Toeplitz structure measurement matrix construction method based on singular value decomposition

Abstract

The invention discloses a Toeplitz structure measurement matrix construction method based on singular value decomposition. The Toeplitz structure measurement matrix construction method comprises the following steps that firstly, a row vector which is composed of elements 0 and 1 and submits to random distribution is generated; secondly, a Toeplitz structure measurement matrix phi is constructed through the vector; thirdly, singular value decomposition is conducted on the Toeplitz structure measurement matrix; fourthly, singular values are optimized, in other words, the maximum value in the singular values in the Toeplitz structure measurement matrix phi is regarded as a nonzero singular value of a newly-constructed matrix; fifthly, a new measurement matrix phi' is constructed; sixthly, approximate processing is conducted on the newly-constructed measurement matrix phi', in other words, negative elements are set to be 0, non negative elements are set to be 1, and the final Toeplitz structure measurement matrix phi'' composed of the elements 0 and 1 is obtained. The Toeplitz structure measurement matrix has the advantages that the computation complexity is low, the storage space is small, the structure is simple, and hardware is easy to achieve. Furthermore, the reconstruction effect is good.

Description

technical field [0001] The invention relates to the technical field of image compression sensing, in particular to an optimized construction method of a Toplitz structure measurement matrix in the field of compressed sensing. Background technique [0002] In the traditional signal processing process, in order to avoid signal distortion, the sampling rate should satisfy the Nyquist sampling law. However, for the acquisition of broadband signals such as images and videos, sampling according to the Nyquist sampling law will result in too high a sampling rate, which is difficult to implement in hardware circuits, and the cost of storage and transmission will be greatly increased due to the large amount of sampled data. ; At the same time, because its data acquisition mode adopts the mode of sampling first and then compressing, it not only wastes sensor elements, but also wastes time and storage space. [0003] The Compressive Sensing theory (Compressive Sensing, CS) proposed by...

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Problems solved by technology

However, compared with random measurement matrices such as Gaussian matrices, the deterministic measurement matrix has a gap in the reconstruction effect, requires more measurements, and has higher requirements for the sparsity of the signal; the measurement matrix in practical applications requires simple and effective construction. , the compression and reconstruction efficiency are high, so it is very meaningful to design a measurement matrix that is easy to implement in hardware. The construction process of the Toeplitz measurement matrix is ​​to use vectors to generate the entire matrix. The process of generating the entire matrix from this vector is through cyclic shift. This kind of cyclic shift is easy to implement in hardware, which is the main reason why the Toeplitz matrix has been widely studied. Like most other deterministic measurement matrices, the Toeplitz measurement matrix still has the situation of ensuring high reconstruction accuracy. However, it has the disadvantage of requiring a large number of measured values, and in many practical applications the acquisition of measured values ​​is very expensive

Therefore, aiming at the problem that the random measurement matrix is ​​not easy to implement in hardware and the reconstruction effect of the Toeplitz matrix that is easy to implement in hardware is not ideal, the present invention proposes a method for designing a measurement matrix with a Toeplitz structure based on singular value decomposition

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