Chapter 13: Matched Filter and Backpropagation Imaging

Learning Objectives

• Derive the matched filter estimator $\hat{\mathbf{c}}^{\text{BP}} = \mathbf{A}^{H} \mathbf{y}$ and interpret it as correlation with steering responses
• Connect backpropagation to inverse Fourier transform of k-space data and delay-and-sum beamforming
• Characterize the point-spread function $\mathbf{A}^{H} \mathbf{A}$ and its role in resolution and sidelobes
• Implement filtered backpropagation with Ram-Lak and Hamming filters for non-uniform k-space
• Apply Capon (MVDR) and MUSIC for adaptive super-resolution imaging
• Identify the fundamental limitations of matched filter imaging and preview how sidelobe structure affects learned post-processing