Regular Undersampling Research Articles

K-UNN: k-space interpolation with untrained neural network.

Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approaches lack the modeling of physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier (PF), regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k-space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k-space data), including transform sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k-space data accuracy. Finally, ablation experiments show that the proposed method can characterize the physical priors of MR images well. Additionally, experiments show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and is even competitive against supervised-trained deep learning methods in PF and regular undersampling reconstruction.

Complex structure reconstruction using segmented random sampling and combined dictionary

The reconstruction of data is a critical preliminary work in the seismic data processing. Compressed sensing (CS) has been well applied in the field of reconstruction. The key point of CS is random sampling, which converts the mutual interference alias caused by regular undersampling into lower-amplitude outside noise. But traditional sampling methods lack constraints on sampling points, emerging too much alias. Segmented random sampling (SRS) effectively controls the distance between sampling points. On the other hand, a single mathematical transformation will lead to incomplete sparse expression and bad restoration effects. Morphological component analysis (MCA) decomposes a signal into several components with outstanding morphological features to approximate the complex internal structure of data. In this paper, we found a new dictionary combination (shearlet + DCT) under the MCA framework and used the block coordinate relaxation algorithm to get the optimal solution to obtain reconstruction results. Tests of 2D data and 3D data have proved that the proposed method can get a better effect when reconstructing the SRS data.

Quantitative Skeletal Muscle Imaging Using 3D MR Fingerprinting With Water and Fat Separation.

Quantitative muscle MRI is a robust tool to monitor intramuscular fatty replacement and disease activity in patients with neuromuscular disorders (NMDs). To implement a 3D sequence for quantifying simultaneously fat fraction (FF) and water T1 (T1,H2O ) in the skeletal muscle, evaluate regular undersampling in the partition-encoding direction, and compare it to a recently proposed 2D MR fingerprinting sequence with water and fat separation (MRF T1 -FF). Prospective. Seventeen-vial phantom at different FF and T1,H2O , 11 healthy volunteers, and 6 subjects with different NMDs. 3T/3D MRF T1 -FF, 2D MRF T1 -FF, STEAM MRS ASSESSMENT: FF and T1,H2O measured with the 2D and 3D sequences were compared in the phantom and in vivo at different undersampling factors (US). Data were acquired in healthy subjects before and after plantar dorsiflexions and at rest in patients. Linear correlations, Bland-Altman analysis, two-way repeated measures analysis of variance (ANOVA), Student's t-test. Up to a US factor of 3, the undersampled acquisitions were in good agreement with the fully sampled sequence (R2 ≥ 0.98, T1,H2O bias ≤10 msec, FF bias ≤4 × 10-4 ) both in phantom and in vivo. The 2D and 3D MRF T1 -FF sequences provided comparable T1,H2O and FF values (R2 ≥ 0.95, absolute T1,H2O bias ≤35 msec, and absolute FF bias ≤0.003). The plantar dorsiflexion induced a significant increase of T1,H2O in the tibialis anterior and extensor digitorum (relative increase of +10.8 ± 1.7% and + 7.7 ± 1.4%, respectively, P < 0.05), that was accompanied by a significant reduction of FF in the tibialis anterior (relative decrease of -16.3 ± 4.0%, P < 0.05). Some subjects with NMDs presented increased and heterogeneous T1,H2O and FF values throughout the leg. Quantitative 3D T1,H2O and FF maps covering the entire leg were obtained within acquisition times compatible with clinical research (4 minutes 20 seconds) and a 1 × 1 × 5 mm3 spatial resolution. 2 TECHNICAL EFFICACY: Stage 2.

An anti-aliasing POCS interpolation method for regularly undersampled seismic data using curvelet transform

Seismic data interpolation are considered the key step in data pre-processing. Most current interpolation methods are just suitable for random undersampled cases. To deal with regular undersampled issue, we propose a novel anti-aliasing Projection Onto Convex Sets (POCS) interpolation method using the curvelet transform. First, we decompose the curvelet transform into two operators: a frequency-wavenumber (f-k) operator and a curvelet tiling operator. These two operators are used to respectively link time-space (t-x) domain to f-k domain, and f-k domain to the curvelet coefficients. In the f-k domain, the two boundaries for dominant dips can be identified by an angular searching within the whole frequency range. Second, we expand the two boundary dips to design a mask function that can eliminate the wraparound aliasing artefacts caused by regular undersampling. Finally, by incorporating the mask function into conventional POCS method, we are able to derive a robust anti-aliasing POCS interpolation method under the curvelet transform. With an exponential threshold model, the satisfactory interpolation result can be obtained by 10–12 iterations. The proposed interpolation method, which has no assumption for linear or quasi-linear events like a Fourier transform-based interpolation method, works for either regularly or randomly undersampled seismic data. Synthetic and real data examples are provided to illustrate the performance of the proposed method.

Estimation of primaries by sparse inversion with scattering-based multiple predictions for data with large gaps

We have solved the estimation of primaries by sparse inversion problem for a seismic record with large near-offset gaps and other contiguous holes in the acquisition grid without relying on explicit reconstruction of the missing data. Eliminating the unknown data as an explicit inversion variable is desirable because it sidesteps possible issues arising from overfitting the primary model to the estimated data. Instead, we have simulated their multiple contributions by augmenting the forward prediction model for the total wavefield with a scattering series that mimics the action of the free surface reflector within the area of the unobserved trace locations. Each term in this scattering series involves convolution of the total predicted wavefield once more with the current estimated Green’s function for a medium without the free surface at these unobserved locations. It is important to note that our method cannot by itself mitigate regular undersampling issues that result in significant aliases when computing the multiple contributions, such as source-receiver sampling differences or crossline spacing issues in 3D acquisition. We have investigated algorithms that handle the nonlinearity in the modeling operator due to the scattering terms, and we also determined that just a few of the terms can be enough to satisfactorily mitigate the effects of near-offset data gaps during the inversion process. Numerical experiments on synthetic data found that the final derived method can significantly outperform explicit data reconstruction for large near-offset gaps, with a similar computational cost and better memory efficiency. We have also found on real data that our scheme outperforms the unmodified primary estimation method that uses an existing Radon-based interpolation of the near-offset gap.

WE‐G‐207‐08: Imaging Dose Reduction and Scatter Removal in Cone Beam CT Via Random Undersampling: A Simulation Study

Purpose:Cone‐beam CT (CBCT) is widely used in image‐guided radiation therapy. The high imaging dose from repeated uses is a clinical concern and its image quality is impeded by a large amount of scattered photons. We propose to solve these two problems via a random undersampling method. We have performed Monte Carlo (MC) simulation studies for an initial test of the method.Methods:We propose to place a moving beam blocker with a random blocking pattern in front of the x‐ray source. It blocks a projection with a random pattern, which varies among projections. Scatter signal is measured in the deliberately created shadows, which is further interpolated to the entire projection. After removing the interpolated scatter from the total signal in the un‐blocked area, the cleaned data were used for CBCT reconstruction under a Tight Frame (TF) based iterative method. The random sampling yields a projection matrix that has a better numerical property compared to regular undersampling, permitting better image reconstruction.Results:360 CBCT projections of a head‐and‐neck cancer patient were generated via MC simulations. We first reconstructed CBCTs using 90 full projections with only primary data. The RMS error was 16%. When scattered photons were included in the projection, reduced contrast was observed and the RMS error was 22%. In our proposed method, 360 projections were used, but each of them was randomly blocked by 75% of pixels. Scatter estimation and was performed and the corrected data were used in reconstruction, yielding a reconstruction error of 15%. In these two approaches, the imaging doses were both reduced by ∼75% compared to a full scan with 360 unblocked projections.Conclusion:we proposed a method to solve the imaging dose and scatter problem in CBCT in a unified manner. Preliminary simulation studies demonstrated its efficacy.

Seismic data reconstruction based on CS and Fourier theory

Traditional seismic data sampling follows the Nyquist sampling theorem. In this paper, we introduce the theory of compressive sensing (CS), breaking through the limitations of the traditional Nyquist sampling theorem, rendering the coherent aliases of regular undersampling into harmless incoherent random noise using random undersampling, and effectively turning the reconstruction problem into a much simpler denoising problem. We introduce the projections onto convex sets (POCS) algorithm in the data reconstruction process, apply the exponential decay threshold parameter in the iterations, and modify the traditional reconstruction process that performs forward and reverse transforms in the time and space domain. We propose a new method that uses forward and reverse transforms in the space domain. The proposed method uses less computer memory and improves computational speed. We also analyze the antinoise and anti-aliasing ability of the proposed method, and compare the 2D and 3D data reconstruction. Theoretical models and real data show that the proposed method is effective and of practical importance, as it can reconstruct missing traces and reduce the exploration cost of complex data acquisition.

High-frequency subband compressed sensing MRI using quadruplet sampling.

To present and validate a new method that formalizes a direct link between k-space and wavelet domains to apply separate undersampling and reconstruction for high- and low-spatial-frequency k-space data. High- and low-spatial-frequency regions are defined in k-space based on the separation of wavelet subbands, and the conventional compressed sensing problem is transformed into one of localized k-space estimation. To better exploit wavelet-domain sparsity, compressed sensing can be used for high-spatial-frequency regions, whereas parallel imaging can be used for low-spatial-frequency regions. Fourier undersampling is also customized to better accommodate each reconstruction method: random undersampling for compressed sensing and regular undersampling for parallel imaging. Examples using the proposed method demonstrate successful reconstruction of both low-spatial-frequency content and fine structures in high-resolution three-dimensional breast imaging with a net acceleration of 11-12. The proposed method improves the reconstruction accuracy of high-spatial-frequency signal content and avoids incoherent artifacts in low-spatial-frequency regions. This new formulation also reduces the reconstruction time due to the smaller problem size.

Combining RF encoding with parallel imaging: a simulation study

The aim of this work was to investigate combining spatial encoding by radio frequency (RF) excitation with conventional parallel imaging (PI) methods to determine whether this could improve overall imaging performance. A simulation framework was developed to predict imaging performance for regular, central and random under-sampled parallel imaging methods augmented by RF spatial signal modulation. Optimisation methods were used to find the RF modulation patterns that produce optimal image reconstruction using the condition number of the PI encoding matrix as a quality metric. The diverse patterns of raw data sampling produced were compared using a measure of data uniformity across k-space. Regular under-sampling of k-space provided the best reconstruction quality. When other under-sampling schemes were employed then RF modulation could be used to improve reconstruction, with the optimum achieved by redistributing the signal in k-space to return to regular sub-sampling. For all tested under-sampling patterns, no further improvements in image quality were attained. Using the simulation framework and metrics described the interaction of different spatial encoding approaches could be investigated. Regular sub-sampling provided optimal reconstruction, independent of whether the spatial encoding was achieved by gradients only or a combination of gradient and RF.

Simply denoise: Wavefield reconstruction via jittered undersampling

We present a new, discrete undersampling scheme designed to favor wavefield reconstruction by sparsity-promoting inversion with transform elements localized in the Fourier domain. The work is motivated by empirical observations in the seismic community, corroborated by results from compressive sampling, that indicate favorable (wavefield) reconstructions from random rather than regular undersampling. Indeed, random undersampling renders coherent aliases into harmless incoherent random noise, effectively turning the interpolation problem into a much simpler denoising problem. A practical requirement of wavefield reconstruction with localized sparsifying transforms is the control on the maximum gap size. Unfortunately, random undersampling does not provide such a control. Thus, we introduce a sampling scheme, termed jittered undersampling, that shares the benefits of random sampling and controls the maximum gap size. The contribution of jittered sub-Nyquist sampling is key in formu-lating a versatile wavefield sparsity-promoting recovery scheme that follows the principles of compressive sampling. After the behavior of the jittered-undersampling scheme in the Fourier domain is analyzed, its performance is studied for curvelet recovery by sparsity-promoting inversion (CRSI). The findings on synthetic and real seismic data indicate an improvement of several decibels over recovery from regularly undersampled data for the same amount of data collected.

X‐f choice: Reconstruction of undersampled dynamic MRI by data‐driven alias rejection applied to contrast‐enhanced angiography

A technique for reconstructing dynamic undersampled MRI data, termed "x-f choice," was developed and applied to dynamic contrast-enhanced MR angiography (DCE-MRA). Regular undersampling in k-t space (a hybrid of k-space and time) creates aliasing in the conjugate x-f space that must be resolved. When regions in the object containing fast dynamic change are sparse, as in DCE-MRA, signal overlap caused by aliasing is often much less than the undersample factor would imply. x-f Choice reconstruction identifies overlapping signals using a model of the full non-aliased x-f space that is automatically generated from the undersampled data, and applies parallel imaging (PI) to separate them. No extra reference scans are required to generate either the model or the coil sensitivity maps. At each location in the reconstructed images, g-factor noise amplification is compared with predicted reconstruction errors to obtain an optimized solution. Acceleration factors greater than the number of receiver coils are possible, but are limited by the sparseness of the dynamic content and the signal-to-noise ratio (SNR) (in DCE-MRA the latter is dominant). Temporal fidelity was validated for up to a factor 10 speed-up using retrospectively undersampled data from a six-coil array. The method was tested on volunteers using fivefold prospective undersampling.

Recovery of limited-extent images aliased because of spectral undersampling.

In imaging situations where observations are made in spatial-frequency space, it is often desirable to lower the number of observations to fewer than that imposed by the Nyquist criterion. It is shown that patterns of regular spectral undersampling lead to aliasing that can be partially eliminated from some regions of a limited-extent image. An algorithm is presented for determining which regions are recoverable and which are not for a given pattern. Noniterative recovery, analogous to that proposed by Walsh and Nielsen-Delaney [J. Opt. Soc. Am. A 11, 572 (1994)], is shown to be feasible in cases of regular undersampling. The work has particular relevance to magnetic resonance imaging and aperture synthesis telescopy.