A novel semi-fragile forensic watermarking scheme for remote sensing images

Peer-reviewedA semi-fragile watermarking scheme for multiple band images is presented. We propose to embed a mark into remote sensing images applying a tree structured vector quantization approach to the pixel signatures, instead of processing each band separately. The signature of themmultispectral or hyperspectral image is used to embed the mark in it order to detect any significant modification of the original image. The image is segmented into threedimensional blocks and a tree structured vector quantizer is built for each block. These trees are manipulated using an iterative algorithm until the resulting block satisfies a required criterion which establishes the embedded mark. The method is shown to be able to preserve the mark under lossy compression (above a given threshold) but, at the same time, it detects possibly forged blocks and their position in the whole image.Se presenta un esquema de marcas de agua semi-frágiles para múltiples imágenes de banda. Proponemos incorporar una marca en imágenes de detección remota, aplicando un enfoque de cuantización del vector de árbol estructurado con las definiciones de píxel, en lugar de procesar cada banda por separado. La firma de la imagen hiperespectral se utiliza para insertar la marca en el mismo orden para detectar cualquier modificación significativa de la imagen original. La imagen es segmentada en bloques tridimensionales y un cuantificador de vector de estructura de árbol se construye para cada bloque. Estos árboles son manipulados utilizando un algoritmo iteractivo hasta que el bloque resultante satisface un criterio necesario que establece la marca incrustada. El método se muestra para poder preservar la marca bajo compresión con pérdida (por encima de un umbral establecido) pero, al mismo tiempo, detecta posiblemente bloques forjados y su posición en la imagen entera.Es presenta un esquema de marques d'aigua semi-fràgils per a múltiples imatges de banda. Proposem incorporar una marca en imatges de detecció remota, aplicant un enfocament de quantització del vector d'arbre estructurat amb les definicions de píxel, en lloc de processar cada banda per separat. La signatura de la imatge hiperespectral s'utilitza per inserir la marca en el mateix ordre per detectar qualsevol modificació significativa de la imatge original. La imatge és segmentada en blocs tridimensionals i un quantificador de vector d'estructura d'arbre es construeix per a cada bloc. Aquests arbres són manipulats utilitzant un algoritme iteractiu fins que el bloc resultant satisfà un criteri necessari que estableix la marca incrustada. El mètode es mostra per poder preservar la marca sota compressió amb pèrdua (per sobre d'un llindar establert) però, al mateix temps, detecta possiblement blocs forjats i la seva posició en la imatge sencera

Statistical mechanics of lossy data compression using a non-monotonic perceptron

The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity problem in the research of neural networks, we utilize a perceptron of which the transfer function is appropriately designed in order to compress and decode the messages. Employing the replica method, we analytically show that our scheme can achieve the optimal performance known in the framework of lossy compression in most cases when the code length becomes infinity. The validity of the obtained results is numerically confirmed.Comment: 9 pages, 5 figures, Physical Review

Lossy compression of discrete sources via Viterbi algorithm

We present a new lossy compressor for discrete-valued sources. For coding a sequence $x^n$, the encoder starts by assigning a certain cost to each possible reconstruction sequence. It then finds the one that minimizes this cost and describes it losslessly to the decoder via a universal lossless compressor. The cost of each sequence is a linear combination of its distance from the sequence $x^n$ and a linear function of its $k^{\rm th}$ order empirical distribution. The structure of the cost function allows the encoder to employ the Viterbi algorithm to recover the minimizer of the cost. We identify a choice of the coefficients comprising the linear function of the empirical distribution used in the cost function which ensures that the algorithm universally achieves the optimum rate-distortion performance of any stationary ergodic source in the limit of large $n$, provided that $k$ diverges as $o(\log n)$. Iterative techniques for approximating the coefficients, which alleviate the computational burden of finding the optimal coefficients, are proposed and studied.Comment: 26 pages, 6 figures, Submitted to IEEE Transactions on Information Theor

Stochastic Interpretation for the Arimoto Algorithm

The Arimoto algorithm computes the Gallager function $\max_Q {E}_{0}^{}(\rho,Q)$ for a given channel ${P}_{}^{}(y \,|\, x)$ and parameter $\rho$, by means of alternating maximization. Along the way, it generates a sequence of input distributions ${Q}_{1}^{}(x)$, ${Q}_{2}^{}(x)$, ... , that converges to the maximizing input ${Q}_{}^{*}(x)$. We propose a stochastic interpretation for the Arimoto algorithm. We show that for a random (i.i.d.) codebook with a distribution ${Q}_{k}^{}(x)$, the next distribution ${Q}_{k+1}^{}(x)$ in the Arimoto algorithm is equal to the type (${Q}'$) of the feasible transmitted codeword that maximizes the conditional Gallager exponent (conditioned on a specific transmitted codeword type ${Q}'$). This interpretation is a first step toward finding a stochastic mechanism for on-line channel input adaptation.Comment: 5 pages, 1 figure, accepted for 2015 IEEE Information Theory Workshop, Jerusalem, Israe