Różnego rodzaje aktorów czytających opowiada dzisiaj zdjęcia dobrej telenoweli oczywiście Because the output of the BWTS is the same size as the input, all strings also have a valid inverse BWTS. The algorithm is described who also extended the idea to the sort transform. The idea is to divide the input string into a set of smaller strings such that the starting index of each substring is at a known, fixed location, such as at the first character. Specifically, the input is partitioned into a lexicographically nonincreasing sequence of words. A word is a string that lexicographically precedes any of its rotations. For example, the factorization of BANANA is A factorization is unique and can be calculated O time. Recall that the inverse BWT is to use a counting sort to calculate T=sort and then to build and traverse a linked list from the i'th occurrence of c T to the i'th occurrence of c BWT. a BWT, this linked list usually forms a single loop that returns to the initially transmitted index when complete. the BWTS, the list forms one loop for each word. The end of each word is detected by traversing the list back to its start. The next loop starts at the first unused element. The words are restored right to left. For example, we compute the BWTS of BANANA by sorting the rotations of its 4 words, and taking the last character of the sorted column as the BWTS: B B B A A A rotations sort last character N N N A B B N A A A A A To compute the inverse BWTS, we construct a linked list just like with a BWT. i T BWTS Next 0 A A 0 A N 4 A N 5 B B 3 N A 1 N A 2 The linked list has 4 cycles: Reversing the order of the cycles and concatenating, we get The corresponding elements of T spell out BANANA. A BWTS is 4 bytes smaller than a BWT. Experimentally, the effect on compression is small. The following table shows the effect of a BWT and BWTS followed by encoding using adaptive order 0 coder and indirect order 0 model For BWT, MSufSort was used. It adds a 4 byte starting index to the beginning. For BWTS, the BWTS program by was used with BLOCKSIZE set to 4000000 the source code. both cases, the input file is sorted a single block. The test files are calgary.tar and book1 from the Calgary corpus File Encoder BWT BWTS book1 fpaq0p 244 244 calgary.tar fpaq0p 985 985 book1 fpaq0f2,338,344 calgary.tar fpaq0f2,526,549 One possible benefit of a bijective compression algorithm is for encryption. Because all possible decryptions are valid inputs to the decompresser, it eliminates one possible test that attacker could use to check whether a guessed key is correct. has also written a bijective arithmetic coder, arb255. Thus, it is possible to make the entire compression algorithm a bijection. A predictive filter is a transform which can be used to compress numeric data such as audio, images, or video. The idea is to predict the next sample, and then encode the difference with order 0 model. The decompresser makes the same sequence of predictions and adds them to the decoded prediction errors. Better predictions lead to smaller errors, which generally compress better. Delta Coding. The simplest predictive filter is a code. The predicted value is just the previous value. For example, the sequence would be coded as A second pass would result Delta coding works well on sampled waveforms containing only low frequencies such as blurry images or low sounds. Delta coding computes a discrete derivative. Consider what happens the frequency domain. A discrete Fourier transform represents the data as a sum of sine waves of different frequencies and phases. the case of a sine wave with frequency ω radians per sample and amplitude A, the derivative is another sine wave with the same frequency and amplitude ωA. From the Nyquist theorem, the highest frequency that can be represented by a sampled waveform is π or half the sampling rate. Frequencies above 1 radian per sample increase amplitude after coding, and lower frequencies decrease. Thus, if high frequencies are absent, it should be possible theory to reduce the amplitude to arbitrarily small values by repeated coding. Eventually this fails because any noise the prediction is added to noise the sample with each pass. Noise can come either from the original data or from quantization errors during sampling. These are opposing sources. Decreasing the number of quantization levels removes noise from the original data but adds quantization noise. The images below show the effects of 3 passes of coding horizontally and vertically of the image .bmp The original image is BMP format, which consists of a 54 byte header and a 512 by 512 array of pixels, scanned rows starting at the bottom left. Each pixel is 3 bytes with the numbers 0 representing the brightness of the blue, green, and red components. The image is coded by subtracting the pixel value to the left of the same color, and again on the result by subtracting the pixel value below. To show the effects better, 128 is added to all pixel values Thus, a pixel equal to its neighbors appears medium gray. The original image is 786 bytes