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Single-pixel imaging has emerged a decade ago as an imaging technique that exploits the theory of compressive sensing. In this research, the problem of optimizing the measurement matrix in compressive sensing framework was addressed. Thus far, random measurement matrices are widely used because they provide small coherence. However, recent reports claim that measurement matrix can be optimized, thereby improving its performance. Based on such proposition, this study proposed an alternative approach of optimizing the measurement matrix in a hierarchical model. In particular, this study constructed the hierarchical model based on an increasing resolution grade by exploiting the guided information and the adaptive step size method. An image with a demanded resolution was then obtained using the l1-norm method. Subsequently, the performance of the introduced method was verified and compared with those of existing approaches via several experiments. Results of the tests indicated that the reconstruction quality of optimizing the measurement matrix was improved when the proposed method was used.

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