Introduction to Inverse Problems in Imaging

A review of GPU-based medical image reconstruction.

The current literature documents a plethora of image denoising techniques in the fields of medical imaging, remote sensing, biometrics, surveillance and vegetation mapping. Therefore it is important to have brief insight into various types of noises in different type of images, for instance medical images, remote sensing images and natural images. This article encompasses the basic definition, history, usage and type of noise affecting some of the major types of imaging modalities. Besides this a brief discussion on the type of noise prevailing in remote sensing and natural images is also given. While designing an effective image denoising algorithm, one needs to be acquainted with the prior information about the noise prevalent in various types of images. Further, a brief idea about the basic principle, outlook, contrast levels and application of medical imaging modalities has also been presented in the context of this article.­­­­­­

Noise Issues Prevailing in Various Types of Medical Images

Breast cancer continues to be a significant public health problem in the world. The diagnosing mammography method is the most effective technology for early detection of the breast cancer. However, in some cases, it is difficult for radiologists to detect the typical diagnostic signs, such as masses and microcalcifications on the mammograms. This paper describes a new method for mammographic image enhancement and denoising based on wavelet transform and homomorphic filtering. The mammograms are acquired from the Faculty of Medicine of the University of Akdeniz and the University of Istanbul in Turkey. Firstly wavelet transform of the mammograms is obtained and the approximation coefficients are filtered by homomorphic filter. Then the detail coefficients of the wavelet associated with noise and edges are modeled by Gaussian and Laplacian variables, respectively. The considered coefficients are compressed and enhanced using these variables with a shrinkage function. Finally using a proposed adaptive thresholding the fine details of the mammograms are retained and the noise is suppressed. The preliminary results of our work indicate that this method provides much more visibility for the suspicious regions.

A Wavelet-Based Mammographic Image Denoising and Enhancement with Homomorphic Filtering

Rejection sampling is a well-known method to generate random samples from arbitrary target probability distributions. It demands the design of a suitable proposal probability density function (pdf) from which candidate samples can be drawn. These samples are either accepted or rejected depending on a test involving the ratio of the target and proposal densities. The adaptive rejection sampling method is an efficient algorithm to sample from a log-concave target density, that attains high acceptance rates by improving the proposal density whenever a sample is rejected. In this paper we introduce a generalized adaptive rejection sampling procedure that can be applied with a broad class of target probability distributions, possibly non-log-concave and exhibiting multiple modes. The proposed technique yields a sequence of proposal densities that converge toward the target pdf, thus achieving very high acceptance rates. We provide a simple numerical example to illustrate the basic use of the proposed technique, together with a more elaborate positioning application using real data.

/pdf/a-generalization-of-the-adaptive-rejection-sampling-2rc8hyktgj.pdf

A generalization of the adaptive rejection sampling algorithm

Parallel CT image reconstruction based on GPUs

Automatic evaluation of the image quality of a mammographic phantom.

Digital mammographic image processing often requires a previous application of filters to reduce the noise level of the image while preserving important details. This may improve the quality of digital mammographic images and contribute to an accurate diagnosis. In the literature, one can find a large amount of denoising techniques available for different kinds of images. We have adapted some of the existing denoising algorithms to mammographic images. We compare the effect of different denoising filters acting on digitized mammograms. The considered filters are: a local Wiener filter, a wavelet filter, a filter based on independent component analysis, and finally, a filter based on the diffusion equation. The noise reduction is measured by the mean squared error.

Comparing methods to denoise mammographic images

In X-ray computed tomography (CT) iterative methods are more suitable for the reconstruction of images with high contrast and precision in noisy conditions and from a small number of projections However, in practice, these methods are not widely used due to the high computational cost of their implementation Nowadays technology provides the possibility to reduce effectively this drawback It is the goal of this work to develop a fast GPU-based algorithm to reconstruct high quality images from under sampled and noisy projection data

CT Image Reconstruction Based on GPUs

The images obtained by X-Ray or computed tomography (CT) in adverse conditions may be contaminated with noise that can affect the detection of diseases. A large number of image processing techniques (filters) have been proposed to remove noise. These techniques depend on the type of noise present in the image. In this work, we propose a method designed to reduce the Gaussian, the impulsive and speckle noise and combined noise. This filter, called PGNDF, combines a non-linear diffusive filter with a peer group with fuzzy metric technique. The proposed filter is able to reduce efficiently the image noise without any information about what kind of noise might be present. To evaluate the filter performance, we use mammographic images from the mini- MIAS database which we have damaged by adding Gaussian, impulsive and speckle noises of different magnitudes. As a result, the proposed method obtains a good performance in most of the different types of noise.

P. Mayo

Papers

Parallel CT image reconstruction based on GPUs

Automatic evaluation of the image quality of a mammographic phantom.

Comparing methods to denoise mammographic images

CT Image Reconstruction Based on GPUs

Medical image restoration with different types of noise