Family Of Filter Banks Research Articles

A Class of Warped Filter Bank Frames Tailored to Non-linear Frequency Scales

A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function. The warping function is a $${\mathcal {C}}^1$$-diffeomorphism that determines the frequency progression and can be chosen freely, apart from minor technical restrictions. The resulting functions are interpreted as filter frequency responses. Combined with appropriately chosen decimation factors, a non-uniform analysis filter bank is obtained. Classical Gabor and wavelet filter banks are special cases of the proposed construction. Beyond the state-of-the-art, we construct a filter bank adapted to a frequency scale derived from human auditory perception and families of filter banks that can be interpreted as an interpolation between linear (Gabor) and logarithmic (wavelet) frequency scales. We derive straightforward conditions on the prototype filter decay and the decimation factors, such that the resulting warped filter bank forms a frame. In particular, a simple and constructive method for obtaining tight frames with bandlimited filters is derived by invoking previous results on generalized shift-invariant systems.

Multidimensional Directional Filter Banks and Surfacelets

In 1992, Bamberger and Smith proposed the directional filter bank (DFB) for an efficient directional decomposition of 2-D signals. Due to the nonseparable nature of the system, extending the DFB to higher dimensions while still retaining its attractive features is a challenging and previously unsolved problem. We propose a new family of filter banks, named NDFB, that can achieve the directional decomposition of arbitrary N-dimensional (N > or =2) signals with a simple and efficient tree-structured construction. In 3-D, the ideal passbands of the proposed NDFB are rectangular-based pyramids radiating out from the origin at different orientations and tiling the entire frequency space. The proposed NDFB achieves perfect reconstruction via an iterated filter bank with a redundancy factor of N in N-D. The angular resolution of the proposed NDFB can be iteratively refined by invoking more levels of decomposition through a simple expansion rule. By combining the NDFB with a new multiscale pyramid, we propose the surfacelet transform, which can be used to efficiently capture and represent surface-like singularities in multidimensional data.

Wavelet-based compression of medical images: filter-bank selection and evaluation

Wavelet-based image coding algorithms (lossy and lossless) use a fixed perfect reconstruction filter-bank built into the algorithm for coding and decoding of images. However, no systematic study has been performed to evaluate the coding performance of wavelet filters on medical images. We evaluated the best types of filters suitable for medical images in providing low bit rate and low computational complexity. In this study a variety of wavelet filters are used to compress and decompress computed tomography (CT) brain and abdomen images. We applied two-dimensional wavelet decomposition, quantization and reconstruction using several families of filter banks to a set of CT images. Discreet Wavelet Transform (DWT), which provides efficient framework of multi-resolution frequency was used. Compression was accomplished by applying threshold values to the wavelet coefficients. The statistical indices such as mean square error (MSE), maximum absolute error (MAE) and peak signal-to-noise ratio (PSNR) were used to quantify the effect of wavelet compression of selected images. The code was written using the wavelet and image processing toolbox of the MATLAB (version 6.1). This results show that no specific wavelet filter performs uniformly better than others except for the case of Daubechies and bi-orthogonal filters which are the best among all. MAE values achieved by these filters were 5 x 10(-14) to 12 x 10(-14) for both CT brain and abdomen images at different decomposition levels. This indicated that using these filters a very small error (approximately 7 x 10(-14)) can be achieved between original and the filtered image. The PSNR values obtained were higher for the brain than the abdomen images. For both the lossy and lossless compression, the 'most appropriate' wavelet filter should be chosen adaptively depending on the statistical properties of the image being coded to achieve higher compression ratio.