Wavelet sparse transfrom has been widely used in compression and reconstruction of image. But in practical application, different images show different geometrical features and image information, so the appropriate method of express and compress is important based on image feature. In the paper, we comparing peak signal noise ratio and compression ratio of some compression methods under wavelet transform, for Shepp - Logan image, using wavelet transform, discrete cosine transform and finite difference transform to transform. And obtain the better sparity base on finite difference transform, and it offer reliable theory support of image compression and reconstruction.%小波稀疏变换被广泛地应用在图像压缩重建中,但在实际运用中,不同的图像它所呈现的几何特性及图像信息的完整性均有所差异.根据图像的特点选择合适的表示方法及压缩方法显得尤为重要.论文比较了小波变换下几种压缩方法的峰值信噪比及压缩比,并以Shepp-Logan图像为实验,通过运用小波变换、离散余弦变换及有限差分变换对其进行稀疏变换,得出基于有限差分变换的Shepp-Logan图像具有较好的稀疏性,为图像的压缩与重建提供可靠的理论支持.
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