The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.

The problem of comparing DNA sequences is one of the most significant tasks in the field of computational biology. It helps locating the similarities and differences between pairs of DNA sequences. This task can be achieved by finding the longest common substrings between DNA sequences and consequently aligning them. The complexity of this task is due to the high computational power and huge space consuming. Comparing DNA sequences leads to infer the cause of a certain disease beside many significant biological applications. This paper introduces a new Heuristic Approach for DNA Sequences Alignment between two DNA sequences. The new approach is based on three processing phases: the first phase finds the multiple common substrings in the two sequences, the second one sorts the obtained common substrings descending according to their lengths, and the last phase generates the optimal two aligned sequences. The modules of the new approach have been implemented and tested in C# language under Windows platform. The obtained results manifest a reduction in both time of processing and memory requirements.