Pixelated images are used to transmit data between computing devices that have cameras and screens. Significant compression of pixelated images has been achieved by an "edge-based transformation and entropy coding" (ETEC) algorithm recently proposed by the authors of this paper. The study of ETEC is extended in this paper with a comprehensive performance evaluation. Furthermore, a novel algorithm termed "prediction-based transformation and entropy coding" (PTEC) is proposed in this paper for pixelated images. In the first stage of the PTEC method, the image is divided hierarchically to predict the current pixel using neighboring pixels. In the second stage, the prediction errors are used to form two matrices, where one matrix contains the absolute error value and the other contains the polarity of the prediction error. Finally, entropy coding is applied to the generated matrices. This paper also compares the novel ETEC and PTEC schemes with the existing lossless compression techniques: "joint photographic experts group lossless" (JPEG-LS), "set partitioning in hierarchical trees" (SPIHT) and "differential pulse code modulation" (DPCM). Our results show that, for pixelated images, the new ETEC and PTEC algorithms provide better compression than other schemes. Results also show that PTEC has a lower compression ratio but better computation time than ETEC. Furthermore, when both compression ratio and computation time are taken into consideration, PTEC is more suitable than ETEC for compressing pixelated as well as non-pixelated images.compression are some of the wavelet-based compressions such as embedded zerotrees of wavelet transforms (EZW), joint photographic experts group (JPEG) and the moving picture experts group (MPEG) compression.A large number of research papers report image compression algorithms. For example, one study [13] is about discrete cosine transform (DCT)-based lossless image compression where the higher energy coefficients in each block are quantized. Next, an inverse DCT is performed only on the quantized coefficients. The resultant pixel values are in the 2-D spatial domain. The pixel values of two neighboring regions are then subtracted to obtain residual error sequence. The error sequence is encoded by an entropy coder such as Arithmetic or Huffman coding [13]. Image compression in the frequency domain using wavelets is reported in several studies [12,[14][15][16][17]]. In the method described in [14] lifting-based bi-orthogonal wavelet transform is used which produces coefficients that can be rounded without any loss of data. In the work of [18] wavelet transform limits the image energy within fewer coefficients which are encoded by "set partitioning in hierarchical trees" (SPIHT) algorithm.In [19] JPEG lossless (JPEG-LS), a prediction-based lossless scheme, is proposed for continuous tone images. In [14] embedded zero tree coding (EZW) method is proposed based on the zero tree hypothesis. The study in [12] proposes a compression algorithm based on combination of discrete wavelet transform ...