In this thesis, modified Kronecker-based CS 1-D and 2-D recovery techniques with random and deterministic measurement matrices are investigated to improve signal quality despite resource restricted acquisition. For regular recovery of individual segments of the compressed signal, the measurement and sparsifying matrices are required. While the regular Kronecker-based CS recovery technique uses expanded Kronecker measurement and basis matrices to achieve one-time recovery of a collection of compressively acquired segmented signal, in the proposed modified Kronecker-based CS recovery, a new basis matrix which is an expanded version of the basis matrix is used. The reduction of mutual coherence between the expanded Kronecker measurement and the expanded basis matrix leads to improvement in the recovery of the signal. Deterministic sensing further improves the recovery and preserves the structure of the acquired signal in the compressed domain which can be exploited for compressed domain signal processing algorithms.