The model-based image reconstruction approaches in photoacoustic tomography have a distinct advantage compared to traditional analytical methods for cases where limited data is available. These methods typically deploy Tikhonov based regularization scheme to reconstruct the initial pressure from the boundary acoustic data. The model-resolution for these cases represents the blur induced by the regularization scheme. A method that utilizes this blurring model and performs the basis pursuit deconvolution to improve the quantitative accuracy of the reconstructed photoacoustic image is proposed and shown to be superior compared to other traditional methods via three numerical experiments. Moreover, this deconvolution including the building of an approximate blur matrix is achieved via the Lanczos bidagonalization (least-squares QR) making this approach attractive in real-time.
A computationally efficient approach that computes the optimal regularization parameter for the Tikhonov-minimization scheme is developed for photoacoustic imaging. This approach is based on the least squares-QR decomposition which is a well-known dimensionality reduction technique for a large system of equations. It is shown that the proposed framework is effective in terms of quantitative and qualitative reconstructions of initial pressure distribution enabled via finding an optimal regularization parameter. The computational efficiency and performance of the proposed method are shown using a test case of numerical blood vessel phantom, where the initial pressure is exactly known for quantitative comparison.
BackgroundCarpal instability is defined as a condition where wrist motion and/or loading creates mechanical dysfunction, resulting in weakness, pain and decreased function. When conventional methods do not identify the instability patterns, yet clinical signs of instability exist, the diagnosis of dynamic instability is often suggested to describe carpal derangement manifested only during the wrist’s active motion or stress. We addressed the question: can advanced MRI techniques provide quantitative means to evaluate dynamic carpal instability and supplement standard static MRI acquisition? Our objectives were to (i) develop a real-time, three-dimensional MRI method to image the carpal joints during their active, uninterrupted motion; and (ii) demonstrate feasibility of the method for assessing metrics relevant to dynamic carpal instability, thus overcoming limitations of standard MRI.MethodsTwenty wrists (bilateral wrists of ten healthy participants) were scanned during radial-ulnar deviation and clenched-fist maneuvers. Images resulting from two real-time MRI pulse sequences, four sparse data-acquisition schemes, and three constrained image reconstruction techniques were compared. Image quality was assessed via blinded scoring by three radiologists and quantitative imaging metrics.ResultsReal-time MRI data-acquisition employing sparse radial sampling with a gradient-recalled-echo acquisition and constrained iterative reconstruction appeared to provide a practical tradeoff between imaging speed (temporal resolution up to 135 ms per slice) and image quality. The method effectively reduced streaking artifacts arising from data undersampling and enabled the derivation of quantitative measures pertinent to evaluating dynamic carpal instability.ConclusionThis study demonstrates that real-time, three-dimensional MRI of the moving wrist is feasible and may be useful for the evaluation of dynamic carpal instability.
OBJECTIVE-To describe the normal motion pattern at the midcarpal compartment during active radial-ulnar deviation of the wrist using dynamic MRI and to determine the observer performance for measurements obtained in asymptomatic volunteers.METHODS-Dynamic MRI of 35 wrists in 19 asymptomatic volunteers (age mean 30.4 yrs, sd 8.6) was performed during active radial-ulnar deviation using a fast gradient-echo pulse sequence with 315 ms temporal resolution (acquisition time, 19 sec). Two independent readers measured the transverse translation of the trapezium at the scaphotrapezium joint (STJ) and the capitate-to-Terms of use and reuse: academic research for non-commercial purposes, see here for full terms. http://www.springer.com/gb/openaccess/authors-rights/aam-terms-v1
Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented.
Traditional image reconstruction methods in rapid dynamic diffuse optical tomography employ ℓ(2)-norm-based regularization, which is known to remove the high-frequency components in the reconstructed images and make them appear smooth. The contrast recovery in these type of methods is typically dependent on the iterative nature of method employed, where the nonlinear iterative technique is known to perform better in comparison to linear techniques (noniterative) with a caveat that nonlinear techniques are computationally complex. Assuming that there is a linear dependency of solution between successive frames resulted in a linear inverse problem. This new framework with the combination of ℓ(1)-norm-based regularization can provide better robustness to noise and provide better contrast recovery compared to conventional ℓ(2)-based techniques. Moreover, it is shown that the proposed ℓ(1)-based technique is computationally efficient compared to its counterpart (ℓ(2)-based one). The proposed framework requires a reasonably close estimate of the actual solution for the initial frame, and any suboptimal estimate leads to erroneous reconstruction results for the subsequent frames.
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