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The purpose of this paper is to develop a compressive sensing (CS) algorithm for noisy solder joint imagery compression and recovery. A fast gradient-based compressive sensing (FGbCS) approach is proposed based on the convex optimization. The proposed algorithm is able to improve performance in terms of peak signal noise ratio (PSNR) and computational cost.

Unlike traditional CS methods, the authors first transformed a noise solder joint image to a sparse signal by a discrete cosine transform (DCT), so that the reconstruction of noisy solder joint imagery is changed to a convex optimization problem. Then, a so-called gradient-based method is utilized for solving the problem. To improve the method efficiency, the authors assume the problem to be convex with the Lipschitz gradient through the replacement of an iteration parameter by the Lipschitz constant. Moreover, a FGbCS algorithm is proposed to recover the noisy solder joint imagery under different parameters.

Experiments reveal that the proposed algorithm can achieve better results on PNSR with fewer computational costs than classical algorithms like Orthogonal Matching Pursuit (OMP), Greedy Basis Pursuit (GBP), Subspace Pursuit (SP), Compressive Sampling Matching Pursuit (CoSaMP) and Iterative Re-weighted Least Squares (IRLS). Convergence of the proposed algorithm is with a faster rate O(k*k) instead of O(1/k).

This paper provides a novel methodology for the CS of noisy solder joint imagery, and the proposed algorithm can also be used in other imagery compression and recovery.

According to the CS theory, a sparse or compressible signal can be represented by a fewer number of bases than those required by the Nyquist theorem. The new development might provide some fundamental guidelines for noisy imagery compression and recovering.