Statistical Compressive Sensing for Efficient Signal Reconstruction and Classification

Ralašić, Ivan; Tafro, Azra; Seršić, Damir

doi:10.1109/icfsp.2018.8552059

Cited by 10 publications

(4 citation statements)

References 18 publications

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“…The model is sparse: it consists from only a few parameters needed for successful object representation. Hence, future research will be oriented to compressed sensing approach (Rani et al, 2018;Ralašić et al, 2018Ralašić et al, , 2019 for reducing the number of projections, in this case reduced radiotracer's concentration. Due to robustness of the proposed reconstruction method, a postfiltering step is not needed.…”

Section: Discussionmentioning

confidence: 99%

“…Zhang et al (2001Zhang et al ( , 1994. The Gaussian mixture model (GMM) is well-known and widely used in a variety of segmentation and classification problems (Friedman and Russell, 1997;Ralašić et al, 2018), as many observed quantities exhibit behaviour congruent with the model. A good overview of the application of GMMs and their generalizations to problems in image classification, image annotation and image retrieval can be found, e.g.…”

Section: Introductionmentioning

confidence: 99%

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2D PET Image Reconstruction Using Robust L1 Estimation of the Gaussian Mixture Model

Tafro¹,

Seršić²,

Kržić³

2022

Informatica

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An image or volume of interest in positron emission tomography (PET) is reconstructed from gamma rays emitted from a radioactive tracer, which are then captured and used to estimate the tracer’s location. The image or volume of interest is reconstructed by estimating the pixel or voxel values on a grid determined by the scanner. Such an approach is usually associated with limited resolution of the reconstruction, high computational complexity due to slow convergence and noisy results. This paper presents a novel method of PET image reconstruction using the underlying assumption that the originals of interest can be modelled using Gaussian mixture models. Parameters are estimated from one-dimensional projections using an iterative algorithm resembling the expectation-maximization algorithm. This presents a complex computational problem which is resolved by a novel approach that utilizes ${L_{1}}$ minimization.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

2D PET Image Reconstruction Using Robust L1 Estimation of the Gaussian Mixture Model

Tafro¹,

Seršić²,

Kržić³

2022

Informatica

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“…Compressive sensing is a signal processing framework which consists of a linear measurement and a nonlinear reconstruction process which is based on sparse optimization [15][16][17]. Research on various applications of the CS framework [18][19][20][21][22] has been very active in the recent years in different scientific areas.…”

Section: Compressive Sensingmentioning

confidence: 99%

Overcoming spatio-angular trade-off in light field acquisition using compressive sensing

et al. 2020

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In contrast to conventional cameras which capture a 2D projection of a 3D scene by integrating the angular domain, light field cameras preserve the angular information of individual light rays by capturing a 4D light field of a scene. On the one hand, light field photography enables powerful post-capture capabilities such as refocusing, virtual aperture, depth sensing and perspective shift. On the other hand, it has several drawbacks, namely, high-dimensionality of the captured light fields and a fundamental trade-off between spatial and angular resolution in the camera design. In this paper, we propose a compressive sensing approach to light field acquisition from a sub-Nyquist number of samples. Using an off-the-shelf measurement setup consisting of a digital projector and a Lytro Illum light field camera, we demonstrate the efficiency of the compressive sensing approach by improving the spatial resolution of the acquired light field. This paper presents a proof of concept with a simplified 3D scene as the scene of interest. Results obtained by the proposed method show significant improvement in the spatial resolution of the light field as well as preserved post-capture capabilities.

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“…Standard modern algorithms in image reconstruction include some sort of stochastic model that utilizes prior or additional knowledge. The Gaussian mixture model (GMM) has been proven suitable for a variety of segmentation problems [32][33][34]. In PET reconstruction problems, the original data (i.e., points of origin) are unobserved, so GMMs are used to model activity at points of observation, with spatial dependence modeled by Markov random fields [35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Gaussian Mixture Estimation from Lower-Dimensional Data with Application to PET Imaging

Tafro,

Seršić

2024

Mathematics

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In positron emission tomography (PET), the original points of emission are unknown, and the scanners record pairs of photons emitting from those origins and creating lines of response (LORs) in random directions. This presents a latent variable problem, since at least one dimension of relevant information is lost. This can be solved by a statistical approach to image reconstruction—modeling the image as a Gaussian mixture model (GMM). This allows us to obtain a high-quality continuous model that is not computationally demanding and does not require postprocessing. In this paper, we propose a novel method of GMM estimation in the PET setting, directly from lines of response. This approach utilizes some well-known and convenient properties of the Gaussian distribution and the fact that the random slopes of the lines are independent from the points of origin. The expectation–maximization (EM) algorithm that is most commonly used to estimate GMMs in the traditional setting here is adapted to lower-dimensional data. The proposed estimation method is unbiased, and simulations and experiments show that accurate reconstruction on synthetic data is possible from relatively small samples.

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Statistical Compressive Sensing for Efficient Signal Reconstruction and Classification

Cited by 10 publications

References 18 publications

2D PET Image Reconstruction Using Robust L1 Estimation of the Gaussian Mixture Model

2D PET Image Reconstruction Using Robust L1 Estimation of the Gaussian Mixture Model

Overcoming spatio-angular trade-off in light field acquisition using compressive sensing

Gaussian Mixture Estimation from Lower-Dimensional Data with Application to PET Imaging

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