Ramon Reig Bolaño

Radix-4 FFT algorithms with ordered input and output data

In this work we derive two families of radix-4 factorizations for the FFT (Fast Fourier Transform) that have the property that both inputs and outputs are addressed in natural order. These factorizations are obtained from another two families of radix-2 algorithms that have the same property. The radix-4 algorithms obtained have the same mathematical complexity (number of multiplications and additions) that Cooley-Tukey radix-4 algorithms but avoid de bit-reversal ordering applied to the input or at the output.

Radix-R FFT and IFFT Factorizations for Parallel Implementation

Two radix-R regular interconnection pattern families of factorizations for both the FFT and the IFFT -also known as parallel or Pease factorizations- are reformulated and presented. Number R is any power of 2 and N, the size of the transform, any power of R. The first radix-2 parallel FFT algorithm -one of the two known radix-2 topologies- was proposed by Pease. Other authors extended the Pease parallel algorithm to different radix and other particular solutions were also reported. The presented families of factorizations for both the FFT and the IFFT are derived from the well-known Cooley-Tukey factorizations, first, for the radix-2 case, and then, for the general radix-R case. Here we present the complete set of parallel algorithms, that is, algorithms with equal interconnection pattern stage-to-stage topology. In this paper the parallel factorizations are derived by using a unified notation based on the use of the Kronecker product and the even-odd permutation matrix to form the rest of permutation matrices. The radix-R generalization is done in a very simple way. It is shown that, both FFT and IFFT share interconnection pattern solutions. This view tries to contribute to the knowledge of fast parallel algorithms for the case of FFT and IFFT but it can be easily applied to other discrete transforms.

A Contour Based Approach for Bilateral Mammogram Registration Using Discrete Wavelet Analysis

Registration of mammograms is an essential step to increase the effectiveness of all screening programs planned to early detect breast cancer in asymptomatic women. New techniques based on data fusion of different spatial views, temporal analysis or sequences follow up, and multimodal data analysis, require accurate data registration: forcing spatial alignment of images taken from different views, at different times or from different natures. In this work we will focus on a new technique for automatic bilateral mammograms registration. However the same registration technique is also useful for temporal analysis of the same patient. Bilateral mammogram registration is a challenging task; the mammographic appearance of breast tissue may vary considerably, because of differences in breast compression and positioning, differences in imaging techniques, and changes in the breast itself; moreover, there are no clear landmarks in a mammogram, except for the nipple when it is visible. In our approach we detect the skin-line contour as a first step, we describe the contour as a chain-code, and we make a wavelet based correlation analysis, finally we get the matching of the contours. At the end we apply a global affine transformation.