Research Of Image Reconstruct Based On FOCUSS In Compressed Sensing

Image is the most intuitive form of information expression. But any meaningful image isredundant. Eliminating redundant and extracting useful information from image, with the dataas little as possible to express image information is always the research target in the field ofimage processing. Traditionally, image compression is based on the Nyquist samplingtheorem, however, along with the increase of information, sampling frequency will alsoincrease, which brings pressure to the real-time process information processing.In recent years the compressed sensing theory processes information from the perspectiveof sparse degrees, making signal acquisition and compression process in one, through theoptimization algorithm, we can reconstruct original signal from a few measurements, whosesampling frequency can break through the Nyquist sampling frequency’s restriction.In this paper, after the analysis of compressed sensing, I apply compressed sensing inimage reconstruction, based on FOCUSS algorithm put forward two improved methods:(1) Block based compressed sensing with FOCUSS.On count of the computional complexity in image reconstruction, combining with blocktheory, this section proposed block based compressed sensing with FOCUSS. Although thel1minimum norm is an effective method to slove1-D signal reconstruction problem, itscomputional complexity is too large to apply in image reconstruction. Orthogonal MatchingPursuit algorithm’s computional complexity is lower than thel1minimum norm, but it needsmore measurements. FOCUSS algorithm asymptotically converged to the minimuml1norm,whose computional complexity is far lower than the minimuml1norm. Firstly, we divide theimage into a few blocks. Then we can use Fourier transform to make the image sparse. Finally,original image can be reconstructed by using FOCCUS. Image by blocking can reduce thecomputional complexity and save storage space. The simulation experiment results show thatthe algorithm could reconstruct the image at a not high computional complexity.(2) Improved FOCUSS with conjugate gradient.In order to reduce the computional complexity of FOCUSS in image reconstruction, thesection improves FOCUSS algorithm. The computional complexity of FOCUSS algorithmmainly concentrated in solving the inverse matrix process. The conjugate gradient method hasthe advantage of simply calculation used in the calculation of large scale linear problem; weintroduce conjugate gradient method to FOCUSS, which could avoid complex computing tosolve the inverse matrix, effectively reduce the computional complexity and improve thequality of reconstructed image.