Validity of non-local mean filter and novel denoising method

Background Image denoising is an important topic in the digital image processing field.This study theoretically investigates the validity of the classical nonlocal mean filter(NLM)for removing Gaussian noise from a novel statistical perspective.Method By considering the restored image as an estimator of the clear image from a statistical perspective,we gradually analyze the unbiasedness and effectiveness of the restored value obtained by the NLM filter.Subsequently,we propose an improved NLM algorithm called the clustering-based NLM filter that is derived from the conditions obtained through the theoretical analysis.The proposed filter attempts to restore an ideal value using the approximately constant intensities obtained by the image clustering process.In this study,we adopt a mixed probability model on a prefiltered image to generate an estimator of the ideal clustered components.Result The experiment yields improved peak signal-to-noise ratio values and visual results upon the removal of Gaussian noise.Conclusion However,the considerable practical performance of our filter demonstrates that our method is theoretically acceptable as it can effectively estimate ideal images.

Super-Resolution Based on Curvelet Transform and Sparse Representation

Super-resolution techniques are used to reconstruct an image with a high resolution from one or more low-resolution image(s).In this paper,we proposed a single image super-resolution algorithm.It uses the nonlocal mean filter as a prior step to produce a denoised image.The proposed algorithm is based on curvelet transform.It converts the denoised image into low and high frequencies(sub-bands).Then we applied a multi-dimensional interpolation called Lancozos interpolation over both sub-bands.In parallel,we applied sparse representation with over complete dictionary for the denoised image.The proposed algorithm then combines the dictionary learning in the sparse representation and the interpolated sub-bands using inverse curvelet transform to have an image with a higher resolution.The experimental results of the proposed super-resolution algorithm show superior performance and obviously better-recovering images with enhanced edges.The comparison study shows that the proposed super-resolution algorithm outperforms the state-of-the-art.The mean absolute error is 0.021±0.008 and the structural similarity index measure is 0.89±0.08.

A Parallel Markov Cerebrovascular Segmentation Algorithm Based on Statistical Model

For segmenting cerebral blood vessels from the time-of-flight magnetic resonance angiography （TOF-MRA） images accurately, we propose a parallel segmentation algorithm based on statistical model with Markov random field （MRF）. Firstly, we improve traditional non-local means filter with patch-based Fourier transformation to preprocess the TOF-MRA images. In this step, we mainly utilize the sparseness and self-similarity of the MRA brain images sequence. Secondly, we add the MRF information to the finite mixture mode （FMM） to fit the intensity distribution of medical images. We make use of the MRF in image sequence to estimate the proportion of cerebral tissues. Finally, we choose the particle swarm optimization （PSO） algorithm to parallelize the parameter estimation of FMM. A large number of experiments verify the high accuracy and robustness of our approach especially for narrow vessels. The work will offer significant assistance for physicians on the prevention and diagnosis of cerebrovascular diseases.