The curvelet transform for image denoising

We describe approximate digital implementations of two new mathematical transforms, namely, the ridgelet transform and the curvelet transform. Our implementations offer exact reconstruction, stability against perturbations, ease of implementation, and low computational complexity. A central tool is Fourier-domain computation of an approximate digital Radon transform. We introduce a very simple interpolation in the Fourier space which takes Cartesian samples and yields samples on a rectopolar grid, which is a pseudo-polar sampling set based on a concentric squares geometry. Despite the crudeness of our interpolation, the visual performance is surprisingly good. Our ridgelet transform applies to the Radon transform a special overcomplete wavelet pyramid whose wavelets have compact support in the frequency domain. Our curvelet transform uses our ridgelet transform as a component step, and implements curvelet subbands using a filter bank of a` trous wavelet filters. Our philosophy throughout is that transforms should be overcomplete, rather than critically sampled. We apply these digital transforms to the denoising of some standard images embedded in white noise. In the tests reported here, simple thresholding of the curvelet coefficients is very competitive with "state of the art" techniques based on wavelets, including thresholding of decimated or undecimated wavelet transforms and also including tree-based Bayesian posterior mean methods. Moreover, the curvelet reconstructions exhibit higher perceptual quality than wavelet-based reconstructions, offering visually sharper images and, in particular, higher quality recovery of edges and of faint linear and curvilinear features. Existing theory for curvelet and ridgelet transforms suggests that these new approaches can outperform wavelet methods in certain image reconstruction problems. The empirical results reported here are in encouraging agreement

Efficient reconfigurable architectures for 3D medical image compression

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Recently, the more widespread use of three-dimensional (3-D) imaging modalities, such as magnetic resonance imaging (MRI), computed tomography (CT), positron emission tomography (PET), and ultrasound (US) have generated a massive amount of volumetric data. These have provided an impetus to the development of other applications, in particular telemedicine and teleradiology. In these fields, medical image compression is important since both efficient storage and transmission of data through high-bandwidth digital communication lines are of crucial importance. Despite their advantages, most 3-D medical imaging algorithms are computationally intensive with matrix transformation as the most fundamental operation involved in the transform-based methods. Therefore, there is a real need for high-performance systems, whilst keeping architectures exible to allow for quick upgradeability with real-time applications. Moreover, in order to obtain efficient solutions for large medical volumes data, an efficient implementation of these operations is of significant importance. Reconfigurable hardware, in the form of field programmable gate arrays (FPGAs) has been proposed as viable system building block in the construction of high-performance systems at an economical price. Consequently, FPGAs seem an ideal candidate to harness and exploit their inherent advantages such as massive parallelism capabilities, multimillion gate counts, and special low-power packages. The key achievements of the work presented in this thesis are summarised as follows. Two architectures for 3-D Haar wavelet transform (HWT) have been proposed based on transpose-based computation and partial reconfiguration suitable for 3-D medical imaging applications. These applications require continuous hardware servicing, and as a result dynamic partial reconfiguration (DPR) has been introduced. Comparative study for both non-partial and partial reconfiguration implementation has shown that DPR offers many advantages and leads to a compelling solution for implementing computationally intensive applications such as 3-D medical image compression. Using DPR, several large systems are mapped to small hardware resources, and the area, power consumption as well as maximum frequency are optimised and improved. Moreover, an FPGA-based architecture of the finite Radon transform (FRAT)with three design strategies has been proposed: direct implementation of pseudo-code with a sequential or pipelined description, and block random access memory (BRAM)- based method. An analysis with various medical imaging modalities has been carried out. Results obtained for image de-noising implementation using FRAT exhibits promising results in reducing Gaussian white noise in medical images. In terms of hardware implementation, promising trade-offs on maximum frequency, throughput and area are also achieved. Furthermore, a novel hardware implementation of 3-D medical image compression system with context-based adaptive variable length coding (CAVLC) has been proposed. An evaluation of the 3-D integer transform (IT) and the discrete wavelet transform (DWT) with lifting scheme (LS) for transform blocks reveal that 3-D IT demonstrates better computational complexity than the 3-D DWT, whilst the 3-D DWT with LS exhibits a lossless compression that is significantly useful for medical image compression. Additionally, an architecture of CAVLC that is capable of compressing high-definition (HD) images in real-time without any buffer between the quantiser and the entropy coder is proposed. Through a judicious parallelisation, promising results have been obtained with limited resources. In summary, this research is tackling the issues of massive 3-D medical volumes data that requires compression as well as hardware implementation to accelerate the slowest operations in the system. Results obtained also reveal a significant achievement in terms of the architecture efficiency and applications performance.Ministry of Higher Education Malaysia (MOHE), Universiti Tun Hussein Onn Malaysia (UTHM) and the British Counci

Row Compression and Nested Product Decomposition of a Hierarchical Representation of a Quasiseparable Matrix

This research introduces a row compression and nested product decomposition of an nxn hierarchical representation of a rank structured matrix A, which extends the compression and nested product decomposition of a quasiseparable matrix. The hierarchical parameter extraction algorithm of a quasiseparable matrix is efficient, requiring only O(nlog(n))operations, and is proven backward stable. The row compression is comprised of a sequence of small Householder transformations that are formed from the low-rank, lower triangular, off-diagonal blocks of the hierarchical representation. The row compression forms a factorization of matrix A, where A = QC, Q is the product of the Householder transformations, and C preserves the low-rank structure in both the lower and upper triangular parts of matrix A. The nested product decomposition is accomplished by applying a sequence of orthogonal transformations to the low-rank, upper triangular, off-diagonal blocks of the compressed matrix C. Both the compression and decomposition algorithms are stable, and require O(nlog(n)) operations. At this point, the matrix-vector product and solver algorithms are the only ones fully proven to be backward stable for quasiseparable matrices. By combining the fast matrix-vector product and system solver, linear systems involving the hierarchical representation to nested product decomposition are directly solved with linear complexity and unconditional stability. Applications in image deblurring and compression, that capitalize on the concepts from the row compression and nested product decomposition algorithms, will be shown

Multiresolution based, multisensor, multispectral image fusion

Spaceborne sensors, which collect imagery of the Earth in various spectral bands, are limited by the data transmission rates. As a result the multispectral bands are transmitted at a lower resolution and only the panchromatic band is transmitted at its full resolution. The information contained in the multispectral bands is an invaluable tool for land use mapping, urban feature extraction, etc. However, the limited spatial resolution reduces the appeal and value of this information. Pan sharpening techniques enhance the spatial resolution of the multispectral imagery by extracting the high spatial resolution of the panchromatic band and adding it to the multispectral images. There are many different pan sharpening methods available like the ones based on the Intensity-Hue-Saturation and the Principal Components Analysis transformation. But these methods cause heavy spectral distortion of the multispectral images. This is a drawback if the pan sharpened images are to be used for classification based applications. In recent years, multiresolution based techniques have received a lot of attention since they preserve the spectral fidelity in the pan sharpened images. Many variations of the multiresolution based techniques exist. They differ based on the transform used to extract the high spatial resolution information from the images and the rules used to synthesize the pan sharpened image. The superiority of many of the techniques has been demonstrated by comparing them with fairly simple techniques like the Intensity-Hue-Saturation or the Principal Components Analysis. Therefore there is much uncertainty in the pan sharpening community as to which technique is the best at preserving the spectral fidelity. This research investigates these variations in order to find an answer to this question. An important parameter of the multiresolution based methods is the number of decomposition levels to be applied. It is found that the number of decomposition levels affects both the spatial and spectral quality of the pan sharpened images. The minimum number of decomposition levels required to fuse the multispectral and panchromatic images was determined in this study for image pairs with different resolution ratios and recommendations are made accordingly

Multiresolution based, multisensor, multispectral image fusion

Spaceborne sensors, which collect imagery of the Earth in various spectral bands, are limited by the data transmission rates. As a result the multispectral bands are transmitted at a lower resolution and only the panchromatic band is transmitted at its full resolution. The information contained in the multispectral bands is an invaluable tool for land use mapping, urban feature extraction, etc. However, the limited spatial resolution reduces the appeal and value of this information. Pan sharpening techniques enhance the spatial resolution of the multispectral imagery by extracting the high spatial resolution of the panchromatic band and adding it to the multispectral images. There are many different pan sharpening methods available like the ones based on the Intensity-Hue-Saturation and the Principal Components Analysis transformation. But these methods cause heavy spectral distortion of the multispectral images. This is a drawback if the pan sharpened images are to be used for classification based applications. In recent years, multiresolution based techniques have received a lot of attention since they preserve the spectral fidelity in the pan sharpened images. Many variations of the multiresolution based techniques exist. They differ based on the transform used to extract the high spatial resolution information from the images and the rules used to synthesize the pan sharpened image. The superiority of many of the techniques has been demonstrated by comparing them with fairly simple techniques like the Intensity-Hue-Saturation or the Principal Components Analysis. Therefore there is much uncertainty in the pan sharpening community as to which technique is the best at preserving the spectral fidelity. This research investigates these variations in order to find an answer to this question. An important parameter of the multiresolution based methods is the number of decomposition levels to be applied. It is found that the number of decomposition levels affects both the spatial and spectral quality of the pan sharpened images. The minimum number of decomposition levels required to fuse the multispectral and panchromatic images was determined in this study for image pairs with different resolution ratios and recommendations are made accordingly