Channel coding: the conclusions about sparsity, randomness and convex optimization in compressive sensing theory can be directly applied to the design of fast error-correcting coding, which is not affected by errors in real-time transmission. In the process of compression coding, the basis needed for sparse representation may be unknown to the encoder. In the process of compressed sensing coding, only the original signal needs to be decoded and reconstructed, so it is not necessary to consider its structure and can be coded with a general coding strategy. Haupt et al. show through experiments that if the image is highly compressible or the signal-to-noise ratio is large enough, the compressed sensing method can still accurately reconstruct the image even if there is noise in the measurement process. DOA estimation: The angle at which the target appears is very small in the whole scanning space. From the perspective of spatial spectrum estimation, DOA estimation is an underdetermined linear inverse problem. DOA estimation of compressed sensing can be completed by sparse restriction of angular degrees.
Beamforming: Traditional adaptive beamforming is widely used because of its high resolution and strong anti-interference ability. But at the same time, its high sidelobe level and high sensitivity of angle mismatch will greatly reduce the receiving performance. In order to improve the performance of Capon beamforming, these sparse beamforming methods limit the number of elements with large array gain in the beam pattern and encourage the array gain to concentrate in the main lobe of the beam, thus reducing the sidelobe level, improving the array gain level in the main lobe and reducing the influence of angle mismatch. Such as maximum sidelobe energy ratio, mixed norm method and minimum total variation. Using the principle of compressive sensing, Rice University has successfully developed a single-pixel compressed digital camera. The design principle is as follows: firstly, the imaging target is projected onto a digital micromirror device (DMD) through an optical path system, and the reflected light is focused on a single photodiode through a lens, and the voltage at both ends of the photodiode is the measured value Y. This projection operation is repeated for m times to obtain the measured vector, and then the original image is reconstructed by a digital signal processor constructed by the minimum total variation algorithm. The digital micromirror device controls the mechanical motion of the micromirror through the digital voltage signal to realize the adjustment of the incident light. Because the camera directly obtains m random linear measurements instead of N(M, n) pixel values of the original signal, the low-pixel camera can shoot high-quality images.
Compressive sensing technology can also be applied to the field of radar imaging. Compared with traditional radar imaging technology, compressed sensing radar imaging has achieved two important improvements: the pulse compression matched filter is cancelled at the receiving end; At the same time, because the direct sampling of the original signal is avoided, the bandwidth requirement of the analog-to-digital converter at the receiving end is reduced, and the design focus is changed from the traditional expensive hardware at the receiving end to a novel signal recovery algorithm, thus simplifying the radar imaging system. The traditional DNA chip in biosensing can measure multiple organisms in parallel, but it can only identify a limited number of organisms. The compressed sensing DNA chip designed by Sheikh et al. based on the principle of compressed sensing and group detection overcomes this shortcoming. Each detection point in the compressed sensing DNA chip can identify a group of targets, thus obviously reducing the number of detection points. In addition, based on the sparsity of biological gene sequences, Sheikh et al. verified that the signal reconstruction in compressed sensing DNA chip can be realized by the method of belief propagation.