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What's the meaning of δ and ρ?

One of the image compression method is using SVD (Singular Value Decom- position). It treats an image as an m x n matrix A, and performs SVD on A Assume m > n, where σί > Ơi +1 for-1, 2, . .. n-1. The compression process only keeps the k largest singular values and their corresponding singular vectors Figure 1 shows an example. The original picture is of size 267x189, as shown in 1.(a). After the compression process performs SVD, the new image only uses 50 singular values and singular vectors to reconstruct the image. The compressed image is shown in 1.(b). The compression ratio is 267 >< 50 + 50 + 50 189 0.45 267 x 189 because we only need to stored the trunked U, Σ, and V. The pixel-wise differ- ence between the original image and the compressed image is given in 1.(c). If we compute the average relative difference, which is Tn we get 0.048 which is about 5%. The result shows that we can store the image with some loss using only half of the storage. Figure 1.(d) plots the singular values of A, the matrix of the original picture.

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