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An Optimization Approach of Compressive Sensing Recovery Using Split Quadratic Bregman Iteration with Smoothed ℓ0 Norm | IEEE Conference Publication | IEEE Xplore

An Optimization Approach of Compressive Sensing Recovery Using Split Quadratic Bregman Iteration with Smoothed ℓ0 Norm


Abstract:

An optimization algorithm for image recovery is a core issue in the field of compressive sensing (CS). This paper deeply studied the CS reconstruction algorithm based on ...Show More

Abstract:

An optimization algorithm for image recovery is a core issue in the field of compressive sensing (CS). This paper deeply studied the CS reconstruction algorithm based on split Bregman iteration with ℓ1 norm, which enables the ℓ1 norm to approximate the original ℓ0 norm during the optimization process. Consequently, we proposed another novel algorithm improving the precision and the convergence speed based on split quadratic Bregman iteration (SQBI) with ℓ0 norm. Besides, we analyzed its convergence by proving two monotonically decreasing theorems. Inspired by previous researches, we applied smoothed ℓ0 norm for the optimization problem to replace the traditional ℓ0 norm in CS. The improvement is made by using a Gaussian function to approximate the ℓ0 norm, transforming it into a convex optimization problem, and eventually achieved a convergent solution by the steepest descent method. The experimental results show that under the same conditions, compared with other state-of-the-art algorithms, the reconstruction accuracy of the CS reconstruction algorithm based on the SQBI with smoothed ℓ0 norm is improved significantly, and its convergence rate is also accelerated as well.
Date of Conference: 12-14 December 2018
Date Added to IEEE Xplore: 09 May 2019
ISBN Information:
Conference Location: Sophia Antipolis, France

References

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