Generalized-series Reconstruction Research Articles

Spatial and temporal resolution effects on dynamic contrast-enhanced magnetic resonance mammography

We tested the hypothesis that partial volume effects due to poor in-plane resolution and/or low temporal resolution used in clinical dynamic contrast-enhanced magnetic resonance imaging results in erroneous diagnostic information based on inaccurate estimates of tumor contrast agent extravasation and tested whether reduced encoding techniques can correct for dynamic data volume averaging. Image spatial resolution was reduced from 469 x 469 microm2 to those reported below by selecting a subset of k-space data. We then compared the top five K(trans)/V(T) "hot spots" obtained from the original data set, 469 x 469-microm in-plane spatial resolution and an 18-s temporal resolution processed by fast Fourier transform (FFT), with values obtained from data sets having in-plane spatial resolutions of 938 x 938, 1875 x 1875 and 2500 x 2500 microm2 and a temporal resolution of 18 s, or data sets with temporal resolutions of 36, 54 and 72 and a spatial resolution of 469 x 469 microm2, and found them to statistically differ from the parent data sets. We then tested four different post processing methods for improving the spatial resolution without sacrificing temporal resolution: zero-filled FFT, keyhole, reduced-encoding imaging by generalized-series reconstruction (RIGR) and two-reference RIGR (TRIGR). The top five values of K(trans)/V(T) obtained from data sets, the in-plane spatial resolutions of which were improved to 469 x 469 microm2 by zero-filling FFT, Keyhole and RIGR, statistically differed from those obtained from the original 469 x 469 microm2 FFT parent image data set. Only the 938 x 938 and 1875 x 1875 microm2 data sets reconstructed to 469 x 469 microm2 with TRIGR reconstruction method yielded values of the top five K(trans)/V(T) hot spots statistically the same as the original parent data set, 469 x 469 microm2 in-plane spatial and 18-s temporal-resolution FFT. That is, partial volume effects from data sets of different in-plane spatial resolution resulted in statistically different values of the top five K(trans)/V(T) hot spots relative to a high spatial and temporal resolution data set, and TRIGR reconstruction of these low resolution data sets to high resolution images provided statistically similar values with a savings in temporal resolution of 2 to 4 times.

Fast algorithms for GS-model-based image reconstruction in data-sharing fourier imaging

Many imaging experiments involve acquiring a time series of images. To improve imaging speed, several "data-sharing" methods have been proposed, which collect one (or a few) high-resolution reference(s) and a sequence of reduced data sets. In image reconstruction, two methods, known as "Keyhole" and reduced-encoding imaging by generalized-series reconstruction (RIGR), have been used. Keyhole fills in the unmeasured high-frequency data simply with those from the reference data set(s), whereas RIGR recovers the unmeasured data using a generalized series (GS) model, of which the basis functions are constructed based on the reference image(s). This correspondence presents a fast algorithm (and two extensions) for GS-based image reconstruction. The proposed algorithms have the same computational complexity as the Keyhole algorithm, but are more capable of capturing high-resolution dynamic signal changes.

Regularization methods in dynamic MRI

In this work we consider an inverse ill-posed problem coming from the area of dynamic magnetic resonance imaging (MRI), where high resolution images must be reconstructed from incomplete data sets collected in the Fourier domain. The reduced-encoding imaging by generalized-series reconstruction (RIGR) method used leads to ill-conditioned linear systems with Hermitian Toeplitz matrix and noisy right-hand side. We analyze the behavior of some regularization methods such as the truncated singular value decomposition (TSVD), the Lavrent'yev regularization method and conjugate gradients (CG) type iterative methods. For what concerns the choice of the regularization parameter, we use some known methods and we propose new heuristic criteria for iterative regularization methods. The simulations are carried on test problems obtained from real data acquired on a 1.5 T Phillips system.

Myocardial Fiber Orientation Mapping Using Reduced Encoding Diffusion Tensor Imaging

A precise knowledge of the myocardial fiber architecture is essential to accurately understand and interpret cardiac electrical and mechanical functions. Diffusion tensor imaging has been used to noninvasively and quantitatively characterize myocardial fiber orientations. However, because the approach necessitates diffusion to be measured in multiple encoding directions and frequently at multiple weighting levels, the required data set size may present a limitation on its acquisition time efficiency. Applying the principles of reduced encoding imaging (REI), four basic reconstruction schemes, keyhole using direct substitution, keyhole with baseline correction, symmetrically encoded REI with generalized-series reconstruction (RIGR), and asymmetrically encoded RIGR, are evaluated in terms of their accuracy in diffusion tensorfiber orientation mapping of excised myocardial samples. Results show that the performances of all REI schemes, at approximately 50% reduced encoding, are at least comparable with that of a control experiment consisting of proportionally reduced number of full k-space images. Moreover, although performances of the symmetrically and asymmetrically encoded RIGR schemes are similar, both methods provide significant improvements over the control experiment and the direct-substitution keyhole technique. These findings demonstrate the potential of the general REI methodology for diffusion tensor imaging and pave the way for modified schemes involving rapid imaging sequences or alternative k-space sampling strategies to achieve even better data acquisition time efficiency and performance.

Partial wavelet encoding: a new approach for accelerating temporal resolution in contrast-enhanced MR imaging.

We propose a new approach using wavelet encoding to improve temporal resolution in contrast-enhanced magnetic resonance (MR) imaging. Exploiting the unique property of wavelets localized in space and frequency, we construct an efficient encoding scheme to capture signal changes due to contrast agent uptake, which in general is spatially localized with low- and mid-range frequency components. On the basis of space-frequency analysis, we describe mathematical formulations of our method and discuss its theoretical advantages over Fourier-based phase-encoding methods (the keyhole and reduced-encoding imaging by generalized-series reconstruction [RIGR] techniques). The results obtained in computer simulations and a phantom study demonstrate the feasibility and practical advantages of our approach.

Maximum cross-entropy generalized series reconstruction

This article addresses the classical image reconstruction problem from limited Fourier data. In particular, we deal with the issue of how to incorporate constraints provided in the form of a high-resolution reference image which approximates the desired image. A new algorithm is described which represents the desired image using a family of basis functions derived from translated and rotated versions of the reference image. The selection of the most efficient basis function set from this family is guided by the principle of maximum cross-entropy. Simulation and experimental results have shown that the algorithm can achieve high resolution with a small number of data points while accounting for relative misregistration between the reference and measured data. The technique proves to be useful for a number of time-sequential magnetic resonance imaging applications, for which significant improvement in temporal resolution can be obtained, even as the object undergoes bulk motion during the acquisition. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol 10, 258–265, 1999

Application of reduced-encoding imaging with generalized-series reconstruction (RIGR) in dynamic MR imaging.

Dynamic MRI has proven to be an important tool in studies of transient physiologic changes in animals and humans. High sensitivity and temporal resolution in such measurements are critical for accurate estimation of dynamic information. Fast imaging, often involving expensive hardware, has evolved for use in such cases. We demonstrate herein the possibility of accelerated data acquisition schemes on conventional machines using standard pulse sequences for dynamic studies. This is achieved by combining reduced-encoded dynamic data (typically 30 to 40 phase encodings) with a priori high-resolution data via a novel constrained image reconstruction algorithm. Such an approach reduces image acquisition time significantly (by a factor of 3 to 4 in the examples described here) without loss in the accuracy of information.

TEMPERATURE MAPPING IN A POTATO USING HALF FOURIER TRANSFORM MRI of DIFFUSION

Two dimensional temperature maps of a potato during heating were obtained using magnetic resonance imaging (MRI) techniques. the molecular pseudo self‐diffusion coefficient of the water in the potato was used as a temperature indicator. Two dimensional half Fourier transform spin‐echo and Generalized Series reconstruction techniques were used to reduce data acquisition time to about 10 s/image and to improve temperature mapping resolution. Thermocouples were implanted into the sample so that temperature and MRI data were acquired simultaneously. the error in MRI measurements caused by noise and the time delay required to collect each data set was less than 0.84C with 0.75 mm2 resolution. the average variation between MRI and thermocouple measurements was less than 0.5C. This is a promising new technique to noninvasively study heat transfer and to measure thermal properties of food materials.

Applications of reduced-encoding MR imaging with generalized-series reconstruction (RIGR).

The RIGR (reduced-encoding imaging by generalized-series reconstruction) technique for magnetic resonance imaging uses a high-resolution reference image as the basis set for the reconstruction of subsequent images acquired with a reduced number of phase-encoding steps. The technique allows increased temporal resolution in applications requiring repeated acquisitions, such as the dynamic imaging of contrast agent biodistribution, and in intrinsically time-consuming protocols such as the acquisition of a series of T2-weighted images. Several examples are presented to demonstrate that a four- to eightfold improvement in spatial or temporal resolution can be achieved with this technique.