Tag Archives: Fast Fourier transform

Lecture Notes on Image processing for beginners

These are lecture notes which I used to study my course related to image processing. I found these medical image processing lecture notes very useful while studying for the subjects even at the last minute. They helped me in overcoming the fear related to image processing . These notes are meant for all those people who are just beginners and know nothing related to medical image processing. They are well framed and collected

Do download the notes from links given below

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Wavelet & Biomedical Imaging Tutorials

Recent Advances in Biomedical Imaging and Signal Analysis

M. Unser slide Proceedings of the Eighteenth European Signal Processing Conference (EUSIPCO’10), Ålborg, Denmark, August 23-27, 2010, EURASIP Fellow inaugural lecture.

Wavelets have the remarkable property of providing sparse representations of a wide variety of “natural” images. They have been applied successfully to biomedical image analysis and processing since the early 1990s.

In the first part of this talk, we explain how one can exploit the sparsifying property of wavelets to design more effective algorithms for image denoising and reconstruction, both in terms of quality and computational performance. This is achieved within a variational framework by imposing some ?1-type regularization in the wavelet domain, which favors sparse solutions. We discuss some corresponding iterative skrinkage-thresholding algorithms (ISTA) for sparse signal recovery and introduce a multi-level variant for greater computational efficiency. We illustrate the method with two concrete imaging examples: the deconvolution of 3-D fluorescence micrographs, and the reconstruction of magnetic resonance images from arbitrary (non-uniform) k-space trajectories.

In the second part, we show how to design new wavelet bases that are better matched to the directional characteristics of images. We introduce a general operator-based framework for the construction of steerable wavelets in any number of dimensions. This approach gives access to a broad class of steerable wavelets that are self-reversible and linearly parameterized by a matrix of shaping coefficients; it extends upon Simoncelli’s steerable pyramid by providing much greater wavelet diversity. The basic version of the transform (higher-order Riesz wavelets) extracts the partial derivatives of order N of the signal (e.g., gradient or Hessian). We also introduce a signal-adapted design, which yields a PCA-like tight wavelet frame. We illustrate the capabilities of these new steerable wavelets for image analysis and processing (denoising).

Slide of the presentation (PDF 17.3 Mb)

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Basic & Detailed Tutorial in CT & MRI for Biomedical Beginners

A extensive tutorial in CT & MRI which will cover all the aspect required by an engineer who has just entered Biomedical Imaging field and wants to explore new avenues of the field

This tutorial will help you in getting familiarized with the operation of CT & MRI

In the first, the terms “CT” (computed tomography) and “CAT” (computer axial tomography; also used: computer assisted tomography) are the usual way to refer to the method involved when x-rays are used to generate the means by which the “target” is examined. (Also in common use is a process connotation: “CATscan“.) When other forms of radiation or waves are involved, specialized terms such as “PET” or “SPECT“, two techniques in emission topography, are applied (some of these are defined by the nature of the signal carrier). Thus, there are many other specialized uses of tomographic techniques, such as in Magnetic Resonance Imaging (MRI), optical tomography, acoustical tomography, and processing of Synthetic Aperture Radar (SAR). As an aside, we now show one example of a geophysical tomography application – specifically, seismic tomography – in which the surface of the subduction zone running south of Japan into the Kurile Islands has been reconstructed from seismic refraction data.

Important to an in-depth understanding of tomography are underlying physics and mathematical operations, which are pertinent to the methods of Signal Processing. This complex subject will not be treated here (an extensive search of the Internet failed to find a good review); intrinsic to some types of tomography are such concepts as image formation, wave transformation, interferometry, and Fast Fourier Transforms.

Three Internet Sites that cover some general aspects of CAT are at: (1), (2), and (3).

We will explain the operating principles by reviewing how a typical CATscan is conducted. As a general statement, the advantage of this and other medical tomographic methods is an improved delineation and differentiation of the various soft tissue organs in humans and other mammals. Thus, x-rays in this mode are usually able to separate these organs discretely, especially when absorbing chemicals (e.g., barium compounds) or dyes are used. We begin by showing a typical CAT Scanner in an examining room:

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