Basic Research Of Compressed Sensing Fluid Animation

In the modern world, computer has become an indispensable tool inpeople’s lives. With the development of computer graphics, fluid simulationsuch as water, smoke and cloud is paid more and more attentions, becomes avery important research branch in computer graphics, and is related topeople’s lives closely.We would like to get a more dazzling and more realistic effect during thefluid simulation process, which requires us to get more sampling points andhigher resolution, so as to get more details. But on the other hand, the morepoints we sample, the more storage space and computational cost we have,therefore it is an important issue to make a balance between effect and time.Aiming at this problem, this paper reduces sampling points greatly bycombining fluid simulation with compressed sensing framework, whichwould sample less data while having a good result.Compressed sensing-based super-resolution technology is very useful forthe fluid simulation. It allows us to get low-resolution data by solving thefluid dynamics equations, and finally get the high-resolution result by usingthe compressed sensing-based super-resolution framework. Under thetraditional compressed sensing framework, this paper tries FFT (Fast FourierTransform) and DCT (Discrete Cosine Transform) as the compressed basis,OMP (Orthogonal Matching Pursuit) and ROMP (Regularized OrthogonalMatching Pursuit) as the reconstruction algorithm, to give a super-resolutionrestoration, so as to get the high-resolution result from the low-resolution one.We should give a super-resolution restoration for each frames for thecontinuous fluid field.Fuzzy fluid field restoration is also of great significance for fluid simulation. During the fluid simulation process, the result solving fromlow-resolution grid could be seen as blurred fluid field as it is fuzzy. We couldget a high-resolution fluid field if we make a good restoration. This papermake a fuzzy field restoration experiment using the total variation method incompressed sensing, and get a high-resolution result restored from thelow-resolution one by compressed sensing.This paper gives a training restoration method based on compressedsensing. Through training a dictionary of low-resolution and high-resolutiondata, we get the same representation coefficients by basis for low-resolutionand high-resolution data. So we could get the high-resolution representationcoefficients by solving the low-resolution ones, and finally get thehigh-resolution result.This paper makes experiment of non-fluid images, fluid images withoutobstacles and fluid images with obstacles for compressed sensing restoration,and gives corresponding experimental results analysis respectively. Comparedwith previous work, the innovations of this paper are:(1) Introduce thecompressed sensing framework into fluid simulation, solve the low-resolutionfluid dynamic equations instead of the high-resolution ones, and then get thehigh-resolution effect by compressed sensing-based restoration method,which would reduce the number of sampling data so as to improve thesimulation efficiency;(2) Make a variety of traditional compressed sensingrestoration experiments, restore the high-resolution result by super-resolutionmethod and fuzzy effect restoration method respectively, and try differentcompressed basis and restoration algorithm and give the result;(3) Use thetraining method for the low-resolution fluid restoration to get a moreconvincing result.