Medical Image Compression Using Wrapping Based Fast Discrete Curvelet Transform and Arithmetic Coding

Due to the development of CT (Computed Tomography), MRI (Magnetic Resonance Imaging), PET (Positron Emission Tomography), EBCT (Electron Beam Computed Tomography), SMRI (Stereotactic Magnetic Resonance Imaging), etc. has enhanced the distinguishing rate and scanning rate of the imaging equipments. The diagnosis and the process of getting useful information from the image are got by processing the medical images using the wavelet technique. Wavelet transform has increased the compression rate. Increasing the compression performance by minimizing the amount of image data in the medical images is a critical task. Crucial medical information like diagnosing diseases and their treatments is obtained by modern radiology techniques. Medical Imaging (MI) process is used to acquire that information. For lossy and lossless image compression, several techniques were developed. Image edges have limitations in capturing them if we make use of the extension of 1-D wavelet transform. This is because wavelet transform cannot effectively transform straight line discontinuities, as well geographic lines in natural images cannot be reconstructed in a proper manner if 1-D transform is used. Differently oriented image textures are coded well using Curvelet Transform. The Curvelet Transform is suitable for compressing medical images, which has more curvy portions. This paper describes a method for compression of various medical images using Fast Discrete Curvelet Transform based on wrapping technique. After transformation, the coefficients are quantized using vector quantization and coded using arithmetic encoding technique. The proposed method is tested on various medical images and the result demonstrates significant improvement in performance parameters like Peak Signal to Noise Ratio (PSNR) and Compression Ratio (CR).

Multi-scale UDCT dictionary learning based highly undersampled MR image reconstruction using patch-based constraint splitting augmented Lagrangian shrinkage algorithm

Recently, dictionary learning(DL) based methods have been introduced to compressed sensing magnetic resonance imaging(CS-MRI), which outperforms pre-defined analytic sparse priors. However, single-scale trained dictionary directly from image patches is incapable of representing image features from multi-scale, multi-directional perspective, which influences the reconstruction performance. In this paper, incorporating the superior multi-scale properties of uniform discrete curvelet transform(UDCT) with the data matching adaptability of trained dictionaries, we propose a flexible sparsity framework to allow sparser representation and prominent hierarchical essential features capture for magnetic resonance(MR) images. Multi-scale decomposition is implemented by using UDCT due to its prominent properties of lower redundancy ratio, hierarchical data structure, and ease of implementation. Each sub-dictionary of different sub-bands is trained independently to form the multi-scale dictionaries. Corresponding to this brand-new sparsity model, we modify the constraint splitting augmented Lagrangian shrinkage algorithm(C-SALSA) as patch-based C-SALSA(PB C-SALSA) to solve the constraint optimization problem of regularized image reconstruction. Experimental results demonstrate that the trained sub-dictionaries at different scales, enforcing sparsity at multiple scales, can then be efficiently used for MRI reconstruction to obtain satisfactory results with further reduced undersampling rate. Multi-scale UDCT dictionaries potentially outperform both single-scale trained dictionaries and multi-scale analytic transforms. Our proposed sparsity model achieves sparser representation for reconstructed data, which results in fast convergence of reconstruction exploiting PB C-SALSA. Simulation results demonstrate that the proposed method outperforms conventional CS-MRI methods in maintaining intrinsic properties, eliminating aliasing, reducing unexpected artifacts, and removing noise. It can achieve comparable performance of reconstruction with the state-of-the-art methods even under substantially high undersampling factors.