Research On Total Variation Algorithm Of Signal Pixel Imaging System Based On Fractional Order

Single-pixel camera is a new imaging system which consists of only a single photon detector and optical components based on compressed sensing theory.It effectively solves the problem of wasting storage resources under traditional Nyquist sampling.In order to deeply study the single-pixel imaging system,this paper has conducted in-depth research on algorithm optimization problems.Through the optimization of the traditional single-pixel imaging algorithm,it can improve the image reconstruction accuracy of single-pixel cameras while reducing the reconstruction time.This article mainly completed the following aspects of the work:1)In order to select a measurement matrix and a reconstruction algorithm with good edge retention that are suitable for simulation experiments and specific experiments,the CS frame and its mathematical formulas are first described.Then three key technologies of compressive sensing:sparse representation,observation matrix and signal reconstruction are introduced in detail.Finally,two sets of comparison experiments were conducted:the effects of randomization matrix?Gaussian matrix,Bernoulli matrix?and deterministic matrix?partial Hadamard matrix,Toeplitz matrix,and circulant matrix?on image performance were compared;The effects of OMP,COSAMP algorithm in ₀l model and BP,IST,TV algorithm in ₁l model on image performance are compared.The experimental results show that the random Gaussian matrix and the partial Hadamard matrix are the most suitable measurement matrixes for numerical simulation and practical application.The TV algorithm is a good reconstruction algorithm with good edge retention.2)In order to analyze the effect of fractional differential on image texture,Three mathematical formulas corresponding to fractional calculus are given.According to the relationship between function and form,the most suitable fractional type for image processing is summarized.Then the influence of different fractional differentials and fractional integrals on the signal is analyzed.The contrasting experiment is used to obtain the order types that can be most used for image texture enhancement.Finally,the fractional differential is generalized to two-dimensional space.The types of algorithms for image enhancement are used to verify the superiority and effectiveness of fractional differentials in image texture enhancement through experimental comparisons,.3)In order to solve the problem of staircase effect existing in the traditional total variation algorithm,this paper proposes a fractional total variation reconstruction algorithm for compressed sensing based on improved nonlocal means combined with the advantages of fractional and non-local mean models.The improved algorithm uses the fractional differential operator to retain the image texture information and effectively improves the staircase effect in the total variation algorithm.In the process of solving the target problem the alternating multiplier algorithm?ADMM?and the non-local mean filter is used respectively to update the Lagrange gradient operator.Simulation experiments show that the improved algorithm can solves the trade-off problem between the reconstruction accuracy and the runtime effectively.Compared with the traditional Total variation algorithm?TVAL3?,the improved algorithm still has obvious advantages in terms of reconstruction performance,visual effect and peak signal-to-noise ratio based on the natural images database of Southern California Universtiy under the lower computing cost,and the improvement of average peak signal-to-noise ratio is about 2.44dB,and the average structural similarity improvement is 0.0945.4)In order to prove that the improved algorithm has certain advantages in practical operation,the working principle and composition of the single-pixel camera are described firstly,and then the actual experimental platform is constructed.Finally,the reconstruction performance of the improved algorithm and the traditional algorithm are analyzed and compared for the classic test image.The experimental results show that the improved signal-to-noise ratio of the improved algorithm is 0.884 dB compared with the traditional TVAL3 algorithm,the reconstruction time of the improved algorithm is saved about 1.13 min compared to the traditional TV algorithm based on non-local mean regularization?TV+nolc?.