A random measurement matrix plays a critical role for the successful use of compressive sensing (CS) theory and has been widely applied in CS. However

a random measurement matrix requires a large storage space

which is unsuitable for large-scale applications. To reduce the storage space for a random measurement matrix

a method for CS signal reconstruction was proposed based on theory of semi-tensor product. We constructed a random measurement matrix

with a dimension smaller than and

where is the length of the sampling vector and is the length of the signal that we intend to reconstruct. Then

we used the iteratively reweighted least square reconstruction algorithm to obtain the estimated values of sparse coefficients. Experiments were conducted using column sparse signals and images with various sizes. During the experiments

the probability of exact reconstruction

error

and peak signal-to-noise ratio (PSNR)

of the proposed method were compared with measurement matrices with different dimensions. The proposed algorithm outperformed a smaller storage space with a suitable PSNR performance. In this study

we proposed a new method to reduce the storage space of the measurement matrix for CS. The experimental results showed that if we appropriately reduced the dimension of the measurement matrix

then nearly no decline in the PSNR of the reconstruction was observed

but the storage space of the measurement matrix could be reduced by at least 1/4 or 1/16 times. All the results verified the validity of the proposed approach and demonstrated the significant potential for hardware implementation of the proposed sensing framework.