating, computational reconstructing and filtering, etc., we obtain reconstructed longitudinal layered surface images of the object with higher signal-to-noise ratio. The results of experiments show that the proposed method is feasible. It is a promising method to be used in fields such as remote sensing, machine vision, etc. (c) 2006 Elsevier GmbH. All rights reserved.