Combined sparse signal dimension reduction gradient tracking reconstruction algorithm based on compressed sensing theory

Abstract

The invention discloses a combined sparse signal dimension reduction reconstruction improvement method based on a compressed sensing theory, and belongs to the field of analog information conversion. According to the method, an original multi-measurement vector is converted into a low-dimension multi-measurement vector, then a sparse solution is recovered from the low-dimension multi-measurement vector by using a gradient tracking algorithm, and dimension reduction reconstruction of signals is realized. According to a correlation theorem and parameter setting requirements based on a compressed sensing theory, a unique solution can be recovered when the signal width of a joint sparse signal with known sparseness reaches a certain value (called as a critical value L1) through theoretical derivation, so that when a high-dimensional signal is reconstructed, the signal width is reduced to L1 and then reconstruction is carried out. During reconstruction, a gradient tracking algorithm is used, calculation of an inverse matrix or a generalized inverse matrix is replaced by a gradient thought in an unconstrained optimization method, and QR decomposition does not need to be used. According to the method, the calculation complexity is reduced, the reconstruction success rate is improved, and the larger the signal width is, the more obvious advantages are achieved.

Description

technical field [0001] The present invention relates to a joint sparse signal (also known as multiple measurement vectors, namely Multiple Measurement Vectors, MMV) dimension reduction gradient tracking reconstruction algorithm (Dimension Reduction Gradient Pursuit Reconstruction Algorithm, DRGP) based on Compressed Sensing (Compressed Sensing, CS) theory ), belonging to the technical fields of analog information conversion, digital signal processing, image processing, etc. Background technique [0002] The analog information converter (AIC) based on compressive sensing (CS) theory greatly relieves the pressure on the ADC based on the traditional sampling theorem, making the sampling method no longer limited by the Shannon-Nyquist sampling theorem and the input bandwidth of the ADC. Compressive sensing theory uses The measurement matrix that satisfies the constraint equidistant condition maps the signal from the high-dimensional space to the low-dimensional space, so that th...

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Problems solved by technology

The iterative process of the greedy iterative algorithm is simple and fast, and it is widely used. However, for joint sparse signals with large signal width, multiple measurement vectors directly lead to the calculation of square complexity, and the computational complexity will increase significantly, which is not convenient for hardware implementation.

Compared with the greedy iterative algorithm, the gradient pursuit algorithm in the convex optimization algorithm uses the gradient idea in the unconstrained optimization method to replace the calculation of the inverse matrix or the generalized inverse matrix. It is not necessary to use QR decomposition for hardware implementation, which reduces the calculation. Complexity, reducing the storage space, but the gradient pursuit algorithm is not suitable for large-scale data processing

[0004] For joint sparse signals, a new optimization algorithm—ReMBo (Reduce MMV and Boost) has emerged. This algorithm simplifies the multi-column measurement vector (MMV) problem into a single-column measurement vector (SMV) problem and then performs signal reconstruction. Although it reduces The computational complexity improves the computational efficiency, but the reconstruction accuracy is significantly reduced, and the reconstruction power is very low, especially for joint sparse signals with a large width, the shortcomings are more prominent

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