a novel image hiding scheme based on block difference to transmit a secret image securely by embedding it into a cover image without drawing the unintended observer s attention a novel image hiding scheme is proposed by exploring the block correlation between the cover image and the secret image the stego image quality can be greatly improved experimental results demonstrate that the stego image has a high peak signal to noise ratio and the stego image is almost the same as the cover image

on general construction for extended visual cryptography schemes numerous visual cryptography schemes vcss have been proposed to protect a secret image with share images most vcss use random looking shares to code a single binary secret image some schemes are designed for color secret images droste s new results on visual cryptography in advances in cryptology crypto 96 lecture notes in computer science vol 1109 springer berlin 1996 pp 401 415 n n vcs is introduced for multiple binary secret images extended vcs evcs by ateniese et al extended capabilities for visual cryptography theoretical computer science 250 2001 143 161 for binary secret image uses meaningful innocent looking shares in this paper we start with a more concise derivation of matrix extension in the ecvs model this is implemented by concatenating an extended matrix to each basis matrix we then present a general construction method for single or multiple binary grayscale color secret images using matrix extension utilizing meaningful shares the result k n visual secret sharing schemes are more general than most existing schemes in terms of the secret share image types using our matrix extension algorithm any existing vcs with random looking shares can be easily modified to utilize meaningful shares the effectiveness of our schemes is demonstrated by real examples

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

tight closure and projective bundles abstract we formulate problems of tight closure theory in terms of projective bundles and subbundles this provides a geometric interpretation of such problems and allows us to apply intersection theory to them this yields new results concerning the tight closure of a primary ideal in a two dimensional graded domain

methods for reconstruction of 2 d sequences from fourier transform magnitude the gerchberg saxton gs algorithm and its generalizations have been the main tools for phase retrieval unfortunately it has been observed that the reconstruction using these algorithms does not always converge to the correct result even if the desired solution satisfies the uniqueness condition in this paper we propose a new deautocorrelation algorithm and a few auxiliary techniques we recommend that a combination of the iterative fourier transform ift algorithm with our new algorithm and techniques can improve the probability of success of phase retrieval a pragmatic procedure is illustrated different reconstruction examples that are difficult to reconstructed using the single ift algorithm are used to show the robustness and effectiveness of the new combination of algorithms if the given fourier modulus data contain no noise it is sometimes possible to get a perfect reconstruction even when the signal to noise ratio snr of the fourier modulus data is only 10 db a meaningful result remains reachable for our examples a concept concerning the intrinsic ambiguity of phase retrieval is suggested we emphasize the necessity of verification of the solution since the available phase retrieval algorithms are incompetent for distinguishing between an intrinsically ambiguous solution and the true solution

some computational problems arising in adaptive optics imaging systems abstract recently there has been growing interest and progress in using numerical linear algebra techniques in adaptive optics imaging control computations real time adaptive optics is a means for enhancing the resolution of ground based optical telescopes beyond the limits previously imposed by the turbulent atmosphere an adaptive optics system automatically corrects for light distortions caused by the medium of transmission the system measures the characteristics of the phase of the arriving wavefront and corrects for the degradations by means of one or more deformable mirrors controlled by special purpose computers no attempt is made in this paper to give a comprehensive survey of recent numerical linear applications in optical imaging rather two fairly representative applications are discussed in some detail the following research topics in the area of adaptive optics control systems each involving the formulation and numerical solution of difficult problems in numerical linear algebra are described 1 jacobi like eigenvalue computations for multiple bandwidth deformable mirror control methods and 2 covariance matrix computations for performance modeling of adaptive optics systems using fast hankel transforms

frobenius amplitude and strong vanishing theorems for vector bundles the primary goal of this paper is to systematically exploit the method of deligne illusie to obtain kodaira type vanishing theorems for vector bundles and more generally coherent sheaves on algebraic varieties the key idea is to introduce a number which provides a cohomological measure of the positivity of a coherent sheaf called the frobenius or f amplitude the f amplitude enters into the statement of the basic vanishing theorem and this leads to the problem of calculating or at least estimating this number most of the work in this paper is devoted to doing this various situations

vcpss a two in one two decoding options image sharing method combining visual cryptography vc and polynomial style sharing pss approaches this paper presents a novel method to combine two major branches of image sharing vc and pss n transparencies are created for a given gray valued secret image if the decoding computer is temporarily not available at or not connected to the decoding scene we can still physically stack any t received transparencies t n is a threshold value to get a vague black and white view of the secret image immediately on the other hand when the decoding computer is finally available then we can get a much finer gray valued view of the secret image using the information hidden in the transparencies in summary each transparency is a two in one carrier of the information and the decoding has two options

semistable sheaves in positive characteristic we prove maruyama s conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field this result implies that in mixed characteristic the moduli spaces of gieseker semistable sheaves are projective schemes of finite type the proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant this inequality also leads to effective restriction theorems in all characteristics improving earlier results in characteristic zero

inconsistent signal feasibility problems least squares solutions in a product space presents parallel projection methods to find least squares solutions to inconsistent convex set theoretic signal synthesis problems the problem of finding a signal that minimizes a weighted average of the squares of the distances to constraint sets is reformulated in a product space where it is equivalent to that of finding a point that lies in a particular subspace and at minimum distance from the cartesian product of the original sets a solution is obtained in the product space via methods of alternating projections which naturally lead to methods of parallel projections in the original space the convergence properties of the proposed methods are analyzed and signal synthesis applications are demonstrated

optical beam shaping and diffraction free waves a variational approach abstract we investigate the problem of shaping radially symmetric annular beams into desired intensity patterns along the optical axis within the fresnel approximation we show that this problem can be expressed in a variational form equivalent to the one arising in phase retrieval using the uncertainty principle we prove various rigorous lower bounds on the functional these lower bounds estimate the l 2 error for the beam shaping problem in terms of the design parameters we also use the method of stationary phase to construct a natural ansatz for a minimizer in the short wavelength limit we illustrate the implications of our results by applying the method of stationary phase coupled with the gerchberg saxton algorithm to beam shaping problems arising in the remote delivery of beams and pulses

phase retrieval from incomplete magnitude information via total variation regularization the phase retrieval problem has drawn considerable attention as many optical detection devices can only measure magnitudes of the fourier transform of the underlying object signal or image this paper addresses the phase retrieval problem from incomplete data where only partial magnitudes of fourier transform are obtained in particular we consider structured illuminated patterns in holography and find that noninteger values used in designing such patterns often yield better reconstruction than the conventional integer valued ones furthermore we demonstrate theoretically and numerically that three diffracted sets of complete magnitude data are sufficient to recover the object to compensate for incomplete information we incorporate a total variation regularization a priori to guarantee that the reconstructed image satisfies some desirable properties the proposed model can be solved efficiently by an alternative directional multiplier method with provable convergence numerical experiments valid

vectorial phase retrieval of 1 d signals reconstruction of signals from measurements of their spectral intensities also known as the phase retrieval problem is of fundamental importance in many scientific fields in this paper we present a novel framework denoted as vectorial phase retrieval for reconstruction of pairs of signals from spectral intensity measurements of the two signals and of their interference we show that this new framework can alleviate some of the theoretical and computational challenges associated with classical phase retrieval from a single signal first we prove that for compactly supported signals in the absence of measurement noise this new setup admits a unique solution next we present a statistical analysis of vectorial phase retrieval and derive a computationally efficient algorithm to solve it finally we illustrate via simulations that our algorithm can accurately reconstruct signals even at considerable noise levels

iterative techniques for minimum phase signal reconstruction from phase or magnitude in this paper we develop iterative algorithms for reconstructing a minimum phase sequence from the phase or magnitude of its fourier transform these iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain this approach is the basis of a new means of computing the hilbert transform of the log magnitude or phase of the fourier transform of a minimum phase sequence which does not require phase unwrapping finally we discuss the potential use of this iterative computation in determining samples of the unwrapped phase of a mixed phase sequence

the rationality of the hilbert kunz multiplicity in graded dimension two we show that the hilbert kunz multiplicity is a rational number for an r primary homogeneous ideal i f1 fn in a two dimensional graded domain r of finite type over an algebraically closed field of positive characteristic more specific we give a formula for the hilbert kunz multiplicity in terms of certain rational numbers coming from the strong harder narasimhan filtration of the syzygy bundle syz f1 fn on the projective curve y projr

tight closure and plus closure in dimension two we prove that the tight closure and the graded plus closure of a homogeneous ideal coincide for a two dimensional n graded domain of finite type over the algebraic closure of a finite field this answers in this case a tantalizing question of hochster

hard constrained inconsistent signal feasibility problems we consider the problem of synthesizing feasible signals in a hilbert space in the presence of inconsistent convex constraints some of which must imperatively be satisfied this problem is formalized as that of minimizing a convex objective measuring the amount of violation of the soft constraints over the intersection of the sets associated with the hard ones the resulting convex optimization problem is analyzed and numerical solution schemes are presented along with convergence results the proposed formalism and its algorithmic framework unify and extend existing approaches to inconsistent signal feasibility problems an application to signal synthesis is demonstrated

lossless image compression and encryption using scan abstract this paper presents a new methodology which performs both lossless compression and encryption of binary and gray scale images the compression and encryption schemes are based on scan patterns generated by the scan methodology the scan is a formal language based two dimensional spatial accessing methodology which can efficiently specify and generate a wide range of scanning paths or space filling curves this paper presents a brief overview of scan compression and decompression algorithms encryption and decryption algorithms and test results of the methodology

an image hiding method with high hiding capacity based on best block matching and k means clustering this paper presents a novel image hiding method that exhibits a high hiding capacity that allows the embedded important image to be larger than the cover image a facility that is seldom described in the literature in the proposed method the entire important image is divided into many nonoverlapping blocks for each block of the important image a block matching procedure is used to search for the best similar block from a series of numbered candidate blocks the obtained indices of the best matching blocks are encoded using huffman coding scheme and then recorded in the least significant bit planes of the cover image through a monoalphabetic transposition cipher the proposed method exhibits the following advantages over existing methods 1 a high hiding capacity such that the embedded important image can be larger than the cover image 2 a stego image with a high quality which improves the secrecy of the hidden image and 3 a small error between the extracted important image and the original important image indicating that the extracted important image is of acceptable quality

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

variational analysis applied to the problem of optical phase retrieval we apply nonsmooth analysis to a well known optical inverse problem phase retrieval the phase retrieval problem arises in many different modalities of electromagnetic imaging and has been studied in the optics literature for over forty years the state of the art for this problem in two dimensions involves iterated projections for solving a nonconvex feasibility problem despite widespread use of these algorithms current mathematical theory cannot explain their success at the heart of projection algorithms is a nonconvex nonsmooth optimization problem we obtain some insight into these algorithms by applying techniques from nonsmooth analysis in particular we show that the weak closure of the set of directions toward the projection generate the subdifferential of the corresponding squared set distance function following a pattern of proof described in f h clarke yu s ledyaev r j stern and p r wolenski nonsmooth analysis and control theory springer verlag new york 1998 this result is generalized to provide conditions under which the subdifferential of an integral function equals the integral of the subdifferential

tight closure of finite length modules in graded rings in this article we look at how the equivalence of tight closure and plus closure or frobenius closure in the homogeneous m coprimary case implies the same closure equivalence in the nonhomogeneous m coprimary case in standard graded rings although our result does not depend upon dimension the primary application is based on results known in dimension 2 due to the recent work of h brenner we also demonstrate a connection between tight closure and the m adic closure of modules extended to r or r we finally show that unlike the noetherian case the injective hull of the residue field over r or r contains elements that are not killed by any power of the maximal ideal of r this fact presents an obstruction to one possible method of extending our main result to all modules

sharing and hiding secret images with size constraint this paper presents a method for sharing and hiding secret images the method is modified from the t n threshold scheme comput graph 26 5 2002 765 the given secret image is shared and n shadow images are thus generated each shadow image is hidden in an ordinary image so as not to attract an attacker s attention any t of the n hidden shadows can be used to recover the secret image the size of each stego image in which a shadow image is hidden is about 1 t of that of the secret image avoiding the need for much storage space and transmission time in the sense that the total size of t stego images is about the size of the secret image experimental results indicate that the qualities of both the recovered secret image and the stego images that contain the hidden shadows are acceptable the photographers who work in enemy areas can use this system to transmit photographs

phase retrieval for characteristic functions of convex bodies and reconstruction from covariograms we propose strongly consistent algorithms for reconstructing the characteristic function 1k of an unknown convex body k in r n from possibly noisy measurements of the modulus of its fourier transform c 1k this represents a complete theoretical solution to the phase retrieval problem for characteristic functions of convex bodies the approach is via the closely related problem of reconstructing k from noisy measurements of its covariogram the function giving the volume of the intersection of k with its translates in the many known situations in which the covariogram determines a convex body up to reflection in the origin and when the position of the body is fixed our algorithms use o k n noisy covariogram measurements to construct a convex polytope pk that approximates k or its reflection k in the origin by recent uniqueness results this applies to all planar convex bodies all three dimensional convex polytopes and all symmetric and most in the sense of baire category arbitrary convex bodies in all dimensions two methods are provided and both are shown to be strongly consistent in the sense that almost surely the minimum of the hausdorff distance between pk and k tends to zero as k tends to infinity

steganography of capacity required using modulo operator for embedding secret image in this paper a novel mechanism using modulus operations to incorporate secret data with image form into a host image is proposed the used modulus is a threshold value that indicates how many bits of the secret image are being incorporated into the host image in our scheme there are two kinds of secret images processed the capacities of these two types are half the size and a quarter the size of the chosen host image respectively as can be seen in the result of our experiment not only can the secret images be totally embedded but the extra information such as the auxiliary table assisting the secret extraction is released as well even then there is still space remaining after the hiding procedure is completed the result is a higher capacity exploration for embedding the secret into a host image upon inspection of the quality of the stego image using the measurement of psnr it is noted that not only does the image display make the grade of the human vision system i e it is imperceptible by human eyes as far as the embedded secret is concerned but also the valued results of psnr remain sufficiently stable for a variety of host image selections therefore our proposal scheme is notably superior to those in the previous literature iee proc vision image signal process 147 1 2000 29 the advantages of this proposed scheme are the higher capacity exploration on secret embedding and better stability on stego image displays

optical wavefront reconstruction theory and numerical methods optical wavefront reconstruction algorithms played a central role in the effort to identify gross manufacturing errors in nasa s hubble space telescope hst nasa s success with reconstruction algorithms on the hst has led to an effort to develop software that can aid and in some cases replace complicated expensive and error prone hardware among the many applications is hst s replacement the next generation space telescope ngst indent this work details the theory of optical wavefront reconstruction reviews some numerical methods for this problem and presents a novel numerical technique that we call extended least squares we compare the performance of these numerical methods for potential inclusion in prototype ngst optical wavefront reconstruction software we begin with a tutorial on rayleigh sommerfeld diffraction theory