The most significant parameters of image processing are image resolution and speed of processing.  Compressing the multimedia datasets, which are rich in quality and volume is challenging.  Wavelet based image compression techniques are the best tools for lossless image compression, however, they suffer by low compression ratio. Conversely fractional cosine transform based compression is a lossy compression technique with less image quality. In this paper, an improved compression technique is proposed by using wavelet transform and discrete fractional cosine transform to achieve high quality of reconstruction of an image at high compression rate. The algorithm uses wavelet transform to decompose image into frequency spectrum with low and high frequency sub bands. Application of quantization process for both sub bands at two levels increases the number of zeroes, however rich zeroes from high frequency sub bands are eliminated by creating the blocks and then storing only non-zero values and kill all blocks with zero values to form reduced array. The arithmetic coding method is used to encode the sub bands. The Experimental results of proposed method are compared with its primitive two dimensional fractional cosine and fractional Fourier compression algorithms and some significant improvements can be observed in peak signal to noise ratio and self-similarity index mode at high compression ratio.