We introduce a novel algorithm to address the challenges in magnetic resonance (MR) spectroscopic imaging. In contrast to classical sequential data processing schemes, the proposed method combines the reconstruction and postprocessing steps into a unified algorithm. This integrated approach enables us to inject a range of prior information into the data processing scheme, thus constraining the reconstructions. We use high resolution, 3-D estimate of the magnetic field inhomogeneity map to generate an accurate forward model, while a high resolution estimate of the fat/water boundary is used to minimize spectral leakage artifacts. We parameterize the spectrum at each voxel as a sparse linear combination of spikes and polynomials to capture the metabolite and baseline components, respectively. The constrained model makes the problem better conditioned in regions with significant field inhomogeneity, thus enabling the recovery even in regions with high field map variations. To exploit the high resolution MR information, we formulate the problem as an anatomically constrained total variation optimization scheme on a grid with the same spacing as the magnetic resonance imaging data. We analyze the performance of the proposed scheme using phantom and human subjects. Quantitative and qualitative comparisons indicate a significant improvement in spectral quality and lower leakage artifacts.

In this paper we reconstruct the 3-D MR spectroscopic data acquired using an echo-planar spectroscopic imaging (EPSI) sequence. We propose to compensate for B0inhomogeneity artifact by using the B0field map and T2* decay estimated from a higher resolution, multi-slice proton imaging data scanned with similar shimming to the EPSI one. We employ total variation (TV) regularization to obtain more uniform spectral peaks and lineshapes, and exploit the sparsity of the spectral data by using the lscr1norm in the reconstruction.

We propose a new family of nonredundant 3D directional transforms that are useful for video signals. In our construction, taking into account the correlation amongst frames of video, we first decorrelate the temporal data using a stage of 1D wavelet transform and then we employ the efficient 2D Hybrid Wavelets and Directional filter banks (HWD) transform family to the resulting spatial data where we achieve 3D HWD transform family. We construct translation-invariant version of the proposed family and show its efficiency in video denoising compared to other wavelet-based methods through several experiments.

We propose a structural design of multidimensional two-channel filter banks with desirable numbers of vanishing moments for the analysis and synthesis banks. We use a three-step lifting scheme as opposed to the conventional two-step lifting method in order to provide more symmetry between the analysis and synthesis filters. Design examples are also provided. H ( z) M M H̃ ( z)

We propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks. We convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks, where we form a nonredundant transform family, which exhibits both directional and nondirectional basis functions. We demonstrate the potential of the proposed transforms using nonlinear approximation. In addition, we employ the proposed family in two key image processing applications, image coding and denoising, and show its efficiency for these applications.

In a previous work, we proposed a new family of nonredundant geometrical image transforms using hybrid wavelets and directional filter banks (HWD). In this paper we further develop and examine the proposed family and provide an efficient realization utilizing regular filters. Furthermore, we extend and employ the new proposed HWD transforms in two key image processing applications, coding and denoising, and demonstrate their promising results. For coding, an SPIHT-like algorithm is developed for HWD; and for denoising, a translation-invariant HWD (TIHWD) transform is constructed. Our simulations illustrate significant improvements under the proposed transforms when compared with other transform variations.

Blind multiplicative watermarking schemes for speech signals using wavelets and discrete cosine transform are presented. Watermarked signals are modeled using a generalized Gaussian distribution (GGD) and Cauchy probability model. Detectors are developed employing generalized likelihood ratio test (GLRT) and locally most powerful (LMP) approach. The LMP scheme is used for the Cauchy distribution, while the GLRT estimates the gain factor as an unknown parameter in the GGD model. The detectors are tested using Monte Carlo simulation and results show the superiority of the proposed LMP/Cauchy detector in some experiments

Different denoising schemes show dissimilar types of artifacts. For example, certain transform-based denoising schemes could introduce artifacts in smooth regions while others eliminate texture regions. Using different schemes for denoising a noisy image, we can consider the denoising results as different estimates of the image. Through linear combination of the results, we minimize the l2norm of the error to find the optimum coefficients in a least-square-error sense. We employ the wavelet transform, contourlet transform, and adaptive 2-D Wiener filtering as our denoising schemes. Then we apply the proposed method to the denoising results of the individual schemes. This approach eliminates most of the artifacts and achieves significant improvement in the PSNR values. We also propose averaging of the denoising results as a special case of linear combination and show that it yields near-optimal performance

Most subsampled filter banks lack the feature of translation invariance, which is an important characteristic in denoising applications. In this paper, we study and develop new methods to convert a general multichannel, multidimensional filter bank to a corresponding translation-invariant (TI) framework. In particular, we propose a generalized algorithme à trous, which is an extension of the algorithme à trous introduced for 1-D wavelet transforms. Using the proposed algorithm, as well as incorporating modified versions of directional filter banks, we construct the TI contourlet transform (TICT). To reduce the high redundancy and complexity of the TICT, we also introduce semi-translation-invariant contourlet transform (STICT). Then, we employ an adapted bivariate shrinkage scheme to the STICT to achieve an efficient image denoising approach. Our experimental results demonstrate the benefits and potential of the proposed denoising approach. Complexity analysis and efficient realization of the proposed TI schemes are also presented.

The contourlet transform, one of the recent geometrical image transforms, lacks the feature of translation invariance due to subsampling in its filter bank (FB) structure. In this paper, we develop a translation-invariant (TI) scheme of a general multi-channel multidimensional FB and apply our findings to the contourlet transform to obtain a TI contourlet transform (TICT). Further, we employ the proposed TICT for image denoising, where we show that a significant improvement in the PSNR values as well as visual results is gained. Moreover, we demonstrate that this proposed denoising scheme outperforms the TI wavelet denoising approach for most experiments. We also introduce a less-redundant variety of the TICT, where we merely make the first stage of contourlets, translation invariant. We show that this transform, which we call semi-TICT (STICT), achieves a performance near that of the TICT in image denoising.

We propose a new family of perfect reconstruction, non-redundant, and multiresolution geometrical image transforms using the wavelet transform in conjunction with modified versions of directional filter banks (DFB). In the proposed versions of DFB, we use either horizontal or vertical directional decomposition. Taking advantage of the wavelet transform that has efficient nonlinear approximation property, we add the important feature of directionality by applying the modified and regular DFB to the subbands of a few finest wavelet levels. This way we can eliminate a major portion of the artifacts usually introduced when DFB are used. The proposed hybrid wavelets and DFB (HWD) transform family provides visual and PSNR improvements over the wavelet and contourlet transforms.

In this paper, we first propose a new family of geometrical image transforms that decompose images both radially and angularly. Our construction comprises two stages of filter banks that are non-redundant and perfect reconstruction and therefore lead to an overall non-redundant and perfect reconstruction transform. Using the wavelet transform as the first stage, we apply directional filter banks to the wavelet coefficients in such a way to maintain the anisotropy scaling law. Furthermore, we propose a new image coding scheme based on the proposed transform, the wavelet-based contourlet transform (WBCT), using a new contourlet-based set partitioning in hierarchical trees (CSPIHT) algorithm that provides an embedded code. Due to differences in parent-child relationships between the WBCT coefficients and wavelet coefficients, under CSPIHT, we developed an elaborated repositioning algorithm for the WBCT coefficients in such a way that we could scan spatial orientation trees that are similar to the original SPIHT algorithm. Our experiments demonstrate that the proposed approach is efficient in coding images that possess mostly textures and contours. Our simulation results also show that this new coding approach is competitive to the wavelet coder in terms of the PSNR-rate curves, and is visually superior to the wavelet coder for the mentioned images.