In the works “Clutter Mitigation in Echocardiography using Sparse Signal Separation”, “Sparse Signal Separation with an Off-line Learned Dictionary for Clutter Reduction in Echocardiography“, and “Fusion of Ultrasound Harmonic Imaging with Clutter Removal Using Sparse Signal Separation“, we implemented the algorithm using an Orthogonal Matching Pursuit (OMP) and K-SVD version that works with complex valued signals. I have released the code in the software section. This code is based on the toolboxes published by Dr. Ron Rubinstein and work with Matlab. We used this code to compute sparse representations for signals with phase that were acquired from an ultrasound scanner.
You are welcome to test it and send me your feedback.