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Sayısal görüntülerin alt band kodlanması

Subband coding of digital images

  1. Tez No: 46285
  2. Yazar: SIDIK DÜNDAR
  3. Danışmanlar: Y.DOÇ.DR. M. ERTUĞRUL ÇELEBİ
  4. Tez Türü: Yüksek Lisans
  5. Konular: Elektrik ve Elektronik Mühendisliği, Electrical and Electronics Engineering
  6. Anahtar Kelimeler: Alt band kodlama, görüntü sıkıştırma, farksal darbe kod modülasyonu, entropi kodlama. vıı
  7. Yıl: 1995
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 57

Özet

ÖZET SAYISAL GÖRÜNTÜLERİN ALTBAND KODLANMASI Bu tezde alt band kodlama tekniği tanımlanarak, uygulaması görüntü üzerinde gerçeldeştmlmiştir. Alt band kodlama tekniğinin amacı veri sıkıştınlmasının sağlanmasıdır. Veri sıkıştırma teknikerinin ortaya çıkış nedeni tez içinde de örnekler verilerek açıklandığı gibi verinin depolanması ve iletimi için gerekli olan bit sayısının çok büyük olmasıdır. Ayrıca iletim için harcanan süre pratikde kabul edilemeyecek kadar uzundur. Veri, sıkıştırma tekniklerinin hızlı bir evrim içerisinde olmasının en temel nedeni bilgisayar teknolojisinde gerçekleştirilen gelişmedir. Veri sıkıştırılmasının sağlanması için gerçekleştirilen yöntemlerden biri olan alt band kodlama tekniği şu şekilde açıklanabilir; bir tüm band işaret fıltreleme işleminden sonra ayrık ilişkisiz altband işaretlere aynin ve daha sonra her alt band tek tek ele alınıp, her birinin diğer altband işaretlere göre sahip oldukları enerjileri ve istatistiksel özelliklerine uygun bir işleve göre her alt band basma bit sayısı verilmektedir. Bu işlemden sonra her alt banda atanan bit sayışma uyularak farksal darbe kod modülasyon yöntemi kullanılarak kodlanmaktadır. Tez çalışmasında da uygulaması gerçekleştirildiği gibi bir tüm band görüntünün altbandlara ayrılması işlemlerinin gerçekleştirildiği analiz süzgeç bankası alçak geçiren ve yüksek geçiren süzgeç takımını içerir. Altbandlar elde edilirken birbirleri ile girişimlerir en küçüklenir. Aksi takdirde örtüşme olarak adlandırılan bir bozulma oluşur. Bu nedenle filtre takımlarının seçimleri çok önemlidir. Bu çalışma da OMF filtreler kullanıldı. Resim iki boyutlu bir işaret olduğundan 2 boyutlu sonlu dürtü yanıtlı QMF kullanılmalıdır. Ancak matematiksel işlemlerin zorluğundan dolayı iki boyutlu filtrelerin bir boyuta indirgenmesini sağlayan aynlabilirlik özelliği kullanılarak bir boyutlu QMF filtreler kullanılır. Bu işlemleri takiben farksal darbe kod modülasyonu ile her alt band kendisine atanan belirli bit sayışma uyularak kodlanmaktadır. Bu çalışmada birinci ve ikinci derece farksal darbe kod modülasyonu kullanılmıştır. Bu aşamadan sonra her alt band başına karşılık gelen bit sayısının daha fazla azaltılması için entropi kodlama tekniklerinden yararlanılır. Bu vıtekniklerden en çok kullanılanları öteleme kodlaması (shift coding) ve süreç U2xınluğu kodlamasıdır.

Özet (Çeviri)

ABSTRACT SUBBAND CODING OF DIGITAL IMAGES The demand for handling images in digital form has increased dramatically in recent years. The performance improvements and significant reductions in the cost of image scanners, photographs, printed text, and other media can be now easily converted into digital form. Many different imaging modalities in medicine, such as computed tomography or magnetic resonance imaging generate images in digital form. Representing images in digital form allows visual information to be easily manipulated in useful and novel ways. Despite the advantages, there is one potential problem with digital images, namely, the large number of bits required to represent them. It is a fortune that digital images in their canonical representation, generally contain a significant amount of redundancy. Image compression which is the science of efficient coding of picture data, aims at taking advantage of this redundacy to reduce the number of bits required to represent an image. This can be result in significant savings in the memory needed for image storage or in the channel capacity required for image transmission. The need for image compression becomes apparent when one computes the number of bits per image resulting from typical samplign rate and quantization schemes. Compression is performed in source and entropy encorders. Source encoder works on the digitized image and using different algorithms reduce the image data by removing the redundant information information above the resolution capability of the human eye. It produces binary codewords as the output. The entropy encoder, uses these binary words as the input and compresses the data rate of them by taking into account their entropies. The image data compression performed by source encoding process is an irreversible process, namely the removed redundant information will be absent throughout the decoding process. In this case a distortion is added to the system by source encoders. In this sense the receiver reconstructs the image without this excessive information. On the other hand, the entropy encoder is reversible coding technique. Subband coding as used as a source endcoding technique. Subband coding is a specific source encoding technipue. vinIn this thesis, subband coding technique is described and investigated. This technique has become quite popular for the medium bandwidth waveform coding of speech. The basic idea of subband coding is to split up the frequency band of the signal and then to code each subband with DPCM using a coder and bit rate accurately matched to the statistics of that band. In addition to the obvious advantages of such an approach, two advantages have been found important in speech coding. First, the error in coding a subband is confined to that subband, thus exploring the mashing effect of speech. Second, by varying the bit assignment amoung the subbands, the noise spectrum can be shaped according to the subjective noise perception of the human ear. The principle of subband coding has recently been succesfully applied to data compression of both still images and video. In subband coding the signal to be coded is decomposed into narrow band pass signals (subbands) which are decimated and subsequently encoded separately. The coding distortions introduced are largely confined to subbands where distortion originated. This makes it possible to allocate distortion amoung the various subbands according to some perceptual criterion. A complete subband coding system consists of four distanct parts. a) An analysis filter bank; splitting the input signal into subbands and subsequently decimation of each subband by a factor equal to the number of subbands. b) An encoder for representing the subband signals in a bit efficient manner c) A decoder whose purpose it is to produce an approximation to the original subband signals based on the compact representation generated by the encoder above. d) A synthesis filter bank that performs interpolation filtering and combination of the decoded subband signals. In this thesis analysis and synthesis filtering is done using quadrature mirror filters (QMF). The name quadrature mirror filter arises from the fact that the filters exhibit mirror symmetry about II/2 radians (which is one quarter of the normalized sampling frequency. ) QMF allows for an alias-free reconstruction in the obsence of coding errors. The philosophy of QMF is to IXallow aliasing to be introduced by using overlapping filters for the analysis bank and then design the synthesis filters in such a way that any aliasing is exactly cancelled out in the reconstruction process. These filters are also designed so that overall amplitude and phase distortions minimized or eliminated. The two dimensional QMF filters can be taken as a separable product of identical one dimensional QMF filters. These find applications in situations where a discrete time signal X(n) is to be split into a number of consecutive bands in the frequency domain, so that each subband signal Xk(n) can be processed in an independent manner. Typical processing includes undersampling the subband signals, encoding them and transmitting over a channel or merely storing the coded signals. Eventually, at some point in the process, the subband signals should somehow be recombined so that the original signal is properly reconstructed. The 1-D QMF filters can be applied first in one dimension and then in the other dimension to generate the subbands. This is the approach used in subband coding of images. Note that subsampling can be done after filtering in the first dimension to reduce the number of operations required for filtering in the other dimension. Decimation which is used in this operation is the process of reducing the sampling rate of a signal by an integer factor M. In the reverse system the interpolation operation is done which is the process of increasing the sampling rate of a signal by the integer factor M. This operator inserts (M- 1) zeros between sample values and reindexes. The filter coefficients are symmetric with respect to the mid point of the filter so only 16 coefficients are sufficient. These coefficients are used directly for low pass filtering operation and multiplied by (-l)n (n: tap number between 0 and 3 1) for high pass filtering operation After filtering DPCM is used as the method to encode the subbands rather than PCM which is often used in subband image encoders. The use of DPCM is motivated by the increased efficiently of a predictive encoder for a non-white power spectral density. Each subband is encoded using DPCM. DPCM encoding is performed only the lowest subband where pixel to pixel correlation is high and straight quantization is performed on all subband uses a different quantizer to allocate noise appropriately. This technique is good for a large number of subband since the higher- order subbands will have power spectral densities that are nearly white. That is, the subbands have very little spatial correlation. DPCM is the most common approach to predictive coding. In a general predictive coding scheme.the correlation between the neighboring pixel values is used to form a prediction for each pixel. In DPCM, the prediction is subtracted from the actual pixel value to form a differential image that is much less correlated than the original image data. The differential image is then quantized and encoded. The quantization process determines the resulting bit rate and image quality. In the puantization process this process is mapping of the post DPCM data into and 2Bii range for each subband. After finding maximum and minimum values of each subband, mapping according the these values is performed. After applying DPCM to obtained subbands further reduction in bit rate can still be achieved by considering some aspects of entropy concepts from the information theory; The entropy H is the theoretically minumum possible average bit rate required in coding a message. Entropy is mainly used as a performance criterion for a coding scheme. One method of the entropy system is shift coding. Shift coding is a simple but efficient entropy coding technique. A shift code can have any n as the bit length for codewords and takes the name Sn code. For example S2 code which is used in this work has 2 bit codewords so there are only 4 distinct codewords. The process is assigning only three of them to most probable three input levels. For the codewords are used with the fourth codewords as a shifter. To show more levels one can use the shifting code word again and again. In this thesis, the efficiency of the SBC technique is investigated under mean square error, normalized mean square error, signal to noise ratio and data rate expressions are given as bits per pixel. The coding techniques do not work on real time since efficient and reliable error measures matched to the physchovisual properties of human eye do not exist in literature. Organisation of the thesis can be outlined as follows. In chapter one, the importance of subband coding technique and the historical backround of this technique is investigated. In chapter two, image data compression techniques used in this work called subband coding is described and extended to two dimensional case. In chapter three, the simulation of the program is given. XIIn chapter four, simulation results with discussions and related photographs are given. Finally in chapter five, main conclusions about the subband coding technique are derived and future work on this technique is proposed. Keywords; Subband Coding, Image Compresion, Differential Pulse Code Modulation, Entropy Coding. xn

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