Spatial Resolution Analysis of Iterative Image Ceconstruction with Separate Regularization of Real and Imaginary par

A common method of improving the conditioning in iterative image reconstruction is to include regularization in the reconstruction algorithm. One such regularization is the roughness penalty, which when used in the algorithm encourages smoother images. For complex valued images, the roughness penalty typically penalizes equally the real and imaginary parts. The desired resolution of the reconstructed image can then be evaluated using the local impulse response. A fast algorithm to calculate it was developed for the typical roughness penalty, used for matching the regularization parameter expediently to the desired resolution. For some cases its advantageous to penalize independently the real and imaginary parts. This paper proposes a fast algorithm to calculate the local impulse response for that penalty and applies it to an fMRI reconstruction problem.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85888/1/Fessler220.pd

Fast joint reconstruction of dynamic R2∗R_2^* and field maps in functional MRI.

Blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) is conventionally done by reconstructing T2 * -weighted images. However, since the images are unitless they are nonquantifiable in terms of important physiological parameters. An alternative approach is to reconstruct R2 * maps which are quantifiable and have comparable BOLD contrast as T2* -weighted images. However, conventional R2 * mapping involves long readouts and ignores relaxation during readout. Another problem with fMRI imaging is temporal drift/fluctuations in off-resonance. Conventionally, a field map is collected at the start of the fMRI study to correct for off-resonance, ignoring any temporal changes. Here, we propose a new fast regularized iterative algorithm that jointly reconstructs R2 * and field maps for all time frames in fMRI data. To accelerate the algorithm we linearize the MR signal model, enabling the use of fast regularized iterative reconstruction methods. The regularizer was designed to account for the different resolution properties of both R2 * and field maps and provide uniform spatial resolution. For fMRI data with the same temporal frame rate as data collected for T2 * -weighted imaging the resulting R2 * maps performed comparably to T2 * -weighted images in activation detection while also correcting for spatially global and local temporal changes in off-resonance.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86002/1/Fessler23.pd

Direct 3D Tomographic Reconstruction and Phase-Retrieval of Far-Field Coherent Diffraction Patterns

We present an alternative numerical reconstruction algorithm for direct tomographic reconstruction of a sample refractive indices from the measured intensities of its far-field coherent diffraction patterns. We formulate the well-known phase-retrieval problem in ptychography in a tomographic framework which allows for simultaneous reconstruction of the illumination function and the sample refractive indices in three dimensions. Our iterative reconstruction algorithm is based on the Levenberg-Marquardt algorithm. We demonstrate the performance of our proposed method with simulation studies

CINENet: deep learning-based 3D cardiac CINE MRI reconstruction with multi-coil complex-valued 4D spatio-temporal convolutions

Cardiac CINE magnetic resonance imaging is the gold-standard for the assessment of cardiac function. Imaging accelerations have shown to enable 3D CINE with left ventricular (LV) coverage in a single breath-hold. However, 3D imaging remains limited to anisotropic resolution and long reconstruction times. Recently deep learning has shown promising results for computationally efficient reconstructions of highly accelerated 2D CINE imaging. In this work, we propose a novel 4D (3D + time) deep learning-based reconstruction network, termed 4D CINENet, for prospectively undersampled 3D Cartesian CINE imaging. CINENet is based on (3 + 1)D complex-valued spatio-temporal convolutions and multi-coil data processing. We trained and evaluated the proposed CINENet on in-house acquired 3D CINE data of 20 healthy subjects and 15 patients with suspected cardiovascular disease. The proposed CINENet network outperforms iterative reconstructions in visual image quality and contrast (+ 67% improvement). We found good agreement in LV function (bias ± 95% confidence) in terms of end-systolic volume (0 ± 3.3 ml), end-diastolic volume (- 0.4 ± 2.0 ml) and ejection fraction (0.1 ± 3.2%) compared to clinical gold-standard 2D CINE, enabling single breath-hold isotropic 3D CINE in less than 10 s scan and ~ 5 s reconstruction time

Comparing D-Bar and Common Regularization-Based Methods for Electrical Impedance Tomography

Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a \u27Pac-Man\u27 shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison

Magnetic resonance-based reconstruction method of conductivity and permittivity distributions at the Larmor frequency

Magnetic resonance electrical property tomography is a recent medical imaging modality for visualizing the electrical tissue properties of the human body using radio-frequency magnetic fields. It uses the fact that in magnetic resonance imaging systems the eddy currents induced by the radio-frequency magnetic fields reflect the conductivity ($\sigma$) and permittivity ($\epsilon$) distributions inside the tissues through Maxwell's equations. The corresponding inverse problem consists of reconstructing the admittivity distribution ($\gamma=\sigma+i\omega\epsilon$) at the Larmor frequency ($\omega/2\pi=$128 MHz for a 3 tesla MRI machine) from the positive circularly polarized component of the magnetic field ${\bf H}=(H_x,H_y,H_z)$. Previous methods are usually based on an assumption of local homogeneity ($\nabla\gamma\approx 0$) which simplifies the governing equation. However, previous methods that include the assumption of homogeneity are prone to artifacts in the region where $\gamma$ varies. Hence, recent work has sought a reconstruction method that does not assume local-homogeneity. This paper presents a new magnetic resonance electrical property tomography reconstruction method which does not require any local homogeneity assumption on $\gamma$. We find that $\gamma$ is a solution of a semi-elliptic partial differential equation with its coefficients depending only on the measured data $H^+$, which enable us to compute a blurred version of $\gamma$. To improve the resolution of the reconstructed image, we developed a new optimization algorithm that minimizes the mismatch between the data and the model data as a highly nonlinear function of $\gamma$. Numerical simulations are presented to illustrate the potential of the proposed reconstruction method