【正文】 第一代小波的的重要特點(diǎn)就是利用特殊函數(shù)的伸縮和平移而得到。分析可知，由 ()t? 縮放 a 倍變成 ()ta? 。 結(jié)構(gòu)編碼首先將圖像紋理、邊緣和輪廓結(jié)構(gòu)特征提取出來(lái) ,然后分別對(duì)它們進(jìn)行編碼。即 ()t? 隨著 t 的變化而上下波動(dòng)，這也就是小波的由來(lái)。然后根據(jù)近些年發(fā)表的 學(xué)術(shù)文章，分析并整理了第二代小波變換的理論與實(shí)現(xiàn)方法，分析了第二代小波變換的優(yōu)點(diǎn) 及這 些優(yōu)點(diǎn) 在圖像壓縮中的應(yīng)用。傳統(tǒng)的傅立葉變換是用周期函數(shù)去逼近圖像信號(hào) ,這樣就使得變換系數(shù)分布 相對(duì) 比較分散。如果預(yù)測(cè)比較準(zhǔn)確，誤差就會(huì)很小。 1996 年 . Calderbank 和 Wim. Sweldens 等提出整數(shù)到整數(shù)的小波變換 ,并結(jié)合提升方案構(gòu)造整數(shù)到整數(shù)小波 。二進(jìn)小波基函數(shù)的表達(dá)式如下： 22, ( ) 2 ( 2 ( ) )k kb x x b?? ? ? ? （ ） 它是連續(xù)小波 , ()abx? 的尺度參數(shù) a 選取 二進(jìn)制離散數(shù)值 2kka ?? 的結(jié)果 。 ○ 2 預(yù)測(cè)過(guò)程：用 a1中的數(shù)據(jù)來(lái)預(yù)測(cè) c1中的數(shù)據(jù)，預(yù)測(cè)算子記作 P，用預(yù)測(cè)值與真實(shí)值的 差 來(lái)替代原來(lái)的 c1，即： 1 1 1()c c P a?? （ ） 預(yù)測(cè)形成新的 c1。 傳統(tǒng)的快速小波變換是把信號(hào)分解成高通部分與低通部分，并在這種情況下進(jìn)行抽樣，然后對(duì)低通部分重復(fù)上述 過(guò)程 ，直 到所需級(jí)數(shù) 。 (2) 快速疊加 與基函數(shù)的疊加鄉(xiāng)保持重構(gòu)的低復(fù)雜度 (3) 良好的時(shí)間和空間局部化 使我們能夠確定信號(hào)的主要成分 。 （ 4）正則性 正則性是對(duì)函數(shù)光滑程度的一種描述，也是函數(shù)頻域能量集中度的一種度量。在主通過(guò)程中在給定的閾值條件下，對(duì)主表進(jìn)行掃描編碼，如果是重要系數(shù)就將其幅值放入副表之中， 然后將該系數(shù)在數(shù)組中置 數(shù) 為零 ,防止在閾 值減小時(shí) ,該系數(shù)影響新零樹(shù)的出現(xiàn) ，而 在副通過(guò)程中 ,對(duì) 要 副表中的重要系數(shù)進(jìn)行細(xì)化 。 SPIHT 的空間方向樹(shù)如圖所示： 圖 SPIHT 中的空間方向樹(shù) 由空間方向樹(shù)的結(jié)構(gòu)示意圖我們可以知道，在于零樹(shù)結(jié)構(gòu)相比時(shí)，這種空間方向樹(shù)的數(shù)據(jù)結(jié)構(gòu)不僅充分利用 了 不同尺度間 小波系數(shù)的相關(guān)性 ,也對(duì)同一尺度下 小波系數(shù)的相關(guān)性做了充分考慮 ,從而更有效的組織了小波系數(shù) 。 第二步：分類(lèi)掃描過(guò)程。 本文首先介紹小波分析及其性質(zhì) ,對(duì)尺度函數(shù)、小波母函數(shù)、多分辨分析等進(jìn)行分析。s Poly Theater. Their show, titled Ulan Muqir on the Grassland, depicted the history and development of the art troupe. Being from the region allowed me to embrace the culture of Inner Mongolia and being a member of the troupe showed me where I belonged, Nasun, the art troupe39。s Liaoning province, decades ago. The solider gave the old man a handmade saddle when they bid farewell. The story inspired Nasun to write Carved Saddle, a song that later became one of his most popular numbers. Now, every year, Nasun recruits young singers and dancers for the troupe. The troupe has also designed a new repertoire, which is mostly based on the daily lives of Mongolian people, especially the lives of nomadic families, and has bined contemporary musical elements with folk songs of the region. Haimu, a 25yearold khoomei (a local variant of overtone singing) singer, joined the troupe three years ago. Along with a sixmember band, he performs fast songs and soft ones that he writes－ all while playing the horsehead fiddle.Although I learned the piano since childhood and grew up listening to various kinds of music, to me, the folk music of Inner Mongolia is the root, he says. Performing in remote villages is pleasant. I feel at home on the boundless grasslands, and the warm people there make me feel fulfilled. The first round of spring auction season in Beijing ended last week, but it failed to create much spring in the art market. Although two pieces of Chinese painting fetched more than 100 million yuan, the decline in trading volume and sa le rate showed a downturn this year. In the ―Grand View: Chinese Painting Highlight‖ session at China Guardian 2021 spring auctions, Pan Tianshou’s representative work Eagle, Rock and Flora hit a record auction price of 279 million yuan, while Li Keran’s masterwork Jinggang Mountain fetched million yuan, an unexpected high in recent years. However, the trading volume fells to billion yuan from billion yuan in the same period the year before. The Huangchen 2021 Spring Auctions, which recorded million yuan in total sales, experienced the same. The section number went down to 5 from 12 pared to last year. According to expert Shao Jianwu, the art market did not attract much excitement this year due to the booming stock market and the persistent problems of fery and fake deals. The two pieces of Chinese painting notched up high price this spring due to their own value not due to a revival in the market. The successful transaction of two works with a hammer price of more than 100 million yuan once again confirms that valuable and rare works of high quality always earn the longlasting high price. Chinese painting and calligraphy is still the pillar of the market. However, the overall sales rate has dropped slightly, which reflects the demand for the ordinary auction goods has weakened,‖ said the president of China Guardian’s Hu Yanyan. Besides, the entry of new buyers also makes certain changes to the direction of purchasing. In a word, the overall market trend is very unpredictable. Although China Guardian 2021 Spring Auctions has achieved remarkable results, it does not mean that the market has walked out of the predicament. We still have to wait for the big economic boom to invigorate the art market.‖ Even so, the hot pursuit of some special items appeared this spring. A special session of China Guardian Spring Auctions titled ―Fine Gilt—Bronze Buddhist Images‖ achieved a great deal with total sales volume of million yuan and 92 percent sale rate. The 5th Shamar Rinpoche Statue from 1617th century of Tibet was sold for million yuan. The Beijing Chengxuan Auctions featured almost 2,800 items of coins and stamps in three sessions with good sale rate. The Huachen Auctions also set a special session of photographs under the condition of largescale decline of auction sessions. There was a palpable dull thud of disappointment that acpanied the return of the imperial entourage of Zhen Huan to her homeland. It followed a couple years of hushed excitement as Chinese fans were fed tidbits about their proud concubine who was supposed to conquer the high ground of the North American market. Zhen Huan is, of course, the title character of The Legend of Zhen Huan, a 2021 television series that swept China off its feet and later took other Asian countries by storm. Two years ago, it was reported that HBO, a premium cable service headquartered in the United States, was going to air it in North America after some modification. Now, a condensed version that provides English subtitles but no dubbing has finally been made available on Netflix for online streaming. This version, highly anticipated as a milestone