Andrew Z. Tirkel

Image and watermark registration

Abstract This paper addresses issues concerned with image registration, where the image contains an invisible watermark. We present a selection of registration masks which can be deliberately overlaid on a watermarked or raw image, allowing the recovery of the correct registration. For visible masks at high signal-to-noise ratio, the window property is useful. For invisible masks, the (aperiodic) autocorrelation peak to sidelobe ratio is important, as is the local pattern balance. Methods of combining watermarks with registration patterns are presented. The masks studied include: perfect maps, perfect even and odd binary arrays, m -arrays and quasi- m -arrays.

Algebraic construction of a new class of quasi-orthogonal arrays for steganography

Watermark recovery is often based on cross-correlating images with pseudo-noise sequences, as access to un-watermarked originals is not required. Successful recovery of these watermarks is determined by the (periodic or aperiodic) sequence auto- and cross-correlation properties. This paper presents several methods of extending the dimensionality of 1D sequences in order to utilize the advantages that this offers. A new type of 2D array construction is described, which meets the above requirements. They are constructed from 1D sequences that have good auto-correlation properties by appending rows of cyclic shifts of the original sequence. The sequence values, formed from the roots of unity, offer additional diversity and security over binary arrays. A family of such arrays is described which have low cross-correlation and can be folded and unfolded, rendering them robust to cryptographic attack. Row and column products of 1D Legendre sequences can also produce equally useful 2D arrays (with interesting properties resulting from the Fourier invariance of Legendre sequences). A metric to characterize all these 2D correlation based watermarks is proposed.

Image watermarking-a spread spectrum application

This paper discusses the feasibility of coding a robust, undetectable, digital watermark on a standard 512*512 intensity image with an 24 bit RGB format. The watermark is capable of carrying such information as authentication or authorisation codes, or a legend essential for image interpretation. This capability is envisaged to find application in image tagging, copyright enforcement, counterfeit protection, and controlled access. The method chosen is based on linear addition of the watermark to the image data. The patterns adopted to carry the watermark are adaptations of m-sequences in one and two dimensions. The recovery process is based on correlation, just as in standard spread spectrum receivers. The technique is quite successful for one dimensional encoding with binary patterns, as shown for a variety of gray scale test images. A discussion of extensions of the method to two dimensions, RGB format and non-binary alphabets is presented. A critical review of other watermarking techniques is included.

New optimal low correlation sequences for wireless communications

This paper presents three new sets of frequency hopping sequences, which are converted into sequences for CDMA. One of the CDMA sequence families is optimal with respect to the Welch bound, and two are nearly optimal. Our sequences are available for more lengths, and have much higher linear complexity than other CDMA sequences. They have a similar structure to the small Kasami set, but are balanced. The CDMA sequences are constructed using a composition method, which combines new shift sequences with pseudonoise columns to form an array. The array dimensions are relatively prime, so it is unfolded using the Chinese Remainder Theorem. Each of our constructions gives rise to two additional families with larger family sizes but worse correlation as explained in Section 4.2.

A unique watermark for every image

We address image security issues by proposing a scheme for watermarking images or video at the camera. Each watermark is unique and identifies the owner, camera, and frame number. Application areas include the security industry (for proof of tampering) and commercial photography (for copyright protection).

Matrix construction using cyclic shifts of a column

This paper describes the synthesis of matrices with good correlation, from cyclic shifts of pseudonoise columns. Optimum matrices result whenever the shift sequence satisfies the constant difference property. Known shift sequences with the constant (or almost constant) difference property are: quadratic (polynomial) and reciprocal shift modulo prime, exponential shift, Legendre shift, Zech logarithm shift, and the shift sequences of some m-arrays. We use these shift sequences to produce arrays for watermarking of digital images. Matrices can also be unfolded into long sequences by diagonal unfolding (with no deterioration in correlation) or row-by-row unfolding, with some degradation in correlation

New Matrices with Good Auto and Cross-Correlation

Large sets of matrices with good auto and cross-correlation are rare. We present two such constructions, a method of extending family size by column multiplication and a method of extending physical size by interlacing. These matrices can be applied to digital watermarking of images.

Three-dimensional periodic optical orthogonal code for OCDMA systems

New families of three-dimensional (3-D) optical orthogonal codes for applications to optical code-division multiple access (OCDMA) networks are proposed. The families are based in the three dimensional periodic Welch Costas array over elementary Abelian groups. These new families are shown to be asymptotically optimal through the Johnson bound.

Multi-dimensional arrays for watermarking

This paper presents two new classes of families of multi-periodic arrays suitable for digital watermarking. These families are large and all arrays have good auto and cross-correlation, and are available in many sizes. The construction is based on log quadratic and exponential quadratic maps. The maps applied to elements in an extension field on a natural multi-dimensional grid. The grid also leads to a generalized multi-dimensional Legendre array, which can be used in the family constructions.

Millimeter wave array for UAV imaging MIMO radar

High resolution imaging radars at millimeter-wave frequencies for obstacle avoidance for Unmanned Aerial Vehicles (UAV) utilize a large antenna aperture and sequential mechanical scanning of the aperture to form images with high fidelity. Planar arrays are an attractive alternative. They do not require mechanical scanning, and images are formed digitally using beamforming techniques [1]. To achieve image quality comparable to mechanically scanned radars, fully populated arrays require inordinate numbers of elements. These are costly, a challenge to design, and difficult to produce. Thinned or sparse arrays are a potential solution to this problem. MIMO (Multiple Input Multiple Output) techniques are an efficient method of thinning an array using spreading sequences to create an overlay of paired transmitter and receiver elements, without sacrificing image quality. The use of MIMO techniques to thin an array is a relatively recent development [2]. To be of practical use at millimeter-wave frequencies, MIMO techniques require the development of novel array geometries and architecture. This paper presents designs for the implementation of millimeter-wave planar arrays which have been thinned using MIMO techniques and considerers the limitations on the length of spreading sequences due to the increasingly pronounced effect of Doppler at higher frequencies. These considerations have led to the first instance of the use of the Moreno-Tirkel sequence Family B for high resolution imaging radar.