Image deconvolution using a Gaussian scale mixtures model to approximate the wavelet sparseness constraint

This paper proposes to use an extended Gaussian Scale Mixtures (GSM) model instead of the conventional ℓ1 norm to approximate the sparseness constraint in the wavelet domain. We combine this new constraint with subband-dependent minimization to formulate an iterative algorithm on two shift-invariant wavelet transforms, the Shannon wavelet transform and dual-tree complex wavelet transform (DTCWT). This extented GSM model introduces spatially varying information into the deconvolution process and thus enables the algorithm to achieve better results with fewer iterations in our experiments. ©2009 IEEE.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

Optical determination of fractal dimensions using Fourier transforms

R. Zwiggelaar and C.R. Bull, 'Optical determination of fractal dimensions using Fourier transforms', Optical Engineering 34 (5), 1325-1332 (1995)

Design of silicon IP cores for biorthogonal wavelet transforms

A methodology for rapid silicon design of biorthogonal wavelet transform systems has been developed. This is based on generic, scalable architectures for the forward and inverse wavelet filters. These architectures offer efficient hardware utilisation by combining the linear phase property of biorthogonal filters with decimation and interpolation. The resulting designs have been parameterised in terms of types of wavelet and wordlengths for data and coefficients. Control circuitry is embedded within these cores that allows them to be cascaded for any desired level of decomposition without any interface logic. The time to produce silicon designs for a biorthogonal wavelet system is only the time required to run synthesis and layout tools with no further design effort required. The resulting silicon cores produced are comparable in area and performance to hand-crafted designs. These designs are also portable across a range of foundries and are suitable for FPGA and PLD implementations.

Custom coprocessor based matrix algorithms for image and signal processing

Matrix algorithms are important in many types of applications including image and signal processing. A close examination of the algorithms used in these, and related, applications reveals that many of the fundamental actions involve matrix algorithms such as matrix multiplication. This paper presents an investigation into the design and implementation of different matrix algorithms such as matrix operations, matrix transforms and matrix decompositions using a novel custom coprocessor system for MATrix algorithms based on Reconfigurable Computing (RCMAT). The proposed RCMAT architectures are scalable, modular and require less area and time complexity with reduced latency when compared with existing structures.

TDM modelling and evaluation of different domain transforms for LSI

Latent semantic indexing (LSI) is a popular technique used in information retrieval (IR) applications. This paper presents a novel evaluation strategy based on the use of image processing tools. The authors evaluate the use of the discrete cosine transform (DCT) and Cohen Daubechies Feauveau 9/7 (CDF 9/7) wavelet transform as a pre-processing step for the singular value decomposition (SVD) step of the LSI system. In addition, the effect of different threshold types on the search results is examined. The results show that accuracy can be increased by applying both transforms as a pre-processing step, with better performance for the hard-threshold function. The choice of the best threshold value is a key factor in the transform process. This paper also describes the most effective structure for the database to facilitate efficient searching in the LSI system.

Neural Network based studies on Spectroscopic Analysis and Image Processing

International School of Photonics, Cochin University of Science and Technology

An Improved Technique for Evolving Wavelet Coefficients for Fingerprint Image Compression

In this paper, an improved technique for evolving wavelet coefficients refined for compression and reconstruction of fingerprint images is presented. The FBI fingerprint compression standard [1, 2] uses the cdf 9/7 wavelet filter coefficients. Lifting scheme is an efficient way to represent classical wavelets with fewer filter coefficients [3, 4]. Here Genetic algorithm (GA) is used to evolve better lifting filter coefficients for cdf 9/7 wavelet to compress and reconstruct fingerprint images with better quality. Since the lifting filter coefficients are few in numbers compared to the corresponding classical wavelet filter coefficients, they are evolved at a faster rate using GA. A better reconstructed image quality in terms of Peak-Signal-to-Noise-Ratio (PSNR) is achieved with the best lifting filter coefficients evolved for a compression ratio 16:1. These evolved coefficients perform well for other compression ratios also.

Faster techniques to evolve wavelet coefficients for better fingerprint image compression

In this article, techniques have been presented for faster evolution of wavelet lifting coefficients for fingerprint image compression (FIC). In addition to increasing the computational speed by 81.35%, the coefficients performed much better than the reported coefficients in literature. Generally, full-size images are used for evolving wavelet coefficients, which is time consuming. To overcome this, in this work, wavelets were evolved with resized, cropped, resized-average and cropped-average images. On comparing the peak- signal-to-noise-ratios (PSNR) offered by the evolved wavelets, it was found that the cropped images excelled the resized images and is in par with the results reported till date. Wavelet lifting coefficients evolved from an average of four 256 256 centre-cropped images took less than 1/5th the evolution time reported in literature. It produced an improvement of 1.009 dB in average PSNR. Improvement in average PSNR was observed for other compression ratios (CR) and degraded images as well. The proposed technique gave better PSNR for various bit rates, with set partitioning in hierarchical trees (SPIHT) coder. These coefficients performed well with other fingerprint databases as well.

Evolution of Better Wavelet Coefficients for Fingerprint Image Compression using cropped images

This paper explains the Genetic Algorithm (GA) evolution of optimized wavelet that surpass the cdf9/7 wavelet for fingerprint compression and reconstruction. Optimized wavelets have already been evolved in previous works in the literature, but they are highly computationally complex and time consuming. Therefore, in this work, a simple approach is made to reduce the computational complexity of the evolution algorithm. A training image set comprised of three 32x32 size cropped images performed much better than the reported coefficients in literature. An average improvement of 1.0059 dB in PSNR above the classical cdf9/7 wavelet over the 80 fingerprint images was achieved. In addition, the computational speed was increased by 90.18 %. The evolved coefficients for compression ratio (CR) 16:1 yielded better average PSNR for other CRs also. Improvement in average PSNR was experienced for degraded and noisy images as well

Development of 2-D MRT based Image Compression Techniques

The thesis explores the area of still image compression. The image compression techniques can be broadly classified into lossless and lossy compression. The most common lossy compression techniques are based on Transform coding, Vector Quantization and Fractals. Transform coding is the simplest of the above and generally employs reversible transforms like, DCT, DWT, etc. Mapped Real Transform (MRT) is an evolving integer transform, based on real additions alone. The present research work aims at developing new image compression techniques based on MRT. Most of the transform coding techniques employ fixed block size image segmentation, usually 8×8. Hence, a fixed block size transform coding is implemented using MRT and the merits and demerits are analyzed for both 8×8 and 4×4 blocks. The N2 unique MRT coefficients, for each block, are computed using templates. Considering the merits and demerits of fixed block size transform coding techniques, a hybrid form of these techniques is implemented to improve the performance of compression. The performance of the hybrid coder is found to be better compared to the fixed block size coders. Thus, if the block size is made adaptive, the performance can be further improved. In adaptive block size coding, the block size may vary from the size of the image to 2×2. Hence, the computation of MRT using templates is impractical due to memory requirements. So, an adaptive transform coder based on Unique MRT (UMRT), a compact form of MRT, is implemented to get better performance in terms of PSNR and HVS The suitability of MRT in vector quantization of images is then experimented. The UMRT based Classified Vector Quantization (CVQ) is implemented subsequently. The edges in the images are identified and classified by employing a UMRT based criteria. Based on the above experiments, a new technique named “MRT based Adaptive Transform Coder with Classified Vector Quantization (MATC-CVQ)”is developed. Its performance is evaluated and compared against existing techniques. A comparison with standard JPEG & the well-known Shapiro’s Embedded Zero-tree Wavelet (EZW) is done and found that the proposed technique gives better performance for majority of images

Image registration and image interpolation in volume rendering of cross sections

We outline a method for registration of images of cross sections using the concepts of The Generalized Hough Transform (GHT). The approach may be useful in situations where automation should be a concern. To overcome known problems of noise of traditional GHT we have implemented a slight modified version of the basic algorithm. The modification consists of eliminating points of no interest in the process before the application of the accumulation step of the algorithm. This procedure minimizes the amount of accumulation points while reducing the probability of appearing of spurious peaks. Also, we apply image warping techniques to interpolate images among cross sections. This is needed where the distance of samples between sections is too large. Then it is suggested that the step of registration with GHT can help the interpolation automation by simplifying the correspondence between points of images. Some results are shown.