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Two model based decomposition (MBD) methods using maximum likelihood estimation (MLE) and matching pursuits (MP) methods are examined for denoising and compressing ultrasonic RF echoes. MBD is a sparse data adaptive and nonorthogonal decomposition. Sparse decompositions provide efficient denoising and high rate compression by representing the signal in terms of a limited number of functions adapted to the signal. We examined MLE and MP methods for sparse decomposition of ultrasonic RF echoes in terms of Gabor functions. MLE requires estimating the parameter sets of an unknown number of Gabor functions that best represent ultrasonic data in presence of noise (superimposed signal estimation). MP requires estimating signal structures by extracting best matching Gabor functions sequentially from ultrasonic data and building up the decomposition (signal approximation). While MLE targets the best representation of signal in noise, MP targets a greedy representation. Denosing and compression capabilities of these two types of signal decomposition methods are examined. MP provides a high fidelity representation of the signal at high compression rates (typically 20:1) while suppressing the noise effectively. However, MLE is computationally costly for long data segments because of the iterative nonlinear estimation involved. MP also provides a good representation of the signal at high compression rates (typically 15:1) while providing a time-frequency (TF) representation of the signal. Furthermore, MP is computationally feasible to implement a real-time ultrasonic data compression system.