Lookup tables are frequently used in many applications to store and retrieve keyvalue pairs. Designing efficient lookup tables can be challenging with constraints placed on storage, query response time and/or result accuracy. This thesis proposes Geometric filter, a lookup table with a space requirement close to the theoretical lower bound, efficient construction, fast querying speed, and guaranteed accuracy. Geometric filter consists of a sequence of hash tables, the sizes of which form a descending geometric series. Compared with its predecessor, Bloomier filter, its encoding runs two times faster, uses less memory, and it allows updates after encoding. We analyze the efficiency of the proposed lookup table in terms of its storage requirement and error bound, and run experiments on Web 1TB 5-gram dataset to evaluate its effectiveness.

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Ultrasound investigation is one of meaningful imaging at present. Advantages of ultrasound are, that it hasn´t side effects as a rtg radiation and it is noninvasive. Ultrasound diagnostic is exploited in all branch of medicine (urology, cardiology, orthopeadist, gynecology etc.) to display organs, tissues and cavities of the human body. We use display in 2D, 3D and most modern display in 4D. We can encounter with many kinds of artifact. Artifacts are described more closely at 3rd chapter. Speckle noise deteriorates informative yiled of ultrasound picture. We try to remove speckle noise by simpler methods or more complex methods of filtration. These methods are described at 5th chapter. Programme for speckle filtering from pictures is part of this master´s thesis.