| 1. |
- Cronie, Ottmar, et al.
(författare)
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The discretely observed immigration-death process : Likelihood inference and spatiotemporal applications
- 2016
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Ingår i: Communications in Statistics - Theory and Methods. - : Taylor & Francis Group. - 0361-0926 .- 1532-415X. ; 45:18, s. 5279-5298
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Tidskriftsartikel (refereegranskat)abstract
- We consider a stochastic process, the homogeneous spatial immigration-death (HSID) process, which is a spatial birth-death process with as building blocks (i) an immigration-death (ID) process (a continuous-time Markov chain) and (ii) a probability distribution assigning iid spatial locations to all events. For the ID process, we derive the likelihood function, reduce the likelihood estimation problem to one dimension, and prove consistency and asymptotic normality for the maximum likelihood estimators (MLEs) under a discrete sampling scheme. We additionally prove consistency for the MLEs of HSID processes. In connection to the growth-interaction process, which has a HSID process as basis, we also fit HSID processes to Scots pine data.
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| 2. |
- Leffler, Klara, 1988-, et al.
(författare)
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An extended block restricted isometry property for sparse recovery with non-Gaussian noise
- 2020
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Ingår i: Journal of Computational Mathematics. - : Global Science Press. - 0254-9409 .- 1991-7139. ; 38:6, s. 827-838
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Tidskriftsartikel (refereegranskat)abstract
- We study the recovery conditions of weighted mixed ℓ2/ℓp minimization for block sparse signal reconstruction from compressed measurements when partial block supportinformation is available. We show theoretically that the extended block restricted isometry property can ensure robust recovery when the data fidelity constraint is expressed in terms of an ℓq norm of the residual error, thus establishing a setting wherein we arenot restricted to Gaussian measurement noise. We illustrate the results with a series of numerical experiments.
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| 3. |
- Leffler, Klara, 1988-
(författare)
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The PET sampling puzzle : intelligent data sampling methods for positron emission tomography
- 2024
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Much like a backwards computed Sudoku puzzle, starting from the completed number grid and working ones way down to a partially completed grid without damaging the route back to the full unique solution, this thesis tackles the challenges behind setting up a number puzzle in the context of biomedical imaging. By leveraging sparse signal processing theory, we study the means of practical undersampling of positron emission tomography (PET) measurements, an imaging modality in nuclear medicine that visualises functional processes within the body using radioactive tracers. What are the rules for measurement removal? How many measurements can be removed without damaging the route back to the full solution? Moreover, how is the original solution retained once the data has been altered? This thesis aims to investigate and answer such questions in relation to PET data sampling, thereby creating a foundation for a PET Sampling Puzzle.The objective is to develop intelligent data sampling strategies that allow for practical undersampling of PET measurements combined with sophisticated computational compensations to address the resulting data distortions. We focus on two main challenges in PET undersampling: low-count measurements due to reduced radioactive dose or reduced scan times and incomplete measurements from sparse PET detector configurations. The methodological framework is based on key aspects of sparse signal processing: sparse representations, sparsity patterns and sparse signal recovery, encompassing denoising and inpainting. Following the characteristics of PET measurements, all elements are considered with an underlying assumption of signal-dependent Poisson distributed noise.The results demonstrate the potential of noise awareness, sparsity, and deep learning to enhance and restore measurements corrupted with signal-dependent Poisson distributed noise, such as those in PET imaging, thereby marking a notable step towards unravelling the PET Sampling Puzzle.
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| 4. |
- Wang, Jianfeng, 1984-, et al.
(författare)
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Error bounds of block sparse signal recovery based on q-ratio block constrained minimal singular values
- 2019
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Ingår i: EURASIP Journal on Advances in Signal Processing. - : Springer. - 1687-6172 .- 1687-6180. ; 2019
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we introduce the q-ratio block constrained minimal singular values (BCMSV) as a new measure of measurement matrix in compressive sensing of block sparse/compressive signals and present an algorithm for computing this new measure. Both the mixed ℓ2/ℓq and the mixed ℓ2/ℓ1 norms of the reconstruction errors for stable and robust recovery using block basis pursuit (BBP), the block Dantzig selector (BDS), and the group lasso in terms of the q-ratio BCMSV are investigated. We establish a sufficient condition based on the q-ratio block sparsity for the exact recovery from the noise-free BBP and developed a convex-concave procedure to solve the corresponding non-convex problem in the condition. Furthermore, we prove that for sub-Gaussian random matrices, the q-ratio BCMSV is bounded away from zero with high probability when the number of measurements is reasonably large. Numerical experiments are implemented to illustrate the theoretical results. In addition, we demonstrate that the q-ratio BCMSV-based error bounds are tighter than the block-restricted isotropic constant-based bounds.
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| 5. |
- Wang, Jianfeng, et al.
(författare)
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Sparsity estimation in compressive sensing with application to MR images
- 2017
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The theory of compressive sensing (CS) asserts that an unknown signal x in C^N canbe accurately recovered from m measurements with m << N provided that x is sparse. Most of the recovery algorithms need the sparsity s = ||x||_0 as an input. However,generally s is unknown, and directly estimating the sparsity has been an open problem.In this study, an estimator of sparsity is proposed by using Bayesian hierarchical model. Its statistical properties such as unbiasedness and asymptotic normality are proved. Inthe simulation study and real data study, magnetic resonance image data is used asinput signal, which becomes sparse after sparsified transformation. The results fromthe simulation study confirm the theoretical properties of the estimator. In practice, theestimate from a real MR image can be used for recovering future MR images under theframework of CS if they are believed to have the same sparsity level after sparsification.
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| 6. |
- Yu, Jun, 1962-, et al.
(författare)
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Stable and robust ℓp-constrained compressive sensing recovery via robust width property
- 2019
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Ingår i: Journal of the Korean Mathematical Society. - : Korean Mathematical Society. - 0304-9914 .- 2234-3008. ; 56:3, s. 689-701
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Tidskriftsartikel (refereegranskat)abstract
- We study the recovery results of ℓp-constrained compressive sensing (CS) with p≥1 via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extendsthe existing results in Cahill and Mixon [2] from ℓ2-constrained CS to ℓp-constrained case with p≥1 and complements the recovery analysisfor robust CS with ℓp loss function.
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| 7. |
- Zhou, Zhiyong, 1989-, et al.
(författare)
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Estimation of block sparsity in compressive sensing
- 2017
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we consider a soft measure of block sparsity, k_α(x)=(∥x∥2,α/∥x∥2,1)^α/(1−α),α∈[0,∞] and propose a procedure to estimate it by using multivariate isotropic symmetric α-stable random projections without sparsity or block sparsity assumptions. The limiting distribution of the estimator is given. Some simulations are conducted to illustrate our theoretical results.
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| 8. |
- Zhou, Zhiyong, 1989-, et al.
(författare)
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Estimation of block sparsity in compressive sensing
- 2017
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Ingår i: FOCM 2017 - Workshop C1 Computational Harmonic Analysis and Compressive Sensing.
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Konferensbidrag (refereegranskat)abstract
- Explicitly using the block structure of the unknown signal can achieve better recovery performance in compressive censing. An unknown signal with block structure can be accurately recovered from underdetermined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we consider a soft measure of block sparsity, kα(x) = (kxk2,α/kxk2,1) α 1−α , α ∈ [0, ∞] and propose a procedure to estimate it by using multivariate isotropic symmetric α-stable random projections without sparsity or block sparsity assumptions. The limiting distribution of the estimator is given. Some simulations are conducted to illustrate our theoretical results
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| 9. |
- Zhou, Zhiyong, et al.
(författare)
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Estimation of block sparsity in compressive sensing
- 2022
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Ingår i: International Journal of Wavelets, Multiresolution and Information Processing. - : World Scientific. - 0219-6913 .- 1793-690X. ; 20:06
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Tidskriftsartikel (refereegranskat)abstract
- Explicitly using the block structure of the unknown signal can achieve better reconstruction performance in compressive sensing. An unknown signal with block structure can be accurately recovered from under-determined linear measurements provided that it is sufficiently block sparse. However, in practice, the block sparsity level is typically unknown. In this paper, we propose a soft measure of block sparsity kα(x) = (||x||2,α/||x||2,1) α/(1−α) with α ∈ [0,∞], and present a procedure to estimate it by using multivariate centered isotropic symmetric α-stable random projections. The limiting distribution of the estimator is given. Simulations are conducted to illustrate our theoretical results.
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| 10. |
- Zhou, Zhiyong, et al.
(författare)
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Minimization of the q-ratio sparsity with 1
- 2020
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the q-ratio sparsity. When 1
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