Chapter 7: The Kronecker Structure and Sensing Operator Properties

Learning Objectives

• Derive the Kronecker product factorization of the sensing matrix under far-field and separable-grid assumptions
• Exploit the factorization for efficient matrix-vector products reducing storage and computation by orders of magnitude
• Analyze the spectral properties of the sensing operator and connect singular value decay to k-space coverage
• Compute the point-spread function from the Gram matrix and interpret it as the imaging resolution kernel
• Evaluate mutual coherence and understand its implications for compressed-sensing recovery guarantees
• Design preconditioners that accelerate iterative reconstruction algorithms
• Quantify the computational complexity savings from Kronecker structure in LMMSE, matched filter, and OAMP