Comments on "phase-shifting for nonseparable 2-D haar wavelets"

In their recent paper, Alnasser and Foroosh derive a wavelet-domain (in-band) method for phase-shifting of 2-D "nonseparable" Haar transform coefficients. Their approach is parametrical to the (a priori known) image translation. In this correspondence, we show that the utilized transform is in fact the separable Haar discrete wavelet transform (DWT). As such, wavelet-domain phase shifting can be performed using previously-proposed phase-shifting approaches that utilize the overcomplete DWT (ODWT), if the given image translation is mapped to the phase component and in-band position within the ODWT

Hybrid Differential Optical Sensing Imager

Methods and systems for a differential compressed sensor optical design is proposed to form a smart optical imager. Specifically, the novel design uses both active (laser) and passive (ambient light) to intelligently sample the direct image information within a Three Dimensional (3-D) spatial frame with potential to 4-D (3-D space plus 1-D time) sampling. An electronically agile lens-based distance sensor is engaged that can produce smart sampling of target by adjusting the size of the laser beam spot on the target sampling grid to produce a boundary outline by a light flooding method. This target dependent direct sampling of the target results in direct compressed sensing. A passive light acquisition pin-hole sampling optical sensor design is proposed that produces the pixel-basis Laplacian to determine the compressed sensed pixels ill the incident image

Super Resolution of Wavelet-Encoded Images and Videos

In this dissertation, we address the multiframe super resolution reconstruction problem for wavelet-encoded images and videos. The goal of multiframe super resolution is to obtain one or more high resolution images by fusing a sequence of degraded or aliased low resolution images of the same scene. Since the low resolution images may be unaligned, a registration step is required before super resolution reconstruction. Therefore, we first explore in-band (i.e. in the wavelet-domain) image registration; then, investigate super resolution. Our motivation for analyzing the image registration and super resolution problems in the wavelet domain is the growing trend in wavelet-encoded imaging, and wavelet-encoding for image/video compression. Due to drawbacks of widely used discrete cosine transform in image and video compression, a considerable amount of literature is devoted to wavelet-based methods. However, since wavelets are shift-variant, existing methods cannot utilize wavelet subbands efficiently. In order to overcome this drawback, we establish and explore the direct relationship between the subbands under a translational shift, for image registration and super resolution. We then employ our devised in-band methodology, in a motion compensated video compression framework, to demonstrate the effective usage of wavelet subbands. Super resolution can also be used as a post-processing step in video compression in order to decrease the size of the video files to be compressed, with downsampling added as a pre-processing step. Therefore, we present a video compression scheme that utilizes super resolution to reconstruct the high frequency information lost during downsampling. In addition, super resolution is a crucial post-processing step for satellite imagery, due to the fact that it is hard to update imaging devices after a satellite is launched. Thus, we also demonstrate the usage of our devised methods in enhancing resolution of pansharpened multispectral images

Phase-shifting for nonseparable 2-d Haar wavelets

In this paper, we present a novel and efficient solution to phase-shifting 2-D nonseparable Haar wavelet coefficients. While other methods either modify existing wavelets or introduce new ones to handle the lack of shift-invariance, we derive the explicit relationships between the coefficients of the shifted signal and those of the unshifted one. We then establish their computational complexity, and compare and demonstrate the superior performance of the proposed approach against classical interpolation tools in terms of accumulation of errors under successive shifting

Phase-Shifting For Nonseparable 2-D Haar Wavelets

In this paper, we present a novel and efficient solution to phase-shifting 2-D nonseparable Haar wavelet coefficients. While other methods either modify existing wavelets or introduce new ones to handle the lack of shift-invariance, we derive the explicit relationships between the coefficients of the shifted signal and those of the unshifted one. We then establish their computational complexity, and compare and demonstrate the superior performance of the proposed approach against classical interpolation tools in terms of accumulation of errors under successive shifting