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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. Measuring Robustness in Deep Learning Based Compressive Sensing

   Zalbagi Darestani, Mohammad; Chaudhari, Akshay; Heckel, Reinhard (July 2021, Proceedings of the 38th International Conference on Machine Learning)

   null (Ed.)

   Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that deep-learning-based image reconstruction methods are sensitive to perturbations and are less robust than traditional methods: Neural networks (i) may be sensitive to small, yet adversarially-selected perturbations, (ii) may perform poorly under distribution shifts, and (iii) may fail to recover small but important features in an image. In order to understand the sensitivity to such perturbations, in this work, we measure the robustness of different approaches for image reconstruction including trained and un-trained neural networks as well as traditional sparsity-based methods. We find, contrary to prior works, that both trained and un-trained methods are vulnerable to adversarial perturbations. Moreover, both trained and un-trained methods tuned for a particular dataset suffer very similarly from distribution shifts. Finally, we demonstrate that an image reconstruction method that achieves higher reconstruction quality, also performs better in terms of accurately recovering fine details. Our results indicate that the state-of-the-art deep-learning-based image reconstruction methods provide improved performance than traditional methods without compromising robustness. 

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3. 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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4. Overdispersed Photon-Limited Sparse Signal Recovery Using Nonconvex Regularization

   https://doi.org/10.1109/CAMSAP58249.2023.10403416  

   Lu, Yu; Marcia, Roummel F. (December 2023, 2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP))

   This paper investigates the application of the ℓp quasinorm, where 0 < p < 1, in contexts characterized by photon-limited signals such as medical imaging and night vision. In these environments, low-photon count images have typically been modeled using Poisson statistics. In related algorithms, the ℓ1 norm is commonly employed as a regularization method to promotes sparsity in the reconstruction. However, recent research suggests that using the ℓp quasi-norm may yield lower error results. In this paper, we investigate the use of negative binomial statistics, which are more general models than Poisson models, in conjunction with the ℓp quasi-norm for recovering sparse signals in low-photon count imaging settings. 

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5. DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures

   Yang, Huanrui; Wen, Wei; Li, Hai (April 2020, International Conference on Learning Representations)

   In seeking for sparse and efficient neural network models, many previous works investigated on enforcing `1 or `0 regularizers to encourage weight sparsity during training. The `0 regularizer measures the parameter sparsity directly and is invariant to the scaling of parameter values. But it cannot provide useful gradients and therefore requires complex optimization techniques. The `1 regularizer is almost everywhere differentiable and can be easily optimized with gradient descent. Yet it is not scale-invariant and causes the same shrinking rate to all parameters, which is inefficient in increasing sparsity. Inspired by the Hoyer measure (the ratio between `1 and `2 norms) used in traditional compressed sensing problems, we present DeepHoyer, a set of sparsity-inducing regularizers that are both differentiable almost everywhere and scale-invariant. Our experiments show that enforcing DeepHoyer regularizers can produce even sparser neural network models than previous works, under the same accuracy level. We also show that DeepHoyer can be applied to both element-wise and structural pruning. The codes are available at https://github.com/yanghr/DeepHoyer. 

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