A New Signal Compression Algorithm Using AllPass Extraction And Its Use In Image Compression And Coding M. F. Fahmy* and G. Fahmy** * University of Assiut , Egypt Email: fahmy@aun.edu.eg ** German University in Cairo, Cairo, Egypt Email: Gamal.Fahmy@guc.edu.eg Abstract – A new signal compression scheme is proposed. It is based on all pass extraction from the received signal's transfer function. The all pass parameters are closely related to a linear prediction polynomial LP of the same order, of the received data. Results have shown that, this new algorithm yields far smaller signal's reconstruction errors when compared with other known methods, for the same compression ratio CR. This algorithm is used in image compression and coding, as follows: First, the image is segmented into blocks and the 2-D DCT of each block, is computed. Next, each 2-D DCT matrix is zigzag scanned to yield a 1-D vector, which is subsequently compressed using the proposed scheme. The image is reconstructed in a reverse manner, using the compressed vectors. The image's compressed parameters is further compressed using schemes like EZW or SPHIT coders. Simulation results have revealed that the proposed compression scheme competes very well with JPEG compression schemes, especially when the images have many details. 1. Introduction In signal processing application, one is always concerned with either extracting information from a specific noisy background, or compressing information either for storage purposes or for transmission over finite bandwidths. In literature, signal de-noising is generally achieved using either adaptive-based techniques [1-3], or through zeroing up noisy wavelet packet coefficients in a typical wavelet decomposition, [4-5].. Recently [6], a method has been devised to compress or de-noise signals, through optimally constructing the orthogonal bases along which a signal can be decomposed. Through projecting the signal along these bases, an enhanced copy of the signal can be optimally constructed. It has been shown that, these bases are constructed using the roots of a forward linear prediction polynomial LP, of the received signal.. In this paper, the formulation of the orthogonal decomposition algorithm has been modified to yield for the same compression capabilities, a smaller signal's reconstruction errors. Next, this scheme is used in image compression and coding. The proposed image compression scheme, starts by segmenting the image under consideration, into blocks. For each block, the 2-D DCT matrix is computed, and transformed to a 1-D vector by zigzag scanning. Each 1-D vector is compressed using the proposed decomposition scheme. Further compression is achieved by coding the compressed image parameters using EZW [7] or SPHIT coder/decoder schemes, [8- 9]. Simulation results have shown that the proposed image compression scheme yields far better signal-to- noise performance over other compression schemes, using JPEG, while in the same time requires smaller memory storage. 2. Prony-based All Pass Signal Extraction Recently [6], a method is proposed for signal compression and de-noising. It is based on expressing a batch of the received signal, as an M weighted sum of damped sinusoids; i.e. 1 0 , ) ( 1 - ≤ ≤  ≅ = L n n x M k n k k μ α (1) It has been mathematically proved that these damped sinusoids s k ' μ are in fact the roots of the M th order linear prediction polynomial LP that approximates the signal in a least squares sense. Signal compression is achieved by only keeping these damped sinusoids and their weights. Simulation results have shown that to reduce the signal's reconstruction errors, the signal should also be decomposed along the error's gradient bases and consequently, the number of compression parameters is increased to be at least 4M. This in turn means that the amount of signal compression is modest. To increase the amount of compression while keeping the reconstruction error very low, the following modification is proposed: • Express the z-transform of the received data x(n) , as ` ) ( ) ( ~ , ) ( ) ( ~ ) ( ) ( 1 1 0 - - - = - = + ≅  = z D z z D z D z D z G z x z X M M M M M N L n n n (2) G K (z) is an FIR function containing K coefficients. It is determined as will shortly be described • Choose D M (z) to be the M th order LP of the batch x(n). Evaluate the impulse response of the all pass function ) ( ) ( ~ z D z D M M , and denote it by h(n). • Evaluate the difference e(n) = x(n)-h(n). Sort its absolute values in descending manner. Associate G K (z) to the K th largest errors. For example, if the j th error, occurs at n=r; it 2006 IEEE International Symposium on Signal Processing and Information Technology 0-7803-9754-1/06/$20.00©2006 IEEE 91