Tomographic Image Reconstruction Using Compressed Sensing
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Solution Overview
Problem
Conventional image reconstruction methods for tomographic images, especially in emission and transmission tomography, face challenges with Poisson noise, requiring numerous measurements and high patient doses, which limits the efficiency and accuracy of image reconstruction.
Innovation Solution
An image reconstruction method using a non-analytical algorithm that minimizes a functional incorporating a system matrix based on geometric or physical contributions of voxels to detector data, along with a sparse representation in an orthogonal basis, effectively addressing Poisson noise and enabling reconstruction from fewer measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional image reconstruction methods are used for tomographic images with Poisson noise, then measurement precision can be maintained, but the number of measurements required increases and patient dose increases
Solution Approach 1:
The patent transforms the Poisson noise model into a Gaussian noise model through variance stabilization transformation, enabling the application of Compressed Sensing techniques. This parameter transformation allows reconstruction from fewer measurements while maintaining accuracy by changing the statistical characteristics of the noise from Poisson to Gaussian distribution
Solution Approach 2:
The patent replaces the conventional analytical reconstruction approach with an iterative optimization-based Compressed Sensing method. This substitution enables accurate reconstruction from undersampled data by solving an optimization problem that incorporates sparsity constraints and transformed noise statistics
2Productivity
If the number of measurements is reduced to decrease patient dose and acquisition time, then productivity improves, but measurement precision deteriorates due to Poisson noise
Solution Approach 1:
The patent applies variance stabilization transformation to change the noise parameter from Poisson (variance equals mean) to Gaussian (constant variance), enabling effective noise handling with fewer measurements and thus improving productivity without sacrificing precision
Solution Approach 2:
The patent performs preprocessing of the detector data through variance stabilization transformation before reconstruction. This preliminary action prepares the data by transforming the noise characteristics, making it suitable for Compressed Sensing reconstruction with reduced measurements
Data Source
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AI summary
An image reconstruction method for reconstructing a tomographic image (f j ) of a region of investigation within an object (1), comprises the steps of providing detector data (y i ) comprising Poisson random values measured at an i-th of a plurality of different positions, e.g. i = (k,l) with pixel index k on a detector device and angular index l referring to both the angular position (a l ) and the rotation radius (r l ) of the detector device (10) relative to the object (1), providing a predetermined system matrix A ij assigning a j-th voxel of the object (1) to the i-th detector data (y i ), and reconstructing the tomographic image (f j ) based on the detector data (y i ), said reconstructing step including a procedure of minimizing a functional F(f) depending on the detector data (y i ) and the system matrix A ij and additionally including a sparse or compressive representation of the object (1) in an orthobasis T, wherein the tomographic image (f j ) represents the global minimum of the functional F(f). Furthermore, an imaging method and an imaging device using the image reconstruction method are described.