Non-Local Means (NLM) and its variants have proven to be effective and robust in many image denoising tasks. In this letter, we study approaches to selecting center pixel weights (CPW) in NLM. Our key contributions are 1) we give a novel formulation of the CPW problem from a statistical shrinkage perspective; 2) we construct the James–Stein shrinkage estimator in the CPW context; and 3) we propose a new local James–Stein type CPW (LJSCPW) that is locally tuned for each image pixel. Our experimental results showed that compared to existing CPW solutions, the LJSCPW is more robust and effective under various noise levels. In particular, the NLM with the LJSCPW attains higher means with smaller variances in terms of the peak signal and noise ratio (PSNR) and structural similarity (SSIM), implying it improves the NLM denoising performance and makes the denoising less sensitive to parameter changes.

In this letter, we propose a so-called probabilistic non-local means (PNLM) method for image denoising. Our main contributions are: 1) we point out defects of the weight function used in the classic NLM; 2) we successfully derive all theoretical statistics of patch-wise differences for Gaussian noise; and 3) we employ this prior information and formulate the probabilistic weights truly reflecting the similarity between two noisy patches. Our simulation results indicate the PNLM outperforms the classic NLM and many NLM recent variants in terms of the peak signal noise ratio (PSNR) and the structural similarity (SSIM) index. Encouraging improvements are also found when we replace the NLM weights with the PNLM weights in tested NLM variants.

Many applications in image processing and computer vision require finding a particular template in an image or a video, that is, template matching. Given a template and an input, the matching algorithm finds the region of interest (ROI) that most closely matches the template in terms of some similarity measurement. According to the way similarity measurements are performed, the template matching methods can roughly be classified into two groups: 1) patch matching schemes, such as the sum of absolute difference (SAD) , the sum of squared difference (SSD) [1], or cross correlation (XCORR), where the similarity measurement directly relies on pixel information from the patch of interest; and 2) feature matching schemes, such as invariant features [4] and bags of features [5], where similarity measurement relies on features describing the template and the frame. Patch matching methods are not robust, especially when noise, skew, or errors occur. Further, they consume a large amount of time, because of expensive sliding window search for calculating the similarity score over all possible locations. Several techniques have been explored for accelerating such matching methods, including early rejections and correlation techniques [1]. However, the computation cost could still be unaffordable when the frame size is large. Typically other techniques, like frame difference, are used to reduce the search space in applications. Feature matching methods process the template and describe it with features, which are ideally invariant to rotation, skew, noise etc. However in many cases, the use of a more complicated model for similarity measurement results in higher computational cost. Further, sliding window search is also a costly stage for such methods. While there exist known algorithms for fast search of object instances in an image using branch-and-bound techniques, in our particular problem, methods of this type have two crucial limitations. First, they require a large number of training samples for each class to learn robust classifiers. Second, interest point detectors like SIFT [5] typically do not generate sufficient number of feature points, because of the small size of the provided logo, large homogenous regions and degradations. Wavelets based approaches have been extensively used in object detection and recognition. In [3], wavelet coefficients based image histogram are collected in bins and are used for classifying logos. In [6], wavelet coefficients are directly used and trained for pedestrian detection. In [8], wavelet coefficients are selected to form rotation-invariant features by using the angular-radial transform. However, matching logos within frames using [3, 6, 8] still requires expensive window searching and thus are not appropriate for real-time processing. In this paper, we propose a new matching method using the wavelet based band-pass filters (WBPFs). Instead of using direct distance measurement requiring expensive window search, the similarity is measured in the indirect way involving two stages. In the stage of offline template processing (see Figure 1), a template is automatically described by a set of three directional WBPFs, where only salient wavelet frequency components of the template are allowed to pass. In the stage of online frame processing (see Figure 2), a frame is transformed to the wavelet domain and its sub-bands are filtered with respect to the corresponding template WBFPs. Finally, the detection is made with respect to the region of the densest responses under spatial constraints [2, 4]. We show that the proposed template matching system has a very low computational cost, which is 50 times faster than the correlation based SSD [1] and 10 times faster than the orthogonal Haar transform (OHT) based SSD [7]. Further, the proposed method does not trade-off accuracy, since the use of subtemplate information makes it robust to skew and camera view change. Experimental results demonstrate our method for real-time logo detection in broadcast videos.

In this paper, a new information entropy based randomness test for image encryption about is proposed. Unlike the conventional information entropy test working on the global image, the new proposed measurement focuses on local image blocks and calculates the sample mean of information entropy over a number of random selected image blocks within a test encrypted image. Reference values are mathematical derived from the ideally encrypted image model. As a result, the randomness of an encrypted image can be easily told by comparing the test values with theoretical ones. Ultimately, a hypothesis test to accept or reject an encrypted image is also derived to accept or reject the null hypothesis that ciphertext image is ideally encrypted/random-like with a significance level α. In such a way, the proposed block entropy test provides both quantitative and qualitative results for image encryption. Experimental results on existing image cipher show the effectiveness of the proposed test. The same idea can be also to other digital data, like videos or audios.

S-Boxes play a vital role in cipher designs and have been researched for years. In this article a new way of dynamically designing S-boxes using Latin Square doubly stochastic matrix is proposed. And it is demonstrated that the enciphering/deciphering process is a mimic of a Markov chain Monte Carlo simulation. Unlike conventional dynamic S-boxes, the proposed S-boxes are not directly defined by keys, but contained in the key dependent doubly stochastic matrix. The created matrix has desired properties including: 1) it implicitly contains S-boxes and thus complicates the internal structure of S-boxes; 2) it naturally defines S-boxes with reversibility and thus any S-boxes used for encryption can be directly used for decryption; 3) it satisfies the Strict Avalanche Criterion (SAC) for S-Boxes and thus it has good resistance to differential or linear cryptanalysis; 4) it guarantees the independence of the ciphertext distribution from plaintext one; and 5) it ensures that the expected ciphertext distribution is uniform and thus attains excellent confusion properties when use these S-Boxes iteratively. Theoretical and experimental results show that the proposed S-box has a high security level and is suitable to design cryptosystem for data encryption. We also extend our S-boxes to a simple image cipher. Experimental results show that the proposed dynamical flexible structure S-boxes has cryptographic properties comparable or better than some existing image encryption methods.

This paper presents a novel block cipher based on the Sudoku matrix. The offered block cipher combines many advantages of chaos-based encryption and traditional transform-based encryption techniques. Computer simulations show that a) the encrypted data have very random-like properties under many statistical metrics, b) unlike most chaos-based encryption methods generating unpredictable output, our new method is robust and effective for generating uniform-like encrypted data; c) it has high sensitivity to the KEY. The offered scheme can be applied to many different data types, such as audio, image and video.

Many problems in security and surveillance require the resolution expansion of a captured image. This paper introduces a new system for expanding the resolution of text images. The system inputs are single instances of low resolution text images which must be restored and transformed into data readable text. To achieve acceptable results, such systems require a robust restoration subsystem. The sub-system proposed in this paper creates a bimodal image which favors polygonal representations, consistent with the characteristics of scripts of most non-cursive languages. The resolution expanded image is generated by iteratively solving a non linear optimization equation in the Radon domain with the imposition of image domain constraints. To the best of our knowledge, the idea of Radon domain restoration is new.

In this letter, we propose a new construction method for a class of parametric Slant-Hadamard transforms that includes but is not limited to the commonly used Slant-Hadamard and Hadamard transforms. This parametric class performs better in generalized Wiener filtering than existing Slant-Hadamard transforms for the first-order Markov and the generalized image correlation models. We also show that the new parametric Slant-Hadamard transform outperforms the commonly used discrete cosine transform for the generalized image correlation model.

At low bit rates, the linear subband coders are susceptible to the ringing effect, which causes rippling and blurring around the edges in the images. On the other hand, the nonlinear coders are affected by the smearing effect wherein the detail regions are removed. In this paper, we introduce fuzzy subband coding system. This system uses fuzzy median filters in the analysis and synthesis stage of the coder. The motivation for this study is to determine if this novel system can reduce both ringing and smearing effect. Experimental results show that this new subband coder does out-perform linear and median filter subband coders, both in PSNR and visually.

The stabilizing functional approach is utilized to restore a distorted signal, the Itakura-Saito distortion measure of communication theory and the Kullback-Leilber distance of statistics are employed as the stabilizing functionals. The minimization of these nonquadratic functionals, subject to some statistical knowledge about the noise corrupting the system, is regarded as the minimization of a distortion measure or directed distance from a prior guess P to the desired signal z. The extremum of the unconstrained problem is then attained through an iterative scheme that allows for the introduction of two novel robust and stable signal restoration algorithms.>

A technique to estimate a spectrum when errors in the autocorrelation function values are present is discussed. The principle of minimum relative entropy is used to derive the spectral estimation technique. It is assumed that some statistics of the noise corrupting the autocorrelation measurements are known; this provides the constraint equations subject to which the relative entropy functional is minimized. Often in practice, the variance of the noise is known (or calculatable) in which case the constraint equation is a mean squared error. An iterative algorithm that utilizes the ability to include a priori guess in the minimum relative entropy principle is derived. Examples using the proposed technique to obtain spectral estimates from noisy autocorrelation data are presented. The spectral estimates are shown to be superior to classical and entropy-based techniques that incorrectly assume the autocorrelation values to be exact. The method is not limited to a white Gaussian noise environment and can be applied to utilize the knowledge of any statistics for any type of noise that is corrupting the autocorrelation function.>

A nonlinear adaptive method is presented for filtering a signal which is corrupted by spikes which take discrete values Mi with probability Pi at random points in time. An unsupervised learning technique is used to estimate the unknown parameters Mi, Pi, and oi. The spikes are then removed using a Bayes classifier. A theoretical and experimental comparison with the MMSE linear filter is presented.

The inverse isoperimetric problem of the entropy functional is considered in this Correspondence. This problem can be stated as follows: Given a known probability density function (pdf), what prior constraints are needed in order for this pdf to be the one that maximizes the entropy functional? The solution is given in terms of a Theorem, and it is compared to the Rozenberg-Rubichev solution. The Theorem is also used in simple applications, one of which illuminates the relationship of the maximum entropy principle (MEP) to the concept of "relative frequencies."