Optimized Image Compression Using Sparse Representations and Fourier Transform

Abstract

Compression is an important step in saving and transmitting images. Compression serves mainly to remove the redundancy of the initial records. In this study, sparsity is used to compress images. Sparsity is an important subject so that during any process we can save a lot of computation. Since certain signals only use a few nonzero coefficients on an acceptable basis. Sparsity refers to the idea that a continuous-time signal can reflect a much lower rate of information than its bandwidth implies. Many physical signals or images are expressed in compressible form using the right basis function. Compression is relatively simple to implement on images, starting with high resolution. After that a transformed base is used in this project, and Fast Fourier transform is used. Then by using sparsity we can truncate and throw away a vast majority of those entries, which means we keep little Fourier coefficients that contribute the most important parts of the original image then after applying inverse Fourier transform we may get a high fidelity representation of the original image. In this case, my picture is compressed by using the sparsity method and to get almost the same efficiency and level of clearness almost 70% of the original size has almost saved.