Hadamard-based image decomposition and compression

Abstract

In this paper, we develop a general algorithm for decomposition and compression of grayscale images. The decomposition can be expressed as a functional relation between the original image and the Hadamard waveforms. The dynamic adaptive clustering procedure incorporates potential functions as a similarity measure for clustering as well as a reclustering phase. The latter is a multi-iteration, convergent procedure which divides the inputs into nonoverlapping clusters. These two techniques allow us to efficiently store and transmit a class of half-tone medical images such as magnetic resonance imaging (MRI) of the human brain. Due to the redundant image structure of MRI, obtained after the decomposition and clustering, almost half of the image can be omitted all together. Naturally, the compression rates for this specific type of grayscale image are increased greatly. A run-length coding is performed in order to compress further the retained information from the first two steps. Although all the techniques applied are simple, they represent an efficient way to compress grayscale images. The algorithm exhibits a performance which is competitive and often outperforming some of the methods reported in the literature.

An efficient algorithm for the conjugate symmetric sequency-ordered complex Hadamard transform

“…As for the required computational complexity, it has been shown that the proposed N-point complex-valued CS-SCHT algorithm requires log N complex additions/subtractions and /2 1 multiplications by . x (15) x (1) x (14) x (2) x (13) x (3) x (12) x (4) x (11) x (5) x (10) x (6) x (9) x (7) x ( …”

Coded-Aperture Imaging Using Photo-Induced Reconfigurable Aperture Arrays for Mapping Terahertz Beams

“…In addition, high-performance and low-cost imaging devices are highly desired for THz beam visualization for scientific metrology applications such as quasi-optical system alignment, quantum-cascade laser (QCL) design and op-timization [9], and THz antenna characterization [10]. To date, the THz imaging systems that have been demonstrated generally fall into one of three categories: (1) single-element imagers that obtain images by mechanical scanning, (2) array imagers [e.g., focal-plane arrays (FPAs)] that consist of an array of imaging sensor elements [6]- [8], and (3) coded-aperture imaging (CAI) using two-dimensional aperture masks [11]- [14]. In many applications, important events happen on the scale of microseconds, making imaging by mechanical scanning impractical due to the inherently low frame rates.…”

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“…Effros et al [14] demonstrate both the failures and the successes of the KLT. Other transforms, such as DCT [38,25,32], DFT [40], Hadamard transform [36], Slant transform [20] are computationally faster than the KLT, while exhibiting slightly worse performance than that of the KLT, in terms of energy compaction and decorrelation. Among them, DCT is the most widely used for image compression.…”