Study On Compressed Sensing Reconstruction Algorithm And Its Application

Compressed sensing (CS) is a theory which is popular in recent years. If the signal issparse or compressible, it can be sampled with far less than the sampling rate based onNyquist/Shannon. At the same time, it can ensure the accuracy of the reconstruction. Comparewith the traditional signal processing methods, CS can accomplish the acquisition andconstruction of data with only a small amount of sampling points, and this avoid the resourceswasting brought by sampling, transmission and storage process effectively.CS theory includes three parts:(1) Sparse transformation, which is to find the sparsetransform domain of a signal;(2) Observation matrix designing, which is to design a matrixthat can ensure the original structure remains and the information integrity;(3) Reconstructionalgorithm, which Using mathematical way of solving optimization problem to complete thereconstruction of the signal.As the core part of CS theory, the signal reconstruction has a direct influence on thequality and speed of the signal reconstruction. This paper expands the research around theexisted defect of greedy algorithm under a deep research on the basic framework and existingreconstruction algorithm. The main work of this paper is summarized as follows.According to the slow speed and time consuming of OMP in the processing of operation,the paper brings in the idea of intelligent information processing and applies the NPSAalgorithm to the choosing of the optimal atoms. We replace the calculation method of greediteration and inner product, and combine the NPSA and OMP effectively. The experimentalresults show that the optimization algorithm can accomplish the perfect reconstruction of thesignal. It has the equal reconstruct quality with OMP algorithm, and the reconstruct speed hasa great advance.After the thorough study to CS theory, we analyze the problems in industrial productionand apply the theory to the processing of oil well logging data. Due to the mass of loggingdata has tremendous pressure in the processing of sampling and transmission, and that wasteresource. The above all caused big trouble for the staff. The paper constructs oil well loggingdata processing system framework based on CS theory, and tests the feasibility through thesimulation. The results show that the theory has a good application in oil well logging dataprocessing.