In this page, we show our numerical experimental results based on our sparse solution techniques for image/movie denoising. Our computation consists of 5 steps: (1) find a tight-wavelet frame representation of a noised image/movie; (2) note that the difference of the noised movie and denoised movie can be represented by sparse solution; (3) Construct a dictionary using hornlets (based on polynomial/spline functions); (4) apply a greedy algorithm to find the spase solution; and (5) add the sparse solution to the denoised movie/image to get a updated denoised image/movie.

Example 1. Image Denoising: We first show a noised image and difference of the noised image and denoised image based on tight wavelet framelets. One can see that there is a lot of structures about the true image (edges or skeleton). This difference should be represented by an appropriate dictionary with a sparse solution.

Next we show the sparse representation of the difference and the new difference of the noised image and the denoised image plus the sparse solution. There is no much information about the true image left.

Finally, we show the denoised image based on combination of tight wavelet frames and sparse solution. One can see it is smoother than the original image.

Example 2. We apply the above techniques to the standard image Lena. We first show the difference of noised image and denoised image by tight wavelet framelets and then sparse representation.

Next we show the denoised image by our approach and the difference of the noised and denoised images. Note that the PSNR is 32.3dB.

Example 3. We apply the same techniques to test for moive denoising. See the movie for performance of our approach by click this sentence.