Recently, adaptive sparse representations of ultrasonic signals have been utilized to improve the performance of scanning acoustic microscopy (SAM), a common nondestructive tool for failure analysis of microelectronic packages. The adaptive sparse representation of an ultrasonic signal is generated by decomposing it in a learned overcomplete dictionary using a sparse basis selection algorithm. Detection and location of ultrasonic echoes are then performed on the basis of the resulting redundant representation. This paper investigates the effect of sparse basis selection algorithms on ultrasonic signal representation. The overcomplete independent component analysis, focal underdetermined system solver (FOCUSS), and sparse Bayesian learning algorithms are examined. Numerical simulations are performed to quantitatively analyze the efficiency of ultrasonic signal representations. Experiments with ultrasonic A-scans acquired from flip-chip packages are also carried out in the study. The efficiency of ultrasonic signal representations are evaluated in terms of the different criteria that can be used to measure its performance for different SAM applications, such as waveform estimation, echo detection, echo location and C-scan imaging. The results show that the FOCUSS algorithm performs best overall.