Smoothed L0 (SL0) Algorithm for Compressed Sensing

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The SL0 algorithm is a novel sparse reconstruction technique in compressed sensing that approximates the L0-norm optimization problem using smooth functions like Gaussian functions, transforming NP-hard problems into smooth convex optimization problems. Based on our tests, SL0 demonstrates significantly higher computational efficiency compared to traditional algorithms like OMP and BP, while maintaining good accuracy, though it has slightly lower noise tolerance.

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In this article, we discuss a new sparse reconstruction algorithm for compressed sensing: the Smoothed L0 (SL0) algorithm. This approach approximates the L0-norm optimization problem in compressed sensing by utilizing smooth functions such as Gaussian functions, converting NP-hard problems into tractable smooth convex optimization problems. Compared to traditional algorithms like OMP and BP, SL0 offers significant advantages in computational efficiency while maintaining good precision in reconstruction results. Although SL0 shows relatively lower stability in handling noisy conditions, the results it provides remain highly valuable. Notably, SL0 can also play important roles in other application domains such as signal processing and image processing. Therefore, SL0 proves to be a highly promising algorithm with substantial potential in the field of compressed sensing.

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