Sparse signal modulation schemes encode a data channel on a substrate in a manner that is robust, flexible to achieve perceptual quality constraints, and provides improved data capacity. The substrate is printed by any of a variety of means to apply the image, with sparse signal, to an object. After image capture of the object, a decoder processes the captured image to detect and extract data modulated into the sparse signal. The sparse signal may incorporate implicit or explicit synchronization components, which are either formed from the data signal or are complementary to it.

Watermark data is converted to watermark coefficients, which may be embedded in an image by converting the image to a frequency domain, embedding the watermark in image coefficients corresponding to medium-frequency components, and converting the modified coefficients to the spatial domain. The watermark data is extracted from the modified image by converting the modified image to a frequency domain, extracting the watermark coefficients from the image coefficients, and determining the watermark data from the watermark coefficients. The watermark data may be truncated image data bits such as truncated least significant data bits. After extraction from the watermark, the truncated image data bits may be combined with data bits representing the original image to increase the bit depth of the image. Watermark data may include audio data portions corresponding to a video frame, reference frames temporally proximate to a video frame, high-frequency content, sensor calibration information, or other image data.

Watermark data is converted to watermark coefficients, which may be embedded in an image by converting the image to a frequency domain, embedding the watermark in image coefficients corresponding to medium-frequency components, and converting the modified coefficients to the spatial domain. The watermark data is extracted from the modified image by converting the modified image to a frequency domain, extracting the watermark coefficients from the image coefficients, and determining the watermark data from the watermark coefficients. The watermark data may be truncated image data bits such as truncated least significant data bits. After extraction from the watermark, the truncated image data bits may be combined with data bits representing the original image to increase the bit depth of the image. Watermark data may include audio data portions corresponding to a video frame, reference frames temporally proximate to a video frame, high-frequency content, sensor calibration information, or other image data.

Sparse signal modulation schemes encode a data channel on a substrate in a manner that is robust, flexible to achieve perceptual quality constraints, and provides improved data capacity. The substrate is printed by any of a variety of means to apply the image, with sparse signal, to an object. After image capture of the object, a decoder processes the captured image to detect and extract data modulated into the sparse signal. The sparse signal may incorporate implicit or explicit synchronization components, which are either formed from the data signal or are complementary to it.

Sparse signal modulation schemes encode a data channel on a host image in a manner that is robust, flexible to achieve perceptual quality constraints, and provides improved data capacity. The host image is printed by any of a variety of means to apply the image, with sparse signal, to an object. After image capture of the object, a decoder processes the captured image to detect and extract data modulated into the sparse signal. The sparse signal may incorporate implicit or explicit synchronization components, which are either formed from the data signal or are complementary to it.