Compressive sensing of 2D signals involves three fundamental steps: sparse representation, linear measurement matrix, and recovery of the signal. This paper focuses on analyzing the efficiency of various measurement matrices for compressive sensing of medical images based on theoretical predictive coding. During encoding, the prediction is efficiently chosen by four directional predictive modes for block-based compressive sensing measurements. In this work, Gaussian, Bernoulli, Laplace, Logistic, and Cauchy random matrices are used as the measurement matrices. While decoding, the same optimal prediction is de-quantized. Peak-signal-to-noise ratio and sparsity are used for evaluating the performance of measurement matrices. The experimental result shows that the spatially directional predictive coding (SDPC) with Laplace measurement matrices performs better compared to scalar quantization (SQ) and differential pulse code modulation (DPCM) methods. The results indicate that the Laplace measurement matrix is the most suitable in compressive sensing of medical images.