FPGA Implementation of an Efficient 3D-WT Temporal Decomposition

2007 IEEE International Symposium on Signal Processing and Information Technology

FPGA Implementation of an Efficient 3D-WT Temporal Decomposition Algorithm for Video Compression Samar Moustafa Ismail', Ali Ezzat Salama2 and Mohamed Fathy Abu-ElYazeed2 'Electronics Dept., German University in Cairo, Cairo, Egypt. 2Electronics and Communication Dept., Cairo University, Cairo, Egypt.

'E-mail: samar.ismailgguc.edu.eg

Abstract - In this paper, the hardware design and FPGA implementation of a new efficient three-dimensional Wavelet

Transposed-Form FIR filter structure as the filter bank of the 1D-WT block used.

This algorithm performs the temporal decomposition of a video

2. DIRECT AND TRANSPOSED FORM FIR FILTERS

Transform (3D- W7) algorithm for video compression is presented.

sequence in a more efficient way than the classical 3D- WT algorithm. It exhibits lower memory demands and lower latencies for the compression and decompression processes than the classical one. This makes the addressed algorithm fits better for real-time video processing. The hardware design is based on the use of the Transposed-Form FIR filter structure which is hereby compared to the Direct-form FIR filter. The former is found to exhibit less clock

latency and less chip area utilization. The reference design is made scalable to any wavelet filter coefficients and to fit for any frame size. The chip area utilization is compared upon the FPGA implementation at different frame sizes. The designed system can be usedfor real-time video applications.

Keywords - 3D Wavelet Transform, Video compression, Temporal Decomposition, Transposed FIR filter, FPGA.

1.

Digital ter algithms areupimi omposedtof

multipliers, adders, and registers. Focusing on FIR filters, the basic Direct-Form structure of an FIR filter is shown in Fig. 1 The multipliers and adders form the heart of an FIR filter. As shown, the input data passes to the multiplier and then to the adder with interleaving delay elements, for pipelining, which results in the convolution of the input data

and the filter coefficients

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INTRODUCTION

Video coding methods using wavelet transforms have been successful in providing high rates of compression while maintaining good image quality. They have been treated as a better alternative to DCT-based compression schemes [1-2], such as those adopted in MPEG standards [2-4]. The design and implementation of image and video compression techniques using the wavelet transform on FPGAs represent a challenge to researchers nowadays [5-7]. The Wavelet Transform, which is used in a wide range for image compression, can be extended to video sequences. Most video compression algorithms rely on 2D based schemes employing motion compensation and estimation techniques. However, there are efficient 3D algorithms which are able to capture temporal redundancies more naturally for 3D wavelet/subband coding, without motion compensation [8-9]. Three dimensional wavelet transform algorithms are based on a group of frames (GOF) concept, similar to the group of pictures (GOP) used in the MPEG standards [10]. This concept has some disadvantages concerning processing and memory requirement. These disadvantages may limit their practical implementation. In this paper, we present the hardware design and FPGA implementation of a novel 3DWT algorithm [11], which overcomes some of these limitations by reducing the space and processing complexity of the 3D-WT process. The design core depends on using the

978-1 -4244-1 835-0/07/$25.00 ©2007 IEEE

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7 Fig.1. Direct FIR Filter Structure Employing Tree of Pipelined Adders.

An alternate implementation structure called the Transposed-Form FIR filter is shown in Fig.2. Utilizing the same resources, data samples are applied in parallel to all the tap multipliers through pipeline registers. The products are applied to a cascaded chain of registered adders, combining the effect of accumulators and registers. The order of tap coefficients must be reversed with the first tap closest to the output. This structure allows expansion of the number of taps required in a filter, since each "tap module" is identical. Since the structure is uniform and symmetric, a single component can be designed and instantiated as many times as required by the number of taps. This is a great advantage of this topology over the Direct-Form one. Both Direct-Form (Fig. 1) and Transposed-Form FIR (Fig.2) filters have trade-offs and limitations. It is up to the designer to choose the style most appropriate to the application. This issue becomes more obvious when very large filters are implemented across multiple devices or even when the small filter is used in a cascadable manner like in our case here of successive filtering operations. The

154

cascadable nature of the tap-slice modules of the TransposedForm allows easy interdevice connections. The input-tooutput latency is reduced with fully pipelined TransposedForm FIR filters [12]. In n

data: rows and columns of the frame, and time. The temporal filter is a ID filter applied on the same pixel in every frame of the video input sequence. This is the classical 3D-WT, which is not efficient because it requires access to all frames in the sequence to perform the temporal wavelet transform, which requires a large storage memory. When the amount of D 0frames in a video sequence is large, this will be unfeasible to DQ D -D 0do. This problem can be easily resolved by decomposing the sequence into group of frames (GOFs) for its temporal decomposition. After the completion of the temporal Xx Y Xdecomposition, every frame is 2D wavelet transformed. This is followed by thresholding and/or quantization steps in the D aL D0 A D D L 4 LI U < case of lossy compression. Finally a lossless codification a method is applied to get the compressed bit-stream. For the decompression process, these steps are done but in the d Fig.2 Transposed-Form FIR Filters Employing Cascaded Pipelined Adders. mverse way. 3. ID DISCRETE WAVELET TRANSFORM 5. GOF-BASED 3D-WT TEMPORAL DECOMPOSITION The one-dimensional discrete wavelet transform (IDDWT) can be described in terms of a filter bank as shown in The 3D-WT algorithm using GOF concept, 3D-GOF, Fig.3. An input signal is applied to the low pass filter Go and decomposition decomposes the frames in a GOF temporally and then filters used inndcmoiin to the high pass h ilesue th filter Ho. The atially into frequency. Temporal decomposition for a group are called analysis filters. The odd samples of the outputs of SPl these filters are then downsampled, corresponding to a of frames decomposes the GOF into 1/2 GOF of high temporal decimation factor of two. The downsampled outputs of these frequency bands and 1/2 GOF of low temporal frequency fisthe c eaetaals te ao sbands. The low temporal frequency bands are decomposed filters constitute the approximation signal and signal. During reconstruction, as shown also in Fig.3, the agamandso on This procedure is shown in Fig.4, it applies 3 temporal opposite happens, upsampling by a factor of two of the approximation and details signals is performed, followed by decomposition levels on a 16 GOF sequence, to get 2 low filtering using the low pass and high pass filters GI and H, temporal frequency frames and 14 high temporal frequency respectively. The filters used in reconstruction are called frames. Most of the energy is concentrated in the temporal synthesis filters. Finally, the outputs of the two synthesis low frequency bands. That's why a higher degree of filters are added together to reconstruct the original signal. compression can be achieved in the high temporal bands. The filters G and H can be implemented using any of the FIR But, to get the maximum number of high temporal frequency bands, maximum number of levels must be applied into a filter structures discussed in section 2. GOF. Fig.5 shows also an input sequence of 16 frames, 4 GOFs,

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each consist of 4 frames. This procedure only requires one of temporal decomposition of each GOF to obtain 8 low outlevel

l+ etails frequency bands and 8 high frequency bands. The number of low frequency bands is larger than the GOF size (4). In this case, the compression is less efficient in compressing. As a solution for this, further temporal decomposition can be Reconstruction Decomiipositioin applied to the low frequency bands in the GOF=4. However, Low Pass Low Pas this results in a more complex process. [i] Doxwi-saiiipligS l I0o I AnlsiF lls Filte SyAitliesis Filter The 3D-GOF algorithm using a little number of frames in a GOF has a great disadvantage, that the decomposition is not High Pa ss [ Higl Pass 2 H0[11] Up-saiplin.. Syiitliesis Filter Aiialysis; Filtei done efficiently. On the other hand, a large number of frames in a GOF needs large memory since all frames in a GOF are Fig.3. One-level decomposition & reconstruction of IDWT. needed for doing temporal decomposition. Also, this procedure causes largeis delay before providing any results and 4. 2D AND 3D WAVELET TRANSFORM long processing time required. Large GOFs are required in The D-WTis prfored b appyingthe D-WTupon many applications to obtain the most temporal redundancies the rows and columns of the image separately. Similarly, the i nu eune ihu uhmto;3-O loih 3D wavelet decomposition iS computed by applying three i o h otsial ehdi hs plctos separate iD transforms along the coordinate axes ofthe video

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Fig.4. Input sequence: 16 frames, Temporal Decomposition of 16 GOF size. 1. GOF: 4 frames

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Fig.6. Input sequence: 16 frames, 3D-V algorithm for temporal

decomposition.

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