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1. Blind polychromatic X-ray CT reconstruction from poisson measurements

   https://doi.org/10.1109/ICASSP.2016.7471805  

   Gu, Renliang ; Dogandzic, Aleksandar ( March 2016 , 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP))

   We develop a sparse image reconstruction method for Poisson-distributed polychromatic X-ray computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident energy spectrum are unknown. We employ our mass-attenuation spectrum parameterization of the noiseless measurements for single-material objects and express the mass-attenuation spectrum as a linear combination of B-spline basis functions of order one. A block coordinate-descent algorithm is developed for constrained minimization of a penalized Poisson negative log-likelihood (NLL) cost function, where constraints and penalty terms ensure nonnegativity of the spline coefficients and nonnegativity and sparsity of the density-map image; the image sparsity is imposed using a convex total-variation (TV) norm penalty term. This algorithm alternates between a Nesterov’s proximal-gradient (NPG) step for estimating the density-map image and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) step for estimating the incident-spectrum parameters. We establish conditions for biconvexity of the penalized NLL objective function, which, if satisfied, ensures monotonicity of the NPG-BFGS iteration. We also show that the penalized NLL objective satisfies the Kurdyka-Łojasiewicz property, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Simulation examples demonstrate the performance of the proposed scheme. 

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2. Blind X-ray CT Image Reconstruction from Polychromatic Poisson Measurements

   https://doi.org/10.1109/TCI.2016.2523431  

   Gu, Renliang ; Dogandzic, Aleksandar ( February 2016 , IEEE Transactions on Computational Imaging)

   We develop a framework for reconstructing images that are sparse in an appropriate transform domain from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and incident-energy spectrum are unknown. Assuming that the object that we wish to reconstruct consists of a single material, we obtain a parsimonious measurement-model parameterization by changing the integral variable from photon energy to mass attenuation, which allows us to combine the variations brought by the unknown incident spectrum and mass attenuation into a single unknown mass-attenuation spectrum function; the resulting measurement equation has the Laplace-integral form. The mass-attenuation spectrum is then expanded into basis functions using B splines of order one. We consider a Poisson noise model and establish conditions for biconvexity of the corresponding negative log-likelihood (NLL) function with respect to the density-map and mass-attenuation spectrum parameters. We derive a block-coordinate descent algorithm for constrained minimization of a penalized NLL objective function, where penalty terms ensure nonnegativity of the mass-attenuation spline coefficients and nonnegativity and gradient-map sparsity of the density-map image, imposed using a convex total-variation (TV) norm; the resulting objective function is biconvex. This algorithm alternates between a Nesterov’s proximal-gradient (NPG) step and a limited-memory Broyden-Fletcher-Goldfarb-Shanno with box constraints (L-BFGS-B) iteration for updating the image and mass-attenuation spectrum parameters, respectively. We prove the Kurdyka-Łojasiewicz property of the objective function, which is important for establishing local convergence of block-coordinate descent schemes in biconvex optimization problems. Our framework applies to other NLLs and signal-sparsity penalties, such as lognormal NLL and ℓ₁ norm of 2D discrete wavelet transform (DWT) image coefficients. Numerical experiments with simulated and real X-ray CT data demonstrate the performance of the proposed scheme. 

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3. High order weight‐adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes

   https://doi.org/10.1002/nme.6823  

   Guo, Kaihang ; Chan, Jesse ( September 2021 , International Journal for Numerical Methods in Engineering)

   This article presents high order accurate discontinuous Galerkin (DG) methods for wave problems on moving curved meshes with general choices of basis and quadrature. The proposed method adopts an arbitrary Lagrangian–Eulerian formulation to map the wave equation from a time‐dependent moving physical domain onto a fixed reference domain. For moving curved meshes, weighted mass matrices must be assembled and inverted at each time step when using explicit time‐stepping methods. We avoid this step by utilizing an easily invertible weight‐adjusted approximation. The resulting semi‐discrete weight‐adjusted DG scheme is provably energy stable up to a term that (for a fixed time interval) converges to zero with the same rate as the optimal error estimate. Numerical experiments using both polynomial and B‐spline bases verify the high order accuracy and energy stability of proposed methods.

    

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4. Exemplar-Based Radio Map Reconstruction of Missing Areas Using Propagation Priority

   Zhang, S. ; Yu, T. ; Tivald, J. ; Choi, B. ; Ouyang, F. ; Ding, Z. ( December 2022 , IEEE Global Communications Conference)

   Radio map describes network coverage and is a practically important tool for network planning in modern wireless systems. Generally, radio strength measurements are collected to construct fine-resolution radio maps for analysis. However, certain protected areas are not accessible for measurement due to physical constraints and security considerations, leading to blanked spaces on a radio map. Non-uniformly spaced measurement and uneven observation resolution make it more difficult for radio map estimation and spectrum planning in protected areas. This work explores the distribution of radio spectrum strengths and proposes an exemplar-based approach to reconstruct missing areas on a radio map. Instead of taking generic image processing approaches, we leverage radio propagation models to determine directions of region filling and develop two different schemes to estimate the missing radio signal power. Our test results based on high-fidelity simulation demonstrate efficacy of the proposed methods for radio map reconstruction. 

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5. Constrained one‐step material decomposition reconstruction of head CT data from a silicon photon‐counting prototype

   https://doi.org/10.1002/mp.16649  

   Schmidt, Taly Gilat ; Sidky, Emil Y. ; Pan, Xiaochuan ; Barber, Rina Foygel ; Grönberg, Fredrik ; Sjölin, Martin ; Danielsson, Mats ( July 2023 , Medical Physics)

   Spectral CT material decomposition provides quantitative information but is challenged by the instability of the inversion into basis materials. We have previously proposed the constrained One‐Step Spectral CT Image Reconstruction (cOSSCIR) algorithm to stabilize the material decomposition inversion by directly estimating basis material images from spectral CT data. cOSSCIR was previously investigated on phantom data.

   This study investigates the performance of cOSSCIR using head CT datasets acquired on a clinical photon‐counting CT (PCCT) prototype. This is the first investigation of cOSSCIR for large‐scale, anatomically complex, clinical PCCT data. The cOSSCIR decomposition is preceded by a spectrum estimation and nonlinear counts correction calibration step to address nonideal detector effects.

   Head CT data were acquired on an early prototype clinical PCCT system using an edge‐on silicon detector with eight energy bins. Calibration data of a step wedge phantom were also acquired and used to train a spectral model to account for the source spectrum and detector spectral response, and also to train a nonlinear counts correction model to account for pulse pileup effects. The cOSSCIR algorithm optimized the bone and adipose basis images directly from the photon counts data, while placing a grouped total variation (TV) constraint on the basis images. For comparison, basis images were also reconstructed by a two‐step projection‐domain approach of Maximum Likelihood Estimation (MLE) for decomposing basis sinograms, followed by filtered backprojection (MLE + FBP) or a TV minimization algorithm (MLE + TV_min) to reconstruct basis images. We hypothesize that the cOSSCIR approach will provide a more stable inversion into basis images compared to two‐step approaches. To investigate this hypothesis, the noise standard deviation in bone and soft‐tissue regions of interest (ROIs) in the reconstructed images were compared between cOSSCIR and the two‐step methods for a range of regularization constraint settings.

   cOSSCIR reduced the noise standard deviation in the basis images by a factor of two to six compared to that of MLE + TV_min, when both algorithms were constrained to produce images with the same TV. The cOSSCIR images demonstrated qualitatively improved spatial resolution and depiction of fine anatomical detail. The MLE + TV_minalgorithm resulted in lower noise standard deviation than cOSSCIR for the virtual monoenergetic images (VMIs) at higher energy levels and constraint settings, while the cOSSCIR VMIs resulted in lower noise standard deviation at lower energy levels and overall higher qualitative spatial resolution. There were no statistically significant differences in the mean values within the bone region of images reconstructed by the studied algorithms. There were statistically significant differences in the mean values within the soft‐tissue region of the reconstructed images, with cOSSCIR producing mean values closer to the expected values.

   The cOSSCIR algorithm, combined with our previously proposed spectral model estimation and nonlinear counts correction method, successfully estimated bone and adipose basis images from high resolution, large‐scale patient data from a clinical PCCT prototype. The cOSSCIR basis images were able to depict fine anatomical details with a factor of two to six reduction in noise standard deviation compared to that of the MLE + TV_mintwo‐step approach.

    

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