Nonlinear Reconstruction Technique Research Articles

Design and Analysis of Field-of-View Independent k-Space Trajectories for Magnetic Resonance Imaging

This manuscript describes a method of three-dimensional k-space sampling that is based on a generalised form of the previously introduced “Seiffert Spirals,” which exploits the equality between undersampling and the reconstruction of a field of view which is larger than what is represented by the primary sampling density, leading to an imaging approach that does not require any prior commitment to an imaging field of view. The concept of reconstructing arbitrary FOVs based on a low-coherently sampled k-space is demonstrated analytically by simulations of the corresponding point spread functions and by an analysis of the noise power spectrum of undersampled datasets. In-vivo images highlight the feasibility of the presented approach by reconstructing white noise governed images from an undersampled datasets with a smaller encoded FOV. Beneficial properties are especially given by an artefact behaviour, which is widely comparable to the introduction of white noise in the image domain. Furthermore, these aliasing properties provide a promising precondition for the combination with non-linear reconstruction techniques such as Compressed Sensing. All presented results show dominant low-coherent aliasing properties, leading to a noise-like aliasing behaviour, which enables parameterization of the imaging sequence according to a given resolution and scan-time, without the need for FOV considerations.

Radial Undersampling-Based Interpolation Scheme for Multislice CSMRI Reconstruction Techniques.

Magnetic Resonance Imaging (MRI) is an important yet slow medical imaging modality. Compressed sensing (CS) theory has enabled to accelerate the MRI acquisition process using some nonlinear reconstruction techniques from even 10% of the Nyquist samples. In recent years, interpolated compressed sensing (iCS) has further reduced the scan time, as compared to CS, by exploiting the strong interslice correlation of multislice MRI. In this paper, an improved efficient interpolated compressed sensing (EiCS) technique is proposed using radial undersampling schemes. The proposed efficient interpolation technique uses three consecutive slices to estimate the missing samples of the central target slice from its two neighboring slices. Seven different evaluation metrics are used to analyze the performance of the proposed technique such as structural similarity index measurement (SSIM), feature similarity index measurement (FSIM), mean square error (MSE), peak signal to noise ratio (PSNR), correlation (CORR), sharpness index (SI), and perceptual image quality evaluator (PIQE) and compared with the latest interpolation techniques. The simulation results show that the proposed EiCS technique has improved image quality and performance using both golden angle and uniform angle radial sampling patterns, with an even lower sampling ratio and maximum information content and using a more practical sampling scheme.

Optimized reconstruction with noise suppression for interferenceless coded aperture correlation holography.

A modified nonlinear reconstruction technique with a noise modulation parameter is proposed for interferenceless coded aperture correlation holography (I-COACH), and thus the signal-to-noise ratio of a reconstructed image is improved without sacrifice of the field of view and temporal resolution of the system. In order to obtain the optimal reconstructed image, no-reference structural sharpness (NRSS) is introduced as the evaluation metric of reconstructed image quality during nonlinear reconstruction. On the other hand, the noise modulation function is built in order to analyze the effect of phase on noise when the amplitude of the point spread hologram and object hologram is unity of 1. Both the NRSS and noise modulation functions are combined with nonlinear reconstruction in I-COACH for improving imaging performance. The validities of the proposed method under different experimental conditions have been demonstrated by experiments.

Efficient 3D Low-Discrepancy k -Space Sampling Using Highly Adaptable Seiffert Spirals.

The overall duration of acquiring a Nyquist sampled 3D dataset can be significantly shortened by enhancing the efficiency of k -space sampling. This can be achieved by increasing the coverage of k -space for every trajectory interleave. Furthermore, acceleration is possible by making use of advantageous undersampling properties. In this paper, a versatile 3D center-out k -space trajectory based on Jacobian elliptic functions (Seiffert's spiral) is presented. The trajectory leads to a low-discrepancy coverage of k -space using a considerably reduced number of readouts compared with other approaches. Such a coverage is achieved for any number of interleaves, and, therefore, even single-shot trajectories can be constructed to be combined with, for example, hyperpolarized media. Furthermore, acceleration is achievable due to non-coherent undersampling properties of the trajectory in combination with non-linear reconstruction techniques like compressed sensing (CS). Simulations of point-spread functions and discrepancy evaluations compare Seiffert's spiral to the established 3D cones approach. Imaging capabilities are evaluated by comparison of in vivo knee images using Nyquist and undersampled datasets in combination with CS reconstructions.

Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH).

Interferenceless coded aperture correlation holography (I-COACH) is an incoherent digital holography technique for imaging 3D objects without two-wave interference. In I-COACH, the object beam is modulated by a pseudorandom coded phase mask (CPM) and propagates to the camera where its intensity pattern is recorded. The image of the object is reconstructed by a cross-correlation of the object intensity pattern with a point intensity response of the system, whereas the light from both the object and the point, are modulated by the same CPM. In order to recover the image of the object without bias level and background noise, multiple intensity recordings are necessary for both objects as well as the point object, which in turn significantly reduces the time resolution of imaging. In this study, a non-linear reconstruction technique is developed to reconstruct the image of the object with only a single camera shot. Furthermore, the proposed technique is adaptive to different experimental conditions in the sense of finding different optimal parameters for each experiment. The new method has been implemented on a regular I-COACH system in both transmission as well as reflection illumination modes.

Evaluating real-time image reconstruction in diffuse optical tomography using physiologically realistic test data.

In diffuse optical tomography (DOT), real-time image reconstruction of oxy- and deoxy-haemoglobin changes occurring in the brain could give valuable information in clinical care settings. Although non-linear reconstruction techniques could provide more accurate results, their computational burden makes them unsuitable for real-time applications. Linear techniques can be employed under the assumption that the expected change in absorption is small. Several approaches exist, differing primarily in their handling of regularization and the noise statistics. In real experiments, it is impossible to compute the true noise statistics, because of the presence of physiological oscillations in the measured data. This is even more critical in real-time applications, where no off-line filtering and averaging can be performed to reduce the noise level. Therefore, many studies substitute the noise covariance matrix with the identity matrix. In this paper, we examined two questions: does using the noise model with realistic, imperfect data yield an improvement in image quality compared to using the identity matrix; and what is the difference in quality between online and offline reconstructions. Bespoke test data were created using a novel process through which simulated changes in absorption were added to real resting-state DOT data. A realistic multi-layer head model was used as the geometry for the reconstruction. Results validated our assumptions, highlighting the validity of computing the noise statistics from the measured data for online image reconstruction, which was performed at 2 Hz. Our results can be directly extended to a real application where real-time imaging is required.

MO‐C‐18A‐01: Advances in Model‐Based 3D Image Reconstruction

Recent years have seen the emergence of CT image reconstruction techniques that exploit physical models of the imaging system, photon statistics, and even the patient to achieve improved 3D image quality and/or reduction of radiation dose. With numerous advantages in comparison to conventional 3D filtered backprojection, such techniques bring a variety of challenges as well, including: a demanding computational load associated with sophisticated forward models and iterative optimization methods; nonlinearity and nonstationarity in image quality characteristics; a complex dependency on multiple free parameters; and the need to understand how best to incorporate prior information (including patient‐specific prior images) within the reconstruction process. The advantages, however, are even greater – for example: improved image quality; reduced dose; robustness to noise and artifacts; task‐specific reconstruction protocols; suitability to novel CT imaging platforms and noncircular orbits; and incorporation of known characteristics of the imager and patient that are conventionally discarded. This symposium features experts in 3D image reconstruction, image quality assessment, and the translation of such methods to emerging clinical applications. Dr. Chen will address novel methods for the incorporation of prior information in 3D and 4D CT reconstruction techniques. Dr. Pan will show recent advances in optimization‐based reconstruction that enable potential reduction of dose and sampling requirements. Dr. Stayman will describe a “task‐based imaging” approach that leverages models of the imaging system and patient in combination with a specification of the imaging task to optimize both the acquisition and reconstruction process. Dr. Samei will describe the development of methods for image quality assessment in such nonlinear reconstruction techniques and the use of these methods to characterize and optimize image quality and dose in a spectrum of clinical applications.Learning Objectives: Learn the general methodologies associated with model‐based 3D image reconstruction. Learn the potential advantages in image quality and dose associated with model‐based image reconstruction. Learn the challenges associated with computational load and image quality assessment for such reconstruction methods. Learn how imaging task can be incorporated as a means to drive optimal image acquisition and reconstruction techniques. Learn how model‐based reconstruction methods can incorporate prior information to improve image quality, ease sampling requirements, and reduce dose.

Sparse Shape Reconstruction

This paper introduces a new shape-based image reconstruction technique applicable to a large class of imaging problems formulated in a variational sense. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right elements and geometrically composing them through basic set operations to characterize desired regions in the image. This combinatorial problem can be relaxed and then solved using classical descent methods. The main component of this relaxation is forming certain compactly supported functions which we call “knolls” and reformulating the shape representation as a basis expansion in terms of such functions. To select suitable elements of the dictionary, our problem ultimately reduces to solving a nonlinear program with sparsity constraints. We provide a new sparse nonlinear reconstruction technique to approach this problem. The performance of the proposed technique is demonstrated with some standard imaging problems including image segmentation, X-ray tomography, and diffusive tomography.

Phase-recovery improvement using analytic wavelet transform analysis of a noisy interferogram cepstrum

We evaluate the extension of the exact nonlinear reconstruction technique developed for digital holography to the phase-recovery problems presented by other optical interferometric methods, which use carrier modulation. It is shown that the introduction of an analytic wavelet analysis in the ridge of the cepstrum transformation corresponding to the analyzed interferogram can be closely related to the well-known wavelet analysis of the interferometric intensity. Subsequently, the phase-recovery process is improved. The advantages and limitations of this framework are analyzed and discussed using numerical simulations in singular scalar light fields and in temporal speckle pattern interferometry.

Compressed sensing sodium MRI of cartilage at 7T: Preliminary study

Sodium MRI has been shown to be highly specific for glycosaminoglycan (GAG) content in articular cartilage, the loss of which is an early sign of osteoarthritis (OA). Quantitative sodium MRI techniques are therefore under development in order to detect and assess early biochemical degradation of cartilage, but due to low sodium NMR sensitivity and its low concentration, sodium images need long acquisition times (15–25 min) even at high magnetic fields and are typically of low resolution. In this preliminary study, we show that compressed sensing can be applied to reduce the acquisition time by a factor of 2 at 7T without losing sodium quantification accuracy. Alternatively, the nonlinear reconstruction technique can be used to denoise fully-sampled images. We expect to even further reduce this acquisition time by using parallel imaging techniques combined with SNR-improved 3D sequences at 3T and 7T.

Approximation of piecewise smooth functions and images by edge-adapted (ENO-EA) nonlinear multiresolution techniques

This paper introduces and analyzes new approximation procedures for bivariate functions. These procedures are based on an edge-adapted nonlinear reconstruction technique which is an intrinsically two-dimensional extension of the essentially non-oscillatory and subcell resolution techniques introduced in the one-dimensional setting by Harten and Osher. Edge-adapted reconstructions are tailored to piecewise smooth functions with geometrically smooth edge discontinuities, and are therefore attractive for applications such as image compression and shock computations. The local approximation order is investigated both in L p and in the Hausdorff distance between graphs. In particular, it is shown that for general classes of piecewise smooth functions, edge-adapted reconstructions yield multiscale representations which are optimally sparse and adaptive approximations with optimal rate of convergence, similar to curvelets decompositions for the L 2 error.

Linear and nonlinear reconstruction for optical tomography of phantoms with nonscattering regions

Most research in optical imaging incorrectly assumes that light transport in nonscattering regions in the head may be modeled by use of the diffusion approximation. The effect of this assumption is examined in a series of experiments on tissue-equivalent phantoms. Images from cylindrical and head-shaped phantoms with and without clear regions [simulating the cerebrospinal fluid (CSF) filled ventricles] and a clear layer (simulating the CSF layer surrounding the brain) are reconstructed with linear and nonlinear reconstruction techniques. The results suggest that absorbing and scattering perturbations can be identified reliably with nonlinear reconstruction methods when the clear regions are also present in the reference data but that the quality of the image degrades considerably if the reference data does not contain these features. Linear reconstruction performs similarly to nonlinear reconstruction, provided the clear regions are present in the reference data, but otherwise linear reconstruction fails. This study supports the use of linear reconstruction for dynamic imaging but suggests that, in all cases, image quality is likely to improve if the clear regions are modeled correctly.

Multiresolution Based on Weighted Averages of the Hat Function II: Nonlinear Reconstruction Techniques

In this paper we describe and analyze a class of nonlinear \mr schemes for the multiresolution setting which corresponds to discretization by local averages with respect to the hat function. These schemes are based on the essentially-non-oscillatory (ENO) interpolatory procedure described in [A. Harten, B. Engquist, S. Osher, and S. Chakravarthy, J. Comput. Phys., 71 (1987), pp. 231--302]. We show that by allowing the approximation to fit the local nature of the data, one can improve the compression capabilities of the multiresolution algorithms. The question of stability for nonlinear (data-dependent) reconstruction techniques is also addressed.