Image compression is of great importance in multimedia systems and applications because it drastically reduces bandwidth requirements for transmission and memory requirements for storage. Although earlier standards for image compression were based on the Discrete Cosine Transform (DCT), a recently developed mathematical technique, called Discrete Wavelet Transform (DWT), has been found to be more efficient for image coding. Despite improvements in compression efficiency, wavelet image coders significantly increase memory usage and complexity when compared with DCT-based coders. A major reason for the high memory requirements is that the usual algorithm to compute the wavelet transform requires the entire image to be in memory. Although some proposals reduce the memory usage, they present problems that hinder their implementation. In addition, some wavelet image coders, like SPIHT (which has become a benchmark for wavelet coding), always need to hold the entire image in memory. Regarding the complexity of the coders, SPIHT can be considered quite complex because it performs bit-plane coding with multiple image scans. The wavelet-based JPEG 2000 standard is still more complex because it improves coding efficiency through time-consuming methods, such as an iterative optimization algorithm based on the Lagrange multiplier method, and high-order context modeling. In this thesis, we aim to reduce memory usage and complexity in wavelet-based image coding, while preserving compression efficiency. To this end, a run-length encoder and a tree-based wavelet encoder are proposed. In addition, a new algorithm to efficiently compute the wavelet transform is presented. This algorithm achieves low memory consumption using line-by-line processing, and it employs recursion to automatically place the order in which the wavelet transform is computed, solving some synchronization problems that have not been tackled by previous proposals. The proposed encode / Oliver Gil, JS. (2006). On the design of fast and efficient wavelet image coders with reduced memory usage [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/1826