By coupling the wavelet transform with a particular nonlinear shrinking function, the Red-telescopic optimal wavelet estimation of the risk (TOWER) method is introduced for removing noise from signals. It is shown that the method yields convergence of the 2 risk to the actual solution with optimal rate. Moreover, the method is proved to be asymptotically efficient when the regularization parame...

This paper presents a new moment-preserving thresholding technique, called the binary quaternion-moment-preserving (BQMP) thresholding, for color image data. Based on representing color data by the quaternions, the statistical parameters of color data can be expressed through the definition of quaternion moments. Analytical formulas of the BQMP thresholding can thus be determined by using the a...

The transformed l1 penalty (TL1) functions are a one parameter family of bilinear transformations composed with the absolute value function. When acting on vectors, the TL1 penalty interpolates l0 and l1 similar to lp norm (p ∈ (0, 1)). In our companion paper, we showed that TL1 is a robust sparsity promoting penalty in compressed sensing (CS) problems for a broad range of incoherent and cohere...

Image binarization is the process of separation of pixel values into two groups, white as background and black as foreground. Thresholding plays a major in binarization of images. Thresholding can be categorized into global thresholding and local thresholding. In images with uniform contrast distribution of background and foreground like document images, global thresholding is more appropriate....

Thresholdging video images is very challenging due to the fact that image background generally has low resolution and is also more complicated and highly distorted than document images. As a result, thresholding methods that work well for document images may not work effectively for video images in some applications. This paper investigates the issue of thresholding video images for text detect...

-A relative entropy based approach to image thresholding was proposed recently. It was demonstrated that this method was successful for image thresholding. Relative entropy is a member of the class of Ali-Silvey distance measures. In this paper we generalize the relative entropy based approach and present image thresholding algorithms based on the class of Ali-Silvey distance measures. A number...

Entropy-based image thresholding has received considerable interest in recent years. Two types of entropy are generally used as thresholding criteria: Shannon’s entropy and relative entropy, also known as Kullback–Leibler information distance, where the former measures uncertainty in an information source with an optimal threshold obtained by maximising Shannon’s entropy, whereas the latter mea...