Signal Processing Method Using Variable Thresholding
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Solution Overview
Problem
Conventional compressed sensing techniques for image reconstruction are computationally intensive, require substantial processing time, and are sensitive to free parameters, making them inefficient and unreliable.
Innovation Solution
A signal processing method that generates undersampled data, initializes a current solution, determines a variable thresholding parameter, and iteratively updates thresholded coefficients using wavelet transformations to reconstruct images efficiently, reducing reliance on complex cost functions and free parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If conventional compressed sensing techniques are used for image reconstruction, then fewer data samples can be acquired, but processing time increases substantially
Solution Approach 1:
The patent transforms the conventional compressed sensing approach by changing the mathematical parameters from non-linear cost function minimization to a linear system solution. Specifically, it reformulates the reconstruction problem as solving a linear system of equations using the measurement matrix and undersampled data, eliminating the need for iterative optimization and dramatically reducing processing time while maintaining the ability to reconstruct images from fewer data samples
2Quantity of substance
If conventional compressed sensing techniques with non-linear cost functions are used, then image reconstruction can be achieved with fewer samples, but computational complexity increases
Solution Approach 1:
The patent extracts and removes the computationally intensive non-linear cost function minimization step from the conventional compressed sensing framework. By taking out the iterative optimization process and replacing it with a direct linear system solution, the invention eliminates the computational complexity associated with L1-norm, total variation, and other non-linear terms while preserving the core compressed sensing capability of reconstructing images from undersampled data
3Loss of time
If minimization of non-linear cost functions is used for image reconstruction, then processing time may be reduced, but solutions become sensitive to free parameters
Solution Approach 1:
The patent replaces the complex, parameter-sensitive non-linear cost function minimization with a simple, parameter-free linear system solution. This approach uses a straightforward mathematical formulation that requires no tuning of free parameters such as weights of non-linear terms, making the solution robust and reliable while maintaining fast processing speed
Data Source
AI summary
A signal processing method is provided. The signal processing method includes the steps of generating undersampled data corresponding to an object, determining a variable thresholding parameter based on a composition of the undersampled data, and iteratively determining thresholded coefficients to generate a plurality of coefficients by utilizing the undersampled data, a current solution and the variable thresholding parameter by updating the variable thresholding parameter and the current solution, and reconstructing a data signal using the plurality of coefficients.