Medical ultrasound, also called sonography, is a mode of medical imaging that has a wide array of clinical applications, both as a primary modality and as an adjunct to other diagnostic procedures. The basis of its operation is the transmission of high frequency sound into the body followed by the reception, processing, and parametric display of echoes returning from structures and tissues within the body. Due to coherence of the backscattered echo signals, images obtained from the ultrasound imaging systems have interference patterns called speckle. The book first aims to propose a method to reduce this speckle depending upon the local statistics of a point in the image which is used to quantify the amount of speckle formation in the image. Ultrasound images when represented in digital form can be archived in huge volumes and later on used for transmission. To allow preservation of high quality images, efficient lossless compression has been adopted in this book for the architectural design of JPEG 2000 entropy encoder. So, the book focusses on the Tier-1 of EBCOT unit (BitPlane Coder) which forms the most computation intensive part of the encoding phase of JPEG2000 standard.