The Research Of Image Compression Technique Based On SVD

The singular value decomposition (SVD) has enjoyed a long history.It was introduced in the 1870s by Beltrami and Jordan for its ownintrinsic interest, it has become an invaluable tool in appliedmathematics and mathematical modeling. Singular value analysis has beenapplied in awide variety of disciplines, recently, it is being used indata mining applications and by search engines to rank documents in verylarge databases, including the Web. Recently, the dimensions of matriceswhich are used in many mathematical models are becoming so large thatclassical algorithms for computing the SVD cannot be used. It' s becomea problem when use SVD method to compress image.Contraposing the big size of matrix, this paper present a new methodto determine the singular values of matrices which are so enormous thatuse of standard algorithms. In our method, rows from the matrix arerandomly selected, and a smaller matrix is constructed from the selectedrows. Next, we compute the singular values of the smaller matrix. Thisprocess of random sampling and computing singular values is repeated asmany times as necessary (usually a few hundred times) Our method is atype of randomized algorithm, i.e., algorithms which solve problemsusing randomly selected samples of data which are too large to beprocessed by conventional means. These algorithms output correct (ornearly correct) answers most of the time as long as the input has certaindesirable properties. We note, however, that the probability of arrivingat an incorrect answer, however small, is not naught since anunrepresentative sample may be drawn from the data.