In this paper, the various research papers related to 'embedded image compression' are studied. The aim of the present work is to study the methods adopted and analysis and results obtained. The different methods are adopted by various researchers. The present paper includes discrete wavelet transform (DWT), such as embedded zero wavelet (EZW) and the set partitioning in hierarchical trees (SPIHT) are studied. Block based discrete cosine transform (DCT) encoders are used in many image and video coding standards. Wavelet-based image coders such as embedded zero tree wavelet (EZW) coder, set partitioning in hierarchical trees (SPIHTs), set partitioning embedded block (SPECK), morphological representations of wavelet data (MRWD) and significance-linked connected component analysis (SLCC) are also the part of embedded image compression. Different types of redundancy present in an image, such as Spatial Redundancy, Statistical Redundancy and Human Vision Redundancy are very necessary for analysis. The JPE-2OOU image compression standard is increasingly gaining widespread importance. Ultra spectral imaging is a relatively recent development which makes quantitative remote sensing of the Earth's surface possible.