A comparison of compressive sensing application for image denoising with wavelet denoising

Compressive Sensing is an effective method which allows us to sample below Nyquist rate and thus store less information, thereby saving space. The recovery of the signal from the compressed measurements is done efficiently by means of optimization algorithms. This paper employs the convex optimisation algorithm for reconstruction, which is implemented using the CVX package. This paper also deals with denoising of signals and images using different algorithms used for compressive sensing based denoising namely direct L1, joint L1 and separation based method and discovers the range of signal to noise ratio in which each algorithm is applicable. Compressive sensing based method of denoising proved to be a more effective method than the existing method of wavelet based denoising. The performance comparison of wavelet and compressive sensing based method are done using the parameters signal to noise ratio and mean square error. Denoising finds application in Medical Image analysis, which will enable us to recover the original image after removing the noise caused due to various disturbances. Denosing finds application in Radio Astronomy, in which it enables us to obtain the spatial information without the effect of back ground radiation.