# INFOCOMMUNICATIONS JOURNAL Mojette Transform Software Hardware Implementations and its Applications

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1 FEBRUARY 011 VOLUME III NUMBER 1 39

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4 INFOCOMMUNICATIONS JOURNAL b a1 10 b a 13 b a 3 37 b a4 137 b a 5 54 b a6 319 b a b a = b * a = 9 6 b a10 34 b a11 15 b a 1 67 b a13 31 b a 14 8 b a15 45 b a (8) The inverse matrix for the previous example (for the 4x4 matrix size) is implemented as it s showed on the next equation, where a i are the original values of the matrix: a b1 10 a b 13 a b 5 3 a b4 35 a b 5 1 a b6 10 a b 7 5 a b = 8 41 a * b = 9 a b10 78 a b15 55 a b 16 3 a b a b a b19 6 a b0 34 IV. EXPERIMENTS WITH MTTOOL (9) files with pixel values of 0 and 55 and the LENA.PGM. First test ran only once, after that the second test was running for 6 times in a row, and the last test was running 4 times. Each test was performed on the sizes of 16x16, 3x3 and on 51x51. the results of the two smallest image sizes are nearly identical and the result were nearly always under 0 millisecond for MT and IMT, but on the 51x51 image size we could see the following difference: TABLE III TEST RESULT OF THE MT AND IMT WITH THE FIRST VERSION IMAGE Black (51x51) White (51x51) Minute: MT and Minute: MT and Second: IMT in Second: IMT in Millisecond Millisecond Millisecond Millisecond MT start 57:14:77 0,16158 MT end IMT start 57:15: , IMT end 57:15: , MT start 57::59 0, MT end IMT start 57:3: , IMT end 57:3: , From this we can see that the difference between the black and the white images is more than 50 percent, when it comes to the MT, and only 0 percent when we apply the IMT on the Mojette files. With the built in ZIP and Huffman coding opportunities (Fig. 5) we can decrease the size of any vectors which are created from the projections of MT [13-17]. The Huffman lossless encoding and decoding algorithm was chosen due to it s binary block encoding attribute and not because of it s compression capability. Good data compression can be achieved with Zip and Unzip which is also implemented. The possibility of time measuring with simple tools, such as labels or easily generated text files which are including the test results can give us a good insight into the MT and IMT. From these results we can estimate and predict the consumed time on hardware implementation and also the cost of it. Fig. 5. Logical system architecture of the MTTool. V. USER INTERFACE OF THE MTTOOL Basically the MTTool program surface is bade on MDI structure of Microsoft. The parent window contains the main menu and nearly all child windows are opened here. The only exception is the Help/Contents (help.html) which appears outside from the parent window in the default internet browser application. At the beginning the main goal of the implementation was to represent both the original and the restored image together with the Mojette files which contained the bins of the Mojette transform described in [11,13-17]. We created two image boxes to show the before and after images for the user, and we duplicated the information on the two tabbed bar to help the users in comparing the original values, the projections and the inverse values to each other. On the Fig. 6. we can see, the amount of information was too much to check it visually even if the different projections were separated not only by their colors but also were listed after each other. Due to the image size of 51 x 51 we had too many bins to display. That s also one of the many things we decided to make different versions as well. The time measurement was applied on three different images with three different image sizes and with three different periods. The images were a black and white PGM 4 FEBRUARY 011 VOLUME III NUMBER 1

5 Fig. 6. MT GUI of the first version. Multiple images in multiple instances can be opened so we are able to compare them not only by the image itself but also by their properties as well we can see the following information from the pictures such as: Original size, Colors used, Pixel size, Size of the DIB-element, Actual size and Last write time. Later on we developed the Mojette transform in a different way and this gave us the opportunity to create a new interface as well for them (Fig. 7). On an image we can perform the Mojette Transform (Block) with the help of the following child window, where all the steps are visible for a better overview. First we have to choose between two differently based Mojette Transform type such as Algorithm and Matrix. After that we can choose from the predefined Block sizes, which we want to use to perform the MT. Here we will automatically see the Number of blocks, Number of projections, the Projections and the number of bins used for the chosen Block size. If both parameters are set we can click the Next button. As soon as we pushed the Next button we will see the result of the MT with the created Red, Green and Blue bin values grouped together and ordered by the blocks. Here we can check the values of each Block where the MT was performed, and see what are the bin values stored in these Blocks. Mojette block window (Fig. 7) represents the blocked version of the MT. As it can be seen we can choose between Matrix and Algorithm versions with different blck sizes from 4 up to 3 from this and from the hardcoded Projections the other values are calculated. Although this information is also stored in a file we are reading it out from the memory. With the help of Show button and the X and Y values we can choose and display the different Blocks and bin values. By hitting the Next button we can create the bin file which contains all the data presented in the step before. Here we have the opportunity to add error to the Blocks, which will result vertical lines in the reconstructed image from the faulty bin file. However we can only see this error on the image if we reconstruct the bin into a BMP file with the IMT which can transform the bin file automatically, so we don t need to set the IMT like we had to do it with the MT. Fig. 7. Mojette transform (Block) window. Fig. 8. Information about the restored BIN file in the Inverse MT window. The Inverse Mojette (Block) window (Fig. 8) shows us some information about the restored image, we can see that the restored image on the right contains error. This was caused in the Mojette Transform phase where we overwrite the value 0 in the Max. errorbins/block field to add some noise to the Mojette Transform. We can also gain information about the MT which was performed on the image. VI. LOW POWER LOW COMPLEXITY HW DESIGN METHODOLOGY FOR SELECTED ALGORITHM- MT AND IMT Power consumption is a very important question of our days. Many energy saving technologies and techniques were developed in different fields. The spread of portable computers and communication devices inspires the developers to design low power consumption devices (CPUs, storage devices, etc.) [8]. In the computer technology there are several options when low power consumption devices are needed (DSPs, μps). One of these options is using field programmable gate arrays (FPGAs) [9].. The MOTIMOT co-processor denotes the hardware implementation of the direct and inverse Mojette transform as coprocessing elements of an embedded processor [1,16,17]. FEBRUARY 011 VOLUME III NUMBER 1 43

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