Research And Analysis Of Compressed Sensing On Construction Of Measurement Matrix And Recovery Mapping

Compressed sensing(CS)is a compression transform and sampling technology for high-dimensional signals,which mainly includes three aspects: sparse representation,compressed transformation and recovery mapping.Nyquist samples not only require high sampling frequency,but also have great disadvantages in terms of data redundancy,computational complexity,and hardware cost of sampling equipment.Researchers are constantly looking for a sampling method with low sampling rate and less data redundancy for large sets of data,which Nyquist theory is hard to process.Compressed sensing is such a technology,it can get the discrete samples from compressible signals with low sampling rate and recover the original signals through solving underdetermined problem.In this paper,a class of measurement matrices based on sparse prior and a signal sampling and recovery method based on neural network are proposed.Simulation results demonstrate that they have better performance than existing counterparts.The main contents are as follows.(1)In the sparse priority-based compressed sensing,the recovery performance will be influenced by the property of measurement matrix.Using protograph-low-density parity-check(PLDPC)matrices and Hadamard matrices,we construct a class of sparse matrices,extended PLDPC sparse matrices(EPLDPC-SMs),which have excellent coherence property,low computational complexity,low time complexity,less storage resources and easy implementation in physical circuits.Both coherence analysis and recovery experiments demonstrate that the proposed EPLDPC-SMs are superior to the well-performing deterministic measurement matrices(i.e.,PLDPC-SMs),random sparse matrices(R-SBMs))and random matrices(i.e.,random Gaussian matrices(R-GMs)for various ratios of N to M.(2)We propose an optimization method(i.e.,1-Optimized-M)for measurements utilizing adaptive gradient optimization based on measurement error.With this optimization method and recovery networks,we can map the measurements to high dimensional signals and reduce the recovery error by minimize the error of measurements sampled from original and recovery image.Then,we train our measurement networks using energy loss which is inspired by RIP property.The trained measurements achieve better recovery improvement with respect to the Gaussian measurements.We also propose the improved 1-Optimized-M(i.e.,2-Optimized-M)utilizing adaptive gradient optimization based on measurement error and energy loss,which has more excellent performance than 1-Optimized-M.