Research On Image Reconstruction Algorithm Based On Compressive Sampling

As the compressive sampling theory brings us a new signal processing method, currently, it has become a research focus. Its relevant theoretical methods develop very fast, and have been widely used in many fields, of which the image compressive sampling and reconstruction form an important part. Different from traditional image sampling methods which would result in the redundancy of data and waste of various resources, the compressive sampling could precisely reconstruct the original signals only by use of a smaller amount of data with sampled data more efficiently used. Methods for its reconstruction mainly include greedy algorithm and optimization algorithm. This paper explores into the image reconstruction which is executed by the use of compressive sampling. It mostly covers the following aspects:(1) Taking Gaussian random matrix as the measurement matrix, it researches into the image reconstruction executed by the use of this simple measurement approach and proposes a new reconstruction algorithm based on pixel value substitution. As a greedy algorithm, it divides an image into many blocks by indirect use of sparse gradient featured by a natural image. A typical value is used to replace the pixel value of each block, which converts Gaussian matrix into a column full rank matrix. A new equation which can be solved by direct use of the generalized least squares comes out. We analyzed some factors that could affect the quality of this algorithm reconstruction, of which the result shows that reconstruction could be repeated many times to get the reconstruction value most suitable for each point. And the blocks should be divided into proper sizes to get better reconstruction effects. The result of simulation experiments has proved the above-mentioned viewpoints, and shows that it could not only improve the reconstruction quality, but also significantly reduce time for reconstruction in comparison with some classical greedy algorithms.(2) A whole image is usually divided into many sub-images, of which all are separately measured and reconstructed to reduce time for reconstruction. This paper explores into the image reconstruction executed by the use of this measurement method. This paper analyzes the relations between the variance of sub-images and actual measured value, proposes a method by which existing measurement data could be used to get the variance of sub-images and puts forward a model for the sub-image non-uniform measurement that corresponding to such a method. This model divides the image measurement into two procedures:basic measurement and additional measurement. Basic measurement is used to obtain some of their actual measured values and variances. Additional sampling rate of all sub-images could be determined according to the variances before carrying out additional measurement. Before the actual measurement data of each sub-image is obtained, this paper executes the reconstruction by the use of an algorithm based on the replacement of pixel values. The simulation result shows that such a measurement method could be used to further improve the quality of reconstructed image while some more time would be consumed to reconstruct. This paper also digs into its feasibility.(3) By digging into the traditional TV algorithm, it proposes a new method to get the initial value for algorithm iteration. As to this method, the algorithm based on pixel value substitution is used to first reconstruct original signals. Reconstructed signals closer to original signals could be properly altered so as to satisfy the measurement equation. And then the already altered signal could be used as a point for the initial value so as to shorten the distance between the initial point and optimal point. The simulation result shows that the improved algorithm could significantly reduce time for reconstruction.