block based progressive visual secret sharing block based progressive visual secret sharing bpvss is an encryption technique that utilizes the human visual system to recover a secret image the recovery method is based on building up different image blocks step by step in the last few years several research projects have been devoted to the study of bpvss however they have some common drawbacks their dispatching matrices are chaotically designed by adding some redundant 0 1s in order to maintain the size as a fixed value which makes the methods hard to be implemented in addition the pixel expansion ratio grows faster when the number of participants increases and the visual quality of the restored image is quite poor in this paper we propose a non expanded block based progressive visual secret sharing scheme with noise like and meaningful shares respectively experimental results demonstrate the feasibility of this scheme our design has several advantages over other related methods 1 the model is concise easy to implement and the number of participants need not be restricted 2 with noise like shares the contrast of the restored image is 50 which means that the hidden message can be clearly recognized by the naked eye 3 when transparencies are transferred from noise like patterns into a meaningful cover image the contrast in the shares and the restored image is 25 which is still superior to that obtained in other studies 4 our scheme is more suitable for grayscale and color secret images and 5 the size of the transparencies is the same as that of the secret image

new bounds on the average information rate of secret sharing schemes for graph based weighted threshold access structures a secret sharing scheme is a protocol by which a dealer distributes shares of a secret key among a set of n participants in such a way that only qualified subsets of participants can reconstruct the secret key from the shares they received while unqualified subsets have no information about the secret key the collection of all qualified subsets is called the access structure of this scheme the information rate resp average information rate of a secret sharing scheme is the ratio between the size of the secret key and the maximum size resp average size of the shares in a weighted threshold scheme each participant has his or her own weight a subset is qualified if and only if the sum of the weights of participants in the subset is not less than the given threshold morillo et al 19 considered the schemes for weighted threshold access structure that can be represented by graphs called k weighted graphs they characterized this kind of access structures and derived a result on the information rate in this paper we deal with the average information rate of the secret sharing schemes for these structures two sophisticated constructions are presented each of which has its own advantages and both of them perform very well when n k is large

visual multiple secret sharing based upon turning and flipping the secret sharing schemes in conventional visual cryptography are capable of sharing one secret image into a set of random transparencies called shares in the form of rectangles which reveal the secret image to the human visual system when they are superimposed recently visual secret sharing schemes involving multiple secrets have attracted much attention by adopting rotations on one of the two encoded circle shares more than two secrets could be shared yet the encoding and decoding processes of circle shares need more sophisticated mechanisms than those of rectangular or square ones in this paper we explore the possibilities of visual multiple secret sharing using simply two rectangular or square shares specifically we define some operations onto a transparency based upon turning over or flipping around then we propose visual cryptographic schemes that are able to encode two or four secrets into two rectangular shares and up to eight secrets into two square shares such that the secrets cannot be obtained from any single share whereas they are revealed by stacking the two shares under various combinations of turning or flipping operations the proposed schemes which solidly elaborate the relationship between the encoded shares and the shared secrets broaden the research scope and enrich the flexibility and applicability of visual cryptography or image encryption theoretically and practically

on the vectoral ekeland s variational principle and minimal points in product spaces abstract phelps 13 noticed that the scalar ekeland s variational principle evp is equivalent to the existence of a minimal point of the epigraph of the corresponding function with respect to an appropriate order attouch and riahi 1 showed that evp is equivalent to the existence of maximal points with respect to cones satisfying some additional conditions taking these into account gopfert and tammer 6 7 established a maximal point theorem in a product space the aim of this paper is to obtain several minimal point theorems in product spaces and the corresponding variants of the vectorial evp

a pre order principle and set valued ekeland variational principle abstract we establish a pre order principle from the principle we obtain a very general set valued ekeland variational principle where the objective function is a set valued map taking values in a quasi ordered linear space and the perturbation contains a family of set valued maps satisfying certain property from this general set valued ekeland variational principle we deduce a number of particular versions of set valued ekeland variational principle which include many known ekeland variational principles their improvements and some new results

a brezis browder principle on partially ordered spaces and related ordering theorems abstract through a simple extension of brezis browder principle to partially ordered spaces a very general strong minimal point existence theorem on quasi ordered spaces is proved this theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems and three general ekeland variational principles in optimization problems where the objective space is quasi ordered then they are applied to prove strong minimal point existence results generalizations of bishop phelps lemma in linear spaces and ekeland variational principles in set valued optimization problems through a set solution criterion

two secret sharing schemes based on boolean operations traditional secret sharing schemes involve complex computation a visual secret sharing vss scheme decodes the secret without computation but each shadow is m times as big as the original probabilistic vss solved the computation complexity and space complexity problems at once in this paper we propose a probabilistic 2 n scheme for binary images and a deterministic n n scheme for grayscale images both use simple boolean operations and both have no pixel expansion the 2 n scheme provides a better contrast and significantly smaller recognized areas than other methods the n n scheme gives an exact reconstruction

the variational principle and fixed point theorems in certain topological spaces abstract the main purpose of this paper is to introduce the concept off type topological spaces and to establish a variational principle and a fixed point theorem in the kind of spaces which extend ekeland s variational principle and caristi s fixed point theorem respectively

eliminating the texture features in visually meaningful cipher images generally most image encryption algorithms transform original images into texture like or noise like ones unfortunately the feature like texture or noise is just a hint of the existence of encryption for attackers to solve this problem bao et al inf sci 324 2015 197 207 proposed a new image encryption algorithm which can transform original images into visually meaningful ones however the resulting cipher images have some texture features which may be a hint of the existence of encryption to some extent to overcome this flaw we present a new visually meaningful image encryption algorithm based on discrete wavelet transform and discrete quantum walks numerical simulation security analysis and performance comparison demonstrate that our proposal is superior to bao et al s scheme it promotes the combination of image encryption and quantum computation

ekeland s variational principle for vectorial multivalued mappings in a uniform space abstract in this paper we establish ekeland s variational principle and an equilibrium version of ekeland s variational principle for vectorial multivalued mappings in the setting of separated sequentially complete uniform spaces our approaches and results are different from those in chen et al 2008 hamel 2005 and lin and chuang 2010 13 14 15 as applications of our results we study vectorial caristi s fixed point theorems and takahashi s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated sequentially complete uniform space we also apply our results to study maximal element theorems which are unified methods of several variational inclusion problems our results contain many known results in the literature fang 1996 21 and will have many applications in nonlinear analysis

ekeland type variational principle with applications to quasi variational inclusion problems abstract in this paper we study the ekeland type variational principle a caristi kirk type fixed point theorem and a maximal element theorem in the setting of uniform spaces by using these results we establish some existence results for solutions of quasi variational inclusion problems quasi optimization problems and equilibrium problems defined on separated and sequentially complete uniformly spaces

the ekeland variational principle for henig proper minimizers and super minimizers abstract in this paper we consider for the first time approximate henig proper minimizers and approximate super minimizers of a set valued map f with values in a partially ordered vector space and formulate two versions of the ekeland variational principle for these points involving coderivatives in the sense of ioffe clarke and mordukhovich as applications we obtain sufficient conditions for f to have a henig proper minimizer or a super minimizer under the palais smale type conditions the techniques are essentially based on the characterizations of henig proper efficient points and super efficient points by mean of the henig dilating cones and the hiriart urruty signed distance function

a novel secret image sharing scheme in color images using small shadow images over the past several years secret image sharing techniques have become another branch of the effort to prevent secret images from being eavesdropped on in addition to traditional cryptography because smaller shadows can speed up the transmission of a secret color image in this paper we combine chang and wu s gradual search algorithm for a single bitmap btc gsbtc and shamir s k n threshold concept to propose a novel secret color image sharing scheme that generates smaller shadows experimental results confirm that the proposed scheme successfully reduces shadow size and that each shadow behaves as a random like image that prevents leakage of information about the secret color image furthermore the correlation between two vertically or horizontally adjacent pixels in each shadow is significantly less than those in a color secret image and the presented scheme also achieves on average an npcr 0 414 and auci 32 78 thus with our scheme one pixel difference could cause a significant difference in the corresponding shadows therefore the security of the presented scheme is also confirmed

distortionless visual multi secret sharing based on random grid we proposed an visual multi secret sharing without secret distortion we define the shape of share as pie not traditional doughnut shape number of secret sharing is more than two we adopt rg based for implementing vmss to void pixel expansion and complex codebook design because visual secret sharing vss has already been well defined visual multi secret sharing vmss is more practical for various fields in a vmss scheme n secret messages are encoded into two shares that appear to be noise and these are later stacked by rotating flipping and turning to visually recognize the secrets vmss is generally classified as visual cryptography vc based vmss or random grid rg based vmss however vc based vmss has the three main drawbacks of pixel expansion the cost of designing a complex codebook and shape distortion in the decoded secret image in order to stack shares at any angle during decoding secrets are encoded into doughnut shaped shares however the traditional doughnut share methods distort the secret after decoding because the shape of each share is doughnut this paper proposes a new rg based vmss scheme that defines the shape of each share as a pie shaped share that does not distort secrets so that multiple secrets are encoded into two pie shares and then decoded by stacking one pie share on another at different angles of rotation experimental results demonstrate the efficiency of the proposed method

equivalents to ekeland s variational principle in uniform spaces abstract a minimal element theorem on sequentially complete uniform spaces is presented that generalizes earlier results of pacific j math 55 2 1974 335 341 proc amer math soc 108 3 1990 707 714 two more equivalent formulations of the minimal element theorem are given it is applied to derive new versions of ekeland type theorems which improve results of j math anal appl 202 1996 398 412 finally the minimal element theorem is used to obtain an ekeland type theorem for functions with values in a linear space without topological structure

extended color visual cryptography for black and white secret image recently de prisco and de santis introduced a k n colored black and white visual cryptography scheme cbw vcs which adopts colored pixels in shadow images to share a black and white secret image only k or more participants can reconstruct the secret image by combining their shadow images it seems that no one study k n cbw vcs with the extended ability revealing meaningful shadow images denoted as cbw extended vcs cbw evcs in this paper we extend the conventional evcs i e bw evcs to the cbw evcs this paper has two main contributions i we construct k n cwb evcss ii all constructions are proven to satisfy security contrast and cover image conditions we propose the k n colored black and white extended visual cryptography scheme cbw evcs our k n cbw evcs has the extended ability revealing meaningful shadow images we extend the conditions of k n cwb evcs to those of k n cwb evcs we prove that our constructions satisfy security contrast and cover image conditions

a discussion on the relationship between probabilistic visual cryptography and random grid abstract in a k n visual cryptography scheme vcs the dealer encodes the secret into n shadow images each pixel of the secret image is expanded into m sub pixels in each share in a k n vcs the secret can be visually reconstructed when k or more shares are available the reconstruction process employs the human visual system and no computations are required to solve the pixel expansion problem of vcss probabilistic vcss are directly converted from vcss with no pixel expansion another well known secret image sharing scheme random grid rg is also provided with this novel stacking to see property compared with vcs the most appealing benefit of rg is that there is no pixel expansion in this paper we use the probabilistic vcs without pixel expansion to study the construction and performance of rg this paper has two main results i we show that each step of the share generation process in all existing 2 2 rg 2 n rg n n rg k n rg incremental rg can be mapped to a corresponding step in pvcss and their shadow images between pvcs and rg are perfectly indistinguishable and the reconstructed images are the same also include our 2 n rg ii from the quality of reconstructed image pixel expansion recognized region size and image types to be considered for evaluating pvcss and rgs we point out that rg and pvcs have no difference other than the terminology furthermore rgs is a subset of pvcss

slic superpixels compared to state of the art superpixel methods computer vision applications have come to rely increasingly on superpixels in recent years but it is not always clear what constitutes a good superpixel algorithm in an effort to understand the benefits and drawbacks of existing methods we empirically compare five state of the art superpixel algorithms for their ability to adhere to image boundaries speed memory efficiency and their impact on segmentation performance we then introduce a new superpixel algorithm simple linear iterative clustering slic which adapts a k means clustering approach to efficiently generate superpixels despite its simplicity slic adheres to boundaries as well as or better than previous methods at the same time it is faster and more memory efficient improves segmentation performance and is straightforward to extend to supervoxel generation

estimation of signal dependent noise level function in transform domain via a sparse recovery model this paper proposes a novel algorithm to estimate the noise level function nlf of signal dependent noise sdn from a single image based on the sparse representation of nlfs noise level samples are estimated from the high frequency discrete cosine transform dct coefficients of nonlocal grouped low variation image patches then an nlf recovery model based on the sparse representation of nlfs under a trained basis is constructed to recover nlf from the incomplete noise level samples confidence levels of the nlf samples are incorporated into the proposed model to promote reliable samples and weaken unreliable ones we investigate the behavior of the estimation performance with respect to the block size sampling rate and confidence weighting simulation results on synthetic noisy images show that our method outperforms existing state of the art schemes the proposed method is evaluated on real noisy images captured by three types of commodity imaging devices and shows consistently excellent sdn estimation performance the estimated nlfs are incorporated into two well known denoising schemes nonlocal means and bm3d and show significant improvements in denoising sdn polluted images

quantum cryptographic algorithm for color images using quantum fourier transform and double random phase encoding abstract a novel encryption decryption method for color images is proposed in which quantum fourier transform qft and double random phase encoding drpe techniques have been used the encryption process can be realized by performing two secret random phase encoding operations respectively in the input and the qft planes because all quantum operations are invertible the decryption process is the inverse of the encryption process supported by detailed numerical simulation and theoretical analysis the method has clarified its robustness security and computational complexity over its classical counterpart and it opens the door for introducing color image encryption into quantum scenarios

homogeneity localization using particle filters with application to noise estimation this paper proposes a method for localizing homogeneity and estimating additive white gaussian noise awgn variance in images the proposed method uses spatially and sparsely scattered initial seeds and utilizes particle filtering techniques to guide their spatial movement towards homogeneous locations this way the proposed method avoids the need to perform the full search associated with block based noise estimation methods to achieve this the paper proposes for the particle filter a dynamic model and a homogeneity observation model based on laplacian structure detectors the variance of awgn is robustly estimated from the variances of blocks in the detected homogeneous areas a proposed adaptive trimmed mean based robust estimator is used to account for the reduction in estimation samples from the full search approach our results show that the proposed method reduces the number of homogeneity measurements required by block based methods while achieving more accuracy

visual secret sharing for multiple secrets conventional visual secret sharing schemes are designed for a single secret image so it is inefficient to generate numerous share images for multiple secret images simultaneously therefore a novel visual secret sharing scheme for multiple secret images is proposed in this paper in the proposed encryption process a stacking relationship graph of secret pixels and share blocks is generated to indicate the encryption functions and a set of visual patterns is defined to produce two share images according to this graph based on the stacking properties of these patterns the secret images can be obtained from the two share images at aliquot stacking angles the proposed scheme makes the number of secret images not restricted and further extends it to be general as a result the proposed scheme enhances visual secret sharing schemes ability for multiple secrets

sharing multiple secrets in visual cryptography the secret sharing schemes in conventional visual cryptography are characterized by encoding one shared secret into a set of random transparencies which reveal the secret to the human visual system when they are superimposed in this paper we propose a visual secret sharing scheme that encodes a set of x 2 secrets into two circle shares such that none of any single share leaks the secrets and the x secrets can be obtained one by one by stacking the first share and the rotated second shares with x different rotation angles this is the first true result that discusses the sharing ability in visual cryptography up to any general number of multiple secrets in two circle shares

low rankness transfer for realistic denoising current state of the art denoising methods such as non local low rank approaches have shown to give impressive results they are however mainly tuned to work with uniform gaussian noise corruption and known variance which is far from the real noise scenario in fact noise level estimation is already a challenging problem and denoising methods are quite sensitive to this parameter moreover these methods are based on shrinkage models that are too simple to reflect reality which results in over smoothing of important structures such as small scale text and textures we propose in this paper a new approach for more realistic image restoration based on the concept of low rankness transfer given a training clean noisy image pair our method learns a mapping between the non local noisy singular values and the optimal values for denoising to be transfered to a new noisy input one single image is enough for training the model and can be adapted to the noisy input by taking a correlated image experiments conducted on synthetic and real camera noise show that the proposed method leads to an important improvement both visually and in terms of psnr ssim

a verifiable threshold secret sharing scheme based on lattices abstract the generalized compact knapsack function is defined as f a x i a i x i where a a 1 a m r for some ring r and x x 1 x m s for a specified subset s r it is known that for appropriate choice of r and s inverting this function is at least as hard as solving certain worst case problems on cyclic lattices in this paper we exploit collision resistance as well as homomorphic properties of this function to propose a threshold verifiable secret sharing scheme with two distinguished features first the security of the scheme is completely based on lattice problems and second upon receiving shares participants can verify consistency of their shares with the secret without any communication

wavelet domain approximation and compression of piecewise smooth images the wavelet transform provides a sparse representation for smooth images enabling efficient approximation and compression using techniques such as zerotrees unfortunately this sparsity does not extend to piecewise smooth images where edge discontinuities separating smooth regions persist along smooth contours this lack of sparsity hampers the efficiency of wavelet based approximation and compression on the class of images containing smooth c sup 2 regions separated by edges along smooth c sup 2 contours for example the asymptotic rate distortion r d performance of zerotree based wavelet coding is limited to d r spl lsim 1 r well below the optimal rate of 1 r sup 2 in this paper we develop a geometric modeling framework for wavelets that addresses this shortcoming the framework can be interpreted either as 1 an extension to the zerotree model for wavelet coefficients that explicitly accounts for edge structure at fine scales or as 2 a new atomic representation that synthesizes images using a sparse combination of wavelets and wedgeprints anisotropic atoms that are adapted to edge singularities our approach enables a new type of quadtree pruning for piecewise smooth images using zerotrees in uniformly smooth regions and wedgeprints in regions containing geometry using this framework we develop a prototype image coder that has near optimal asymptotic r d performance d r spl lsim logr sup 2 r sup 2 for piecewise smooth c sup 2 c sup 2 images in addition we extend the algorithm to compress natural images exploring the practical problems that arise and attaining promising results in terms of mean square error and visual quality

multi image encryption by circular random grids visual secret sharing vss can encode a secret image into several share images where the original secret can be reconstructed and recognized by sight by stacking all share images there are two categories of vss schemes visual cryptography vc and random grids rg vc has three main drawbacks the large size the need for the codebook to be redesigned for specific applications and the ability to encode only one secret image at a time rg removes the first two drawbacks this paper proposes a novel rg based vss scheme that encodes multiple secret images at a time the scheme encrypts multiple secret images into two circular cipher grids and decrypts the images by stacking two circular cipher grids to obtain the first secret and gradually rotating one circular cipher grid at a fixed degree based on the quantity of the secret images encrypted to disclose other secrets compared with conventional vc based vss the proposed scheme has no pixel expansion a higher capacity for secret sharing and no need for a complex vc codebook to be redesigned theoretical analysis of visual quality and security is demonstrated

probabilistic visual secret sharing schemes for grey scale images and color images visual secret sharing vss scheme is an encryption technique that utilizes the human visual system in recovering the secret image and does not require any cryptographic computation pixel expansion has been a major issue of vss schemes a number of probabilistic vss schemes with minimum pixel expansion have been proposed for binary secret images this paper presents a general probabilistic k n vss scheme for grey scale images and another scheme for color images with our schemes the pixel expansion can be set to a user defined value when this value is 1 there is no pixel expansion at all the quality of reconstructed secret images measured by average contrast or average relative difference is equivalent to the contrast of existing deterministic vss schemes previous probabilistic vss schemes for black and white images can be viewed as special cases in the schemes proposed here

a multiple level visual secret sharing scheme without image size expansion in traditional vss schemes the size of the share image is substantially expanded since each pixel of the secret image is mapped onto a block consisting of several pixels in addition the quality of the reconstructed secret image is normally degraded in contrast especially for halftone images this study proposes a vss scheme that maps a block in a secret image onto one corresponding equal sized block in each share image without image size expansion two types of techniques including histogram width equalization and histogram depth equalization are proposed to generate the corresponding share blocks containing multiple levels rather than two levels based on the density of black pixels on the blocks for a secret block in the former technique the gray scale image histogram is obtained by uniformly splitting the range of the pixel gray levels in the secret image while in the latter the buckets are created so that the area of each bucket is roughly constant by containing approximately the same number of pixels the proposed schemes significantly improve the quality of the reconstructed secret image compared to several previous investigations

image cryptographic algorithm based on the haar wavelet transform lossless encryption methods are more applicable than lossy encryption methods when marginal distortion is not tolerable in this research the authors propose a novel lossless symmetric key encryption decryption technique in the proposed algorithm the image is transformed into the frequency domain using the haar wavelet transform then the image sub bands are encrypted in a such way that guarantees a secure reliable and an unbreakable form the encryption involves scattering the distinguishable frequency data in the image using a reversible weighting factor amongst the rest of the frequencies the algorithm is designed to shuffle and reverse the sign of each frequency in the transformed image before the image frequencies are transformed back to the pixel domain the results show a total deviation in pixel values between the original and encrypted image the decryption algorithm reverses the encryption process and restores the image to its original form the proposed algorithm is evaluated using standard security and statistical methods results show that the proposed work is resistant to most known attacks and more secure than other algorithms in the cryptography domain

efficient visual secret sharing scheme for color images a k out of n visual secret sharing scheme vsss resolves the visual variant of the k out of n secret sharing problem where only k or more out of n participants can reveal the secret by human visual system without any cryptographic computation the best pixel expansion of the general k out of n vsss for c colored images was cxm by yang and laih new colored visual secret sharing schemes des codes cryptogr 24 2000 325 335 where m is the pixel expansion of an existing binary k out of n vsss regarding the c colored n out of n scheme the best pixel expansion is c 1 2 n 1 c 2 and c c 1 2 n 2 c when n is odd and even respectively by blundo et al improved schemes for visual cryptography des codes cryptogr 24 2001 255 278 in this paper we propose a new c colored k out of n vsss by using a pixel expansion of log 2c xm that is more efficient than ever

image encryption to protect image contents most existing encryption algorithms are designed to transform an original image into a texture like or noise like image which is however an obvious visual sign indicating the presence of an encrypted image and thus results in a significantly large number of attacks to address this problem this paper proposes a new image encryption concept to transform an original image into a visually meaningful encrypted one as an example of the implementation of this concept we introduce an image encryption system simulation results and security analysis demonstrate excellent encryption performance of the proposed concept and system

image encryption by multiple random grids in this paper we first give a formal definition to the visual cryptograms of n 2 random grids vcrg n for encrypting an image specifically a set of vcrg n with respect to image p consists of n random grids printed on transparencies such that only when the n transparencies are superimposed altogether can p be recognized by human vision without any computing device while any group of less than n transparencies obtains no information about p then we design novel vcrg n encryption schemes for binary gray level and color images validate the correctness by formal proofs and demonstrate the feasibility by computer simulations our schemes do not require any extra pixel expansion neither any encoding basis matrix which are necessary and inevitable in the approaches of conventional visual cryptography these attractive advantages make our schemes more informative in theoretical interests and much applicable in practical applications

the drop theorem the petal theorem and ekeland s variational principle on montre que le principe variationnel d ekeland ou plus precisement une forme legerement modifiee est une consequence d un resultat geometrique connu sous le terme de theoreme de la goutte

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

image encryption by random grids a random grid in this paper is a transparency comprising a two dimensional array of pixels that are either transparent or opaque determined in a totally random way we design algorithms by using random grids to accomplish the encryption of the secret gray level and color images in such a way that neither of the two encrypted shares alone leaks the information of the secret image whereas the secret can be seen when these two shares are superimposed the decryption process is done by our visual system and no computation is required as compared to the approaches in visual cryptography our algorithms do not need the basis matrices to encode the shares so that the problem of pixel expansion exists no more that is the sizes of the secret image and the encrypted shares are the same

automatic estimation and removal of noise from a single image image denoising algorithms often assume an additive white gaussian noise awgn process that is independent of the actual rgb values such approaches cannot effectively remove color noise produced by today s ccd digital camera in this paper we propose a unified framework for two tasks automatic estimation and removal of color noise from a single image using piecewise smooth image models we introduce the noise level function nlf which is a continuous function describing the noise level as a function of image brightness we then estimate an upper bound of the real nlf by fitting a lower envelope to the standard deviations of per segment image variances for denoising the chrominance of color noise is significantly removed by projecting pixel values onto a line fit to the rgb values in each segment then a gaussian conditional random field gcrf is constructed to obtain the underlying clean image from the noisy input extensive experiments are conducted to test the proposed algorithm which is shown to outperform state of the art denoising algorithms

some generalizations of ekeland type variational principle with applications to equilibrium problems and fixed point theory abstract in this paper we introduce the concept of a q function defined on a quasi metric space which generalizes the notion of a function and a w distance we establish ekeland type variational principles in the setting of quasi metric spaces with a q function we also present an equilibrium version of the ekeland type variational principle in the setting of quasi metric spaces with a q function we prove some equivalences of our variational principles with caristi kirk type fixed point theorems for multivalued maps the takahashi minimization theorem and some other related results as applications of our results we derive existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps we also extend the nadler s fixed point theorem for multivalued maps to a q function and in the setting of complete quasi metric spaces as a consequence we prove the banach contraction theorem for a q function and in the setting of complete quasi metric spaces the results of this paper extend and generalize many results appearing recently in the literature

meaningful secret sharing technique with authentication and remedy abilities lin and tasi yang et al and chang et al s meaningful secret sharing schemes provided authentication mechanisms but none included a remedy ability that would cause the secret image never to be completely obtained while some information of the stego images are losing or tampering with this paper proposes a meaningful secret sharing scheme which includes both authentication and remedy abilities that allow for detection of the corrupted area and use of the hidden information to repair the secret image with reasonable visual quality in comparison with previous schemes this approach results in superior visual qualities of the stego images by an average of more than 3db

almost aspect ratio invariant visual cryptography without adding extra subpixels we propose a k n almost aspect ratio invariant vcs aaivcs our k n aaivcs does not need extra subpixels our k n aaivcs does not find out a mapping pattern for arranging subpixels we theoretically prove that our scheme has the smallest aspect ratio difference a visual cryptographic scheme is a method to decompose a secret image into shadow images by expanding a secret pixel into m subpixels only legitimate subsets of participants can reconstruct the original image by combining their shadows because the size of the subpixel is the same as that of the pixel the shadow size is expanded m times in cases where m is not a square number the aspect ratio of the reconstructed image is distorted accordingly an aspect ratio invariant vcs arivcs was proposed to address this distortion problem however arivcs requires extra subpixels and a mapping pattern showing how to arrange the subpixels a large m creates a significant challenge when attempting to derive this pattern in this paper we propose the almost aspect ratio invariant vcs aaivcs which simulates the principle of a jigsaw puzzle the proposed aaivcs has the smallest loss of aspect ratio when we do not add extra subpixels