This paper investigates the sensitivity of compressed sensing (CS) to basis mismatch in spectrum analysis and beamforming. Compressed sensing suggests that images of the physical world can be reconstructed with fewer measurements than classical methods, assuming sparsity in an a priori known basis. However, physical fields are not sparse in such bases, leading to significant performance degradation when using CS for modal analysis. The paper compares CS with classical methods like matched filtering and linear prediction, showing that CS is less robust to basis mismatch. The paper analyzes the impact of basis mismatch on CS performance, showing that the ℓ₁-norm of reconstruction errors increases linearly with the mismatch between the assumed and actual sparsity bases. Numerical experiments demonstrate that CS performs poorly when the assumed basis (e.g., DFT) does not match the actual basis, even with a large number of measurements. In contrast, classical methods like linear prediction provide more reliable results in the presence of basis mismatch. The paper also discusses the limitations of CS in radar and sonar applications, where the actual field parameters do not align with the assumed grid. This mismatch leads to non-zero values spilling into multiple grid cells, reducing the effectiveness of CS. The paper concludes that while CS offers potential for high-resolution imaging, its performance is significantly affected by basis mismatch, and further refinement is needed for practical applications. The study highlights that the core challenge of image inversion is identifying actual source modes, not selecting from a presumed set, which is a key difference between CS and classical methods.This paper investigates the sensitivity of compressed sensing (CS) to basis mismatch in spectrum analysis and beamforming. Compressed sensing suggests that images of the physical world can be reconstructed with fewer measurements than classical methods, assuming sparsity in an a priori known basis. However, physical fields are not sparse in such bases, leading to significant performance degradation when using CS for modal analysis. The paper compares CS with classical methods like matched filtering and linear prediction, showing that CS is less robust to basis mismatch. The paper analyzes the impact of basis mismatch on CS performance, showing that the ℓ₁-norm of reconstruction errors increases linearly with the mismatch between the assumed and actual sparsity bases. Numerical experiments demonstrate that CS performs poorly when the assumed basis (e.g., DFT) does not match the actual basis, even with a large number of measurements. In contrast, classical methods like linear prediction provide more reliable results in the presence of basis mismatch. The paper also discusses the limitations of CS in radar and sonar applications, where the actual field parameters do not align with the assumed grid. This mismatch leads to non-zero values spilling into multiple grid cells, reducing the effectiveness of CS. The paper concludes that while CS offers potential for high-resolution imaging, its performance is significantly affected by basis mismatch, and further refinement is needed for practical applications. The study highlights that the core challenge of image inversion is identifying actual source modes, not selecting from a presumed set, which is a key difference between CS and classical methods.