Quantitative T1ρ MRI of the Head and Neck Discriminates Carcinoma and Benign Hyperplasia in the Nasopharynx.

BACKGROUND AND PURPOSE: T1ρ imaging is a new quantitative MR imaging pulse sequence with the potential to discriminate between malignant and benign tissue. In this study, we evaluated the capability of T1ρ imaging to characterize tissue by applying T1ρ imaging to malignant and benign tissue in the nasopharynx and to normal tissue in the head and neck. MATERIALS AND METHODS: Participants with undifferentiated nasopharyngeal carcinoma and benign hyperplasia of the nasopharynx prospectively underwent T1ρ imaging. T1ρ measurements obtained from the histogram analysis for nasopharyngeal carcinoma in 43 participants were compared with those for benign hyperplasia and for normal tissue (brain, muscle, and parotid glands) in 41 participants using the Mann-Whitney U test. The area under the curve of significant T1ρ measurements was calculated and compared using receiver operating characteristic analysis and the Delong test, respectively. A P < . 05 indicated statistical significance. RESULTS: There were significant differences in T1ρ measurements between nasopharyngeal carcinoma and benign hyperplasia and between nasopharyngeal carcinoma and normal tissue (all, P < . 05). Compared with benign hyperplasia, nasopharyngeal carcinoma showed a lower T1ρ mean (62.14 versus 65.45 × ms), SD (12.60 versus 17.73 × ms), and skewness (0.61 versus 0.76) (all P < .05), but no difference in kurtosis (P = . 18). The T1ρ SD showed the highest area under the curve of 0.95 compared with the T1ρ mean (area under the curve = 0.72) and T1ρ skewness (area under the curve = 0.72) for discriminating nasopharyngeal carcinoma and benign hyperplasia (all, P < .05). CONCLUSIONS: Quantitative T1ρ imaging has the potential to discriminate malignant from benign and normal tissue in the head and neck.

SURE-LET multichannel image denoising: interscale orthonormal wavelet thresholding.

We propose a vector/matrix extension of our denoising algorithm initially developed for grayscale images, in order to efficiently process multichannel (e.g., color) images. This work follows our recently published SURE-LET approach where the denoising algorithm is parameterized as a linear expansion of thresholds (LET) and optimized using Stein's unbiased risk estimate (SURE). The proposed wavelet thresholding function is pointwise and depends on the coefficients of same location in the other channels, as well as on their parents in the coarser wavelet subband. A nonredundant, orthonormal, wavelet transform is first applied to the noisy data, followed by the (subband-dependent) vector-valued thresholding of individual multichannel wavelet coefficients which are finally brought back to the image domain by inverse wavelet transform. Extensive comparisons with the state-of-the-art multiresolution image denoising algorithms indicate that despite being nonredundant, our algorithm matches the quality of the best redundant approaches, while maintaining a high computational efficiency and a low CPU/memory consumption. An online Java demo illustrates these assertions.

MOMS: maximal-order interpolation of minimal support.

We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly-supported basis function phi(x). We first give the expression for the cases of phi's that have minimal support for a given accuracy (also known as "approximation order"). This class of functions, which we call maximal-order-minimal-support functions (MOMS) is made of linear combinations of the B-spline of the same order and of its derivatives. We provide an explicit form of the MOMS that maximizes the approximation accuracy when the step-size is small enough. We compute the sampling gain obtained by using these optimal basis functions over the splines of the same order. We show that it is already substantial for small orders and that it further increases with the approximation order L. When L is large, this sampling gain becomes linear; more specifically, its exact asymptotic expression is 2/(pie)L. Since the optimal functions are continuous, but not differentiable, for even orders, and even only piecewise continuous for odd orders, our result implies that regularity has little to do with approximating performance. These theoretical findings are corroborated by experimental evidence that involves compounded rotations of images.

Least-squares image resizing using finite differences.

We present an optimal spline-based algorithm for the enlargement or reduction of digital images with arbitrary (noninteger) scaling factors. This projection-based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are B-splines of any degree n. A noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a. For a given choice of basis functions, the results of our method are consistently better than those of the standard interpolation procedure; the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal-to-noise ratio. The method can be generalized to include other classes of piecewise polynomial functions, expressed as linear combinations of B-splines and their derivatives.

Interpolation revisited.

Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. We show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, we call their use generalized interpolation; they involve a prefiltering step when correctly applied. We explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order can be expressed as the convolution of a B-spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. We discuss implementation and performance issues, and we provide experimental evidence to support our claims.