A novel weighted compressive sensing using L1-magic recovery technique in medical image compression

Recent technological advancement in computing technology, communication systems, and machine learning techniques provides opportunities to biomedical engineers to achieve the requirements of clinical practice. This requires storage and/or transmission of medical images with the conservation of the medical information over the communication channel. Accordingly, medical compression is necessary for efficient channel bandwidth utilization. To solve the trade-off between the compression ratio and the preservation of significant information, compressed sensing (CS) can be used. During image recovery in CS, an optimization algorithm is used, such as greedy pursuit, convex relaxation, and Bayesian framework. In the present work, a convex relaxation optimization called L1-magic is employed, where the objective function can be relaxed to the nearest convex norm, i.e., ℓ1-norm. In addition, the discrete cosine transform is used for recovery by transforming the image from time- to frequency-domain. To improve the medical image recovery, a weighted L1-magic is proposed using a threshold based on the image content, where high weight is given to the significant details in the image. Thus, the significant information in the image (values greater than the threshold) is multiplied by a weight factor according to the image characteristics for a successful recovery process. A comparative study of the proposed weighted L1-magic and orthogonal matching pursuit (OMP), one of the greedy algorithms, was conducted. Different metrics were measured, including the Structural Similarity Index Measure and Peak Signal-to-Noise Ratio (PSNR) to evaluate CS performance using the proposed weighted L1-magic as well as the weighted OMP and the principal component analysis (PCA) as a traditional compression method at different compression ratios (CR). The experimental results on diabetic retinopathy images dataset proved the superiority of the weighted L1-magic method, where for example as 0.4 CR, average PSNR is 19.37, 17.95, and 15.64 using the weighted L1-magic, weighted OMP, and PCA, respectively.