A multiresolution sparse signal representation approach for the decomposition of overlapping echoes in complex ultrasonic signals

Modern 3D microelectronic packages frequently exhibit a significant overlap of reflected ultrasonic echoes, often exceeding 50 % due to the diminishing thickness of internal structural layers. This overlap results in a marked degradation of ultrasonic image quality during C-scanning. To tackle this issue, a novel multiresolution sparse signal representation algorithm is proposed to achieve multiresolution decomposition of overlapping ultrasonic signals.The algorithm begins with SMP algorithm using a standard Gabor dictionary for initial decomposition. In each subsequent iteration, the dictionary is refined by narrowing the dictionary parameter boundaries while dividing the signal into shorter segments. Through this iterative refinement, the decomposition achieves increased precision without necessitating the enlargement of the dictionary size.Our approach not only ensures a more precise decomposition but also enhances the alignment of dictionary atoms with ultrasonic echoes, especially in instances of echo overlap. The efficacy of this algorithm in accurately separating and estimating ultrasonic echoes has been validated through both simulated and experimental ultrasonic signals. This study strengthens Sparse Signal Representation (SSR) in ultrasonic Non-Destructive Evaluation (NDE) by addressing the challenge of unstable decomposition when the dictionary size surpasses a certain threshold, thereby enhancing the reliability of SSR in the failure analysis of 3D microelectronic packaging.