Research And Implementation On Image Processing Based On P-tensor Product Compressed Sensing

The communication technology and the Internet develops rapidly nowadays,the requirement of information transmission efficiency becomes higher and higher.How to transmit massive data better and faster is a hot research problem.In the traditional Nyquist sampling theorem,the requirement for the sampling frequency of the signal is strong,the compressed sensing technology breaks through the limitation,and once it was proposed,it has attracted widespread attention.The compressed sensing has three parts,including the signal sparse representation,measurement,and reconstruction.Because of the big size of the signal,the semi-tensor product compressed sensing can make the original measurement matrix become larger by the tensor product operation,so as to match the dimension of the image and then do the multiplication operation*.In a word,the design of measurement matrix should focus on how to reduce the storage space of the measurement matrix and ensure the similar measurement result.In the traditional vector and matrix operation,the dimension matching is still an unsolved problem.As for the traditional vector or matrix multiplication,only have matched dimensions can the two vectors do the operations.If the dimensions of the two vectors are not matched,it should make the dimensions be matched by the transformation.For example,it cannot make the multiplication of a line and a plane,so the inner angle between them cannot be got.The common method to solve this problem is to project the line vertically onto the plane,and represent the plane by the projection line,then calculate the inner angle between the projection line and the original line,which can be seen as the inner angle between a plane and a line.However,there are many lines on the plane actually,using only one line to represent the plane is too restrictive.In view of the above problems,this paper proposed an image processing technology based on P-tensor product compressed sensing.In this paper,the main research results and innovation points are as follows:(1)We proposed a P-tensor product model,which extends the traditional definition.This paper proposes P-tensor product(PTP)model,extends the traditional inner product and inner angle between two vectors,and defines the inner product and angle between two unmatched dimension vectors under the transform P.Meanwhile,we apply the P-tensor product to matrix multiplication operation,which breaks through the limitation of the traditional matrix multiplication.The P-tensor product can improve the traditional semi-tensor product model and make the matrix multiplication more flexible.(2)We apply the P-tensor product to the compressed sensing field,which called P-tensor product compressed sensing(PTP-CS).The PTP-CS has better universality and lower demand of storage space.By using the PTP to design the measurement matrix,the low-dimensional matrix can be enlarged to a high-dimensional matrix,not only the storage space of the measurement matrix is reduced,but also optimize the property of the matrix.From the three properties of the measurement matrix,namely,the Spark,Coherence,RIP,we analyze the PTP-CS in a qualitative aspect,and prove that the PTP has a better performance on measurement matrix optimization.Also,we propose a new reconstruction model for PTP-CS and verify the recovery performance in the experiment simulations.Compare with the traditional compressed sensing and semi-tensor compressed sensing(STP-CS),it can be proved that the PTP-CS has a good performance on image processing.Not only for the two-dimensional image signal,but also for other dimension signals,such as one-dimensional signal and high-dimensional signal,the PTP-CS still maintains a good effect on compression and recovery.