Hyperpolarized [1-13C]-pyruvate has shown tremendous promise as an agent for imaging tumor metabolism with unprecedented sensitivity and specificity. Imaging hyperpolarized substrates by magnetic resonance is unlike traditional MRI because signals are highly transient and their spatial distribution varies continuously over their observable lifetime. Therefore, new imaging approaches are needed to ensure optimal measurement under these circumstances. Constrained reconstruction algorithms can integrate prior information, including biophysical models of the substrate/target interaction, to reduce the amount of data that is required for image analysis and reconstruction. In this study, we show that metabolic MRI with hyperpolarized pyruvate is biased by tumor perfusion, and present a new pharmacokinetic model for hyperpolarized substrates that accounts for these effects. The suitability of this model is confirmed by statistical comparison to alternates using data from 55 dynamic spectroscopic measurements in normal animals and murine models of anaplastic thyroid cancer, glioblastoma, and triple-negative breast cancer. The kinetic model was then integrated into a constrained reconstruction algorithm and feasibility was tested using significantly under-sampled imaging data from tumor-bearing animals. Compared to naïve image reconstruction, this approach requires far fewer signal-depleting excitations and focuses analysis and reconstruction on new information that is uniquely available from hyperpolarized pyruvate and its metabolites, thus improving the reproducibility and accuracy of metabolic imaging measurements.

Abstract. We present a novel deconvolution approach to accurately restore piecewise smooth signals from blurred data. The first stage uses Higher Order Total Variation restorations to obtain an estimate of the location of jump discontinuities from the blurred data. In the second stage the estimated jump locations are used to determine the local orders of a Variable Order Total Variation restoration. The method replaces the first order derivative approximation used in standard Total Variation by a variable order derivative operator. Smooth segments as well as jump discontinuities are restored while the staircase effect typical for standard first order Total Variation regularization is avoided. As compared to first order Total Variation, signal restorations are more accurate representations of the true signal, as measured in a relative l 2 norm. The method can also be used to obtain an accurate estimation of the locations and sizes of the true jump discontinuities. The approach is independent of the algorithm used for the standard Total Variation problem and is, consequently, readily incorporated in existing Total Variation restoration codes.1. Introduction. The accurate identification and quantification of physical structures in signals, from small to large scales, presents a number of challenges which are dependent on the data acquisition and reconstruction architectures. Whereas an underlying signal of interest may contain jump discontinuities, its recorded or reconstructed data is usually contaminated by both blur and noise 1 . In restoring the original signal it is important to retain or determine its original properties. The edges and inherently smooth regions should be preserved, while the jump discontinuities that separate smooth regions should be identified.Signal deblurring and edge detection are typically addressed independently. For example, in standard image deblurring for given recorded data and a known Point Spread Function (PSF), or blurring kernel, restoration of the signal subject to First Order Total Variation (FOTV) regularization leads to preservation of the edges [5,18,13,25]. But because the method relies on the assumption that the underlying signal consists of piecewise constant components, the restored signal also exhibits many false jump discontinuities (edges); the so-called staircase effect. On the other hand, high accuracy detection of edges in unblurred signals has been addressed separately, e.g. by the polynomial annihilation edge detection method in [1] or by renormalized local (undivided) differences in [8]. Through the combination of both edge detection and Total Variation (TV) regularized deconvolution, we seek to eliminate the staircase effect while also accurately detecting true jump discontinuities.The main idea of our new approach is to replace the linear first order derivative operator used in FOTV by a linear variable order difference operator. The variable order difference operator applies different order undivided differences to the signal depending on the locations of ju...

We present a new method for estimating the edges in a piecewise smooth function from blurred and noisy Fourier data. The proposed method is constructed by combining the so called concentration factor edge detection method, which uses a finite number of Fourier coefficients to approximate the jump function of a piecewise smooth function, with compressed sensing ideas. Due to the global nature of the concentration factor method, Gibbs oscillations feature prominently near the jump discontinuities. This can cause the misidentification of edges when simple thresholding techniques are used. In fact, the true jump function is sparse, i.e. zero almost everywhere with non-zero values only at the edge locations. Hence we adopt an idea from compressed sensing and propose a method that uses a regularized deconvolution to remove the artifacts. Our new method is fast, in the sense that it only needs the solution of a single l 1 minimization. Numerical examples demonstrate the accuracy and robustness of the method in the presence of noise and blur.

[1] An area of the core-mantle boundary to the east of Australia is investigated for the existence of ultralow-velocity zones (ULVZs). High-frequency recordings of deep Vanuatu and Tonga-Fiji earthquakes are studied from the small-aperture Warramunga Seismic Array in central Australia. The Tonga-Fiji data were used in a previous ULVZ study, while earthquakes from the Vanuatu subduction zone were newly collected for this study. Core-reflected ScP waves were analyzed, which possess observable precursory and postcursory arrivals in the presence of ULVZ structure. We apply a total variation deconvolution algorithm to our data, which significantly sharpens observed signals, hence, increasing our vertical resolution and therefore allowing us to detect thinner ULVZs than previously possible. The minimum ULVZ thickness detection threshold is approximately 2-3 km with this method. This data set samples a spot at the boundary of the large low shear velocity province beneath the Pacific. The new analysis provides evidence for a 5-6 km thick ULVZ to the north of a previously detected 8.5 km thick ULVZ. A second sampled region shows evidence for an even thinner ULVZ structure, with thicknesses of ∼3 km. These findings are largely consistent with the hypothesis that ULVZs are most likely to be found along the inside margin of large low shear velocity regions that have been attributed to dense, chemically distinct material.

A streamlined scan protocol was developed to further investigate the effects of CTDIvol and rotation time while limiting data collection to the DEQC body phantom. Further data collection will be pursued to determine baseline values and statistically based failure thresholds for the validation of long-term DECT scanner performance.